CA2187789A1 - Apparatus and method for determining particle size distributions - Google Patents

Abstract

An apparatus and method are disclosed for obtaining and analyzing light scattering data to determine the size distribution of a group of dispersedparticles that scattered the light. The apparatus and method use a two-dimensional array of photosensitive pixels such as a charge-coupled device (CCD) or an array of solid-state photodiodes. The analyzer illuminates the particles with a dose of light in a collimated beam from a light source so as to scatter light of the beam, and at least a portion of the light interacting with the particles is detected with the photosensitive pixel array. The pixels are functionally equivalent and the analyzer dynamically configures and re-configures at least a portion of the pixels into a variable number of data collection areas which correspond to a selected set of scattering angles. The analyzer also determines whether and, from the pixel output data, where an unscattered center of the incident light beam intersects the pixel array. Thus, no precision mechanical alignment of the light source and the pixel array detector is required prior to operation of the analyzer. Furthermore, the ability of the analyzer to determine the unscattered beam center allows the analyzer to classify each of at least a portion of the pixels to data collection areas according to a function of the geometric relationship the pixel bears to the location of the beam center.

Description

21 8778~

"APPARATUS AND METHOD FOR DETERMINING
PARTICLE SIZE DISTRIBUTIONS"

FIELD OF THE INVENTION

This invention relates in general to light scattering instrumentation and more particularly to instruments and methods for determining the size distribution of particles by light scattering.

BACKGROUND OF THE lNVENllON
Light traveling in a homogeneous medium travels in straight lines.
However, when light travels through a medium cont:lining particles of material, the particles scatter the light. For a single particle, the amount of scattering in a particular direction depends upon the size, shape, and composition of the particle and the wavelength of the light. For a collection of particles, light scattered from all of the particles contributes to the total intensity of light scattered in a particular direction relative to the incident light. By m.o~cllring the amount or intensity of light scattered throughout a number of angles relative to the incident light, it is possible to infer properties of the particles that induce the scattering. In particular, for particles of small size and similar composition, the pattern of scattered light is indicative of the sizes of the scattering particles. Prior analytical instruments have used the technique of analyzing the scattered light intensity to determine the spectrum of particle sizes for a mixture of small particles of varying sizes. A
particle size analyzer using this technique typically samples the angular distribution of the intensity of the light scattered from the mixture, processes the data, and wo gs/28630 2 1 8 7 7 8 9 p~US95/04638 produces numerical values and possibly a graph or a histograrn as output. The analyzer output represents the number or volume fraction of scattering particles in the ~ Lure as a function of the size of the particles and is usually called a particle size distribution.
The prior art has provided many different techniques of measuring and analyzing the light scattered by small particles. For example, a technique called optical particle counting has been developed for separately detecting the light scattered by individual particles in extremely dilute concentrations of particles, but this techrlique is time conc--ming and is impractical for samples cont~ining a large number of particles. On the other hand, if the concentration of particles is toogreat, light scatters multiple times from the sc~ttering particles before being observed, and the multiple scatterings obscure the effect of each particle's contribution to the observed intensity of scattered light. Particle size analyzers have therefore primarily addressed the experimental conditions where the concentration of scattering particles is such that each observed light ray is deflected only once by a single scattering particle. Under these conditions, called single scattering, the scattered light has been analyzed either by m~aCIlring the time variation of the light scattered in a particular direction or by time averaging the scattered light over a range of directions. The former technique is called dynamic light scattering, and the latter is termed static, or classical, light sc~ .ring.
For classical scattering, the problem of relating the angular distribution of scattered light to the size of the scattering particle has been solved mathematically for the case of a spherical particle illumin~ted by a beam of unpolarized light. The mathematical solution is given by a theory proposed by Gustav Mie. The Mie theory is set forth in Chapter 4 of the book, Absorption andScattering of Light by Small Particles, by Craig F. Bohren and Donald R. Huffman(John Wiley & Sons, 1983), which book is incorporated by reference. A particle size analyzer may employ the Mie theory to determine particle size distributionsfrom the observed pattern of scattered light. Such an analyzer is not limited to the analysis of only samples containing particles of spherical shape; the sizes are reported as radii of spheres that are equivalent to the actual particles in terrns of light scattering. For most applications, the equivalent-sphere specification of a particle size distribution is sufficient to characterize the actual particle size distribution.
Mathematical models have also been derived for particular particle shapes other than wo gs/28630 3 Pcr/uS95Jo4638 spherical, but they have been found to have limited value since, for scattering, only the average behavior of a large number of particles is of interest.
Since sc~ttering is also a function of the wavelength of the incident light, prior art analyzers have found it convenient to use incident light of a single 5 wavelength. For this purpose, a laser has been the typical source. Lasers havebeen used which produce light in the visible and near-visible wavelength range.
The descriptions herein of the prior art, and of the invention, use the term "light,"
but it must be recognized that the sC~ttering being described is a phenomenon ofelectromagnetic radiation in general. Thus, the term "light" herein should be read 10 as referring to any such radiation that meets whatever constraints are imposed by the characteristics of the various components of the analyzer (such as the transparency of the sample holders at the wavelength of interest and the frequency response of the detectors), the nature of the scattering particles (such as the refractive index and absorption coefficient as a function of wavelength), and the 15 overall construction of the analyzer.
In a typical prior art arrangement, a particle size analyzer has a source of unpolarized light that is projected in a beam to impinge upon a sample.
The sample contains the particles whose sizes are under investigation. The particles are dispersed in the region of the sarnple that is illllmin~tecl by the incident light 20 beam. The particles scatter light in patterns that are dependent on the ratio of the size of the particle to the wavelength of the light, and on the refractive index of the particle material. The refractive index, a complex function of wavelength, is a measure of how much the light is refracted, reflected, and absorbed by the material.
For a beam of unpolarized light incident on a random mixture of small particles, the 25 scattering pattern is symrnetric about the axis of the incident bearn. The scattering is the result of the refraction, reflection, and absorption by the particles, as well as diffraction at each particle surface where a light ray in the incident beam is tangent to the particle surface.
Light that scatters at a particular angle with respect to the incident 30 beam may be rotated about the beam axis without ch~nging the scattering angle. A
large number of rays scattering from a single particle at a given scattering angle will fill all rotational orientations and thus form a cone of light, with the apex at the scattering particle and with the generating angle (one-half the apex angle) of the cone equal to the scattering angle. The pattern of light rays scattering at all angles 35 from a single particle may thus be thought of as made up of a continuous series of

2 1 877~
wo gs/28630 open cones of light, with the generating angle for a given cone corresponding to the scatt~ring angle for the light compri.~ing the surface of that cone. The axes of all of the cones are collinear with the line defined by the incident beam, and the apexes of the cones are located at the scattering particle. At a ~ t~n~e from the scattering 5 particle, a plane perpendicular to the incident beam will intersect a given cone in a circle. Planes not perpe.nrlicul~r to the in~i(lent beam will int~.rsçct a given cone in a curved line comprising a conic section, i.e., an ellipse, a parabola, or a hyperbola, depending upon the orientation of the plane. Regardless of form, the curved line of intersection represents a single sc~ttçring angle.
In any practical particle size detector, it is not possible or nece.ss~ry to meas,ure the sC~ttftring angle with infinite precision. Nevertheless, better angular resolution in the analyzer provides better particle size resolution. In order toaddress angular precision effects directly, we will refer to the set of all scattering angles falling between a precise lower angular limit and a precise upper angularlimit as an "angle class" of some interrn~-liate angle q. Light scattered within an angle class scatters into the region between two cones of slightly different size.
The smaller (inner) of the two cones is generated by the lower angular limit of the angle class and the larger (outer) cone is generated by the upper angular limit. The apexes of both cones are located at the sc~ttçnng particle.
The inner and outer cones of an angle class define a circular annular region on a plane perpendicular to the incident beam and a more complex shaped region (corresponding to a conic section) on a plane not perpendicular to the incident beam. Scattered light rays intersecting the interior of such a region are rays which have scattered through an angle between the two generating angles of the cones. Thus any light ray intersecting such a region belongs to the angle class defined by that region. Prior analyzers have employed ring-shaped light detectors to measure the amount of light that scatters in an angle class determined by theradius and width of the ring and its distance from the scattering region. To correlate correctly the detected light with a scattering angle, these ring-shaped detectors must be mounted and aligned precisely perpendicular to the incident beam.
Since the interaction region of the incident beam with the particles generally has a finite extent, multiple particles at different locations in the incident beam will each contribute multiple overlapping cones of scattered light, with the apexes of the cones offset by the distance between the particles. Particles of the ~_ w095/28630 21 8778~ pCT/US95/04638 same size will have overlapping scattered-light cones of similar intensity variations, whereas particles of different sizes will have overlapping scattered-light cones of dirr~lcnt hllensi~y variations.
When the light beam illt-min~tes a sample volume of finite extent, a 5 converging lens may be used to direct parallel rays of light, each by definition - scattered through the same sc~tfçring angle (by dirr~l~nt particles), to a single point on a light detector in the focal plane of the lens. A lens that functions in this manner performs a Fourier transform, so that all light arriving at a given point on the detector is known to have been scattered by the sample through a particular 10 scattering angle, regardless of the location of the scattering particle in the sample volume.
The effect of the converging lens is to transform the spatial distribution of the scattered light it receives to that of an equivalent virtual system in which the light distribution in the focal plane of the lens is the same as if all the 15 scattering particles were located at a point coincident with the optic center of the lens. The light detectors are placed in the focal plane of the lens. The line from the optic center of the lens to the focal point of the lens is usually called the optic axis.
If a scattered ray passes through different refracting media, such as air and a sample suspension fluid, before detection, then an appro~liate correction 20 must be applied to the ray's apparent angle of scatter to tletermine its true angle of scatter. Use of a lens and recognition of the virtual scattering system simplifies the correction.
The intensity of light scattered as a function of scattering angle, when expçriment~lly determined as above for a sample composed of many particles 25 of a range of different sizes, consists of the sl-mm~tion of the scattered light from all the particles. If we assume that each size particle in the sample scatters light according to a given mathematical theory and in proportion the relative number of such size particles present, then it is mathematically possible to determine from the experimental data the relative numbers of each size particle constituting the sample, 30 i.e., to determine the size distribution of the sarnple. The well-known mathematical process by which the size distribution may extracted from the composite data is called an inversion process, or sometimes a deconvolution process.
In the usual convention, a scattering angle of zero degrees coincides with unscattered light, and a scattering angle of 180 degrees represents light WO 95/28630 PCI~/US95/04638 _ 6 reflecting directly back into the incident beam. Scattering angles between 90 and 180 degrees are termed b~r~c~ttering.
Light scattering particle size analyærs are typically employed for particles ranging in size from less than one micrometer to several hundred 5 micrometers. Within this size range, and for light in the visible or near-visible portion of the spectrum, the smaller particles tend to scatter light somewhat uniformly in all directions, whereas the larger particles scatter light mostly in the forward direction (small angle with respect to the incident beam direction).
However, the larger particles also scatter much more light than the smaller particles.
10 Thus particles of all sizes will contribute to the amount of light scattered in a particular direction. To extract particle size information accurately from measurements of scattered light intensity, a particle size analyzer usually measures the intensity of light scattered at a number of angles relative to the incident beam.
It is important, especially in the forward direction, that a particle size 15 analyzer provide high angular resolution of the light intensity data. It is characteristic of the mathematical inversion process that the number of distinctparticle sizes post~ te~ to exist in the sample cannot exceed the number of angular positions for which sc~ttenng intensity data values are measured. Therefore, high angular resolution, allowing independent scattçring intensity data to be obtained at 20 many closely spaced angles, will enable an analyzer to distinguish the quantity of particles at more closely spaced particle sizes and will lead to more precision and higher resolution in the particle size distribution obtained by the inversion process.
A good discussion of the desirability of obtaining high resolution in particle scattering data is contained in the Coulter Corporation Technical Monograph, 2~ "LS Series Resolution," which monograph is incorporated by reference.
The problem of achieving an accurate characterization of a given particle distribution may be illustrated with a specific example. Assume that sc~ttering intensity data are obtained for n sc~3ttering classes qi and are represented by the scattering intensity function I(qi), with i = 1, ..., n. A particular 30 mathematical model, such as (but not limited to) the Mie theory, is chosen torepresent the light scattering by the particles in each class. Computations with the theory predict sij as the amount of scattering in angle class i for a particle of size j, with j = 1, ..., m. The particle size parameter j represents m particle sizes ranging from 0.1 micrometers to 1 000 micrometers . Typically j will represent 2 1 877~
~_, WO 95/28630 PCI/US95/04638 equally-spaced intervals on a log-based size scale. The particle size distribution S
is related to the intensity I(qi) through the matrix equation [I(qi)] = [sij] tsj]-Thus, Sj may be cl~t~rrT-ined through inversion [Sj] = [sij]~1[sij] [Sj] = [sij]-l[I(qi)]
Since the fortieth root of ten is 1.05925, 40 equally-spaced log intervals per size decade must be employed in the computation of [sij~ to achieve a resolution of 6%
in the particle size distribution. To achieve this size resolution through four decades (particle sizes ranging from 0.1 micrometers to 1000 micrometers), [sij]10 must have 160 elements in the j dimension. This implies that the analyzer must employ at least 160 angle classes, and preferably at least 320 classes, to ensure a well-behaved inversion. For an analyzer that operates in the scattering angle range of 0 to 32, 320 angle classes implies an angular resolution of 0.1 if all of the angle classes are equally spaced.
Many prior art devices have addressed the need of a particle size analyzer to achieve high angular resolution and to respond to a wide range of scattered light intensities. For example, U.S. Patent Nos. 4,953,978, 5,056,918;and 5,104,221, issued to Bott, disclose a plurality of discrete annular silicon photodetector sectors, of circular shape and increasing radius, disposed in a fixed 20 position relative to the nominal beam axis. These detectors are responsive to the cone of scattered light that intersects the detector in a region defined by the circular shape of the detector. Additional silicon photodetectors can be deployed in a line extending beyond the annular detectors, extending the angular range of the analyzer. The intent in these patents is that each of the discrete photodetectors is 25 selected and mounted to be responsive to light scattered in a fixed angular interval with respect to the nominal beam axis. In this manner, the geometrical shape of the photodetector and its intensity response can be configured so that the sensitivity and dynamic characteristics of the detector match the light intensity expected for the angular position of the photodetector. Similar design considerations have been 30 employed by prior art analyzers that employ fixed deployments of ring-shaped photodetectors .
However, the use of fixed deployments of discrete solid-state photodetectors leads to many problems. For example, these deployments require precise calibration and alignment with the light source in order to obtaun valid light 35 scattering data. The calibration and alignment must be re-done at any time that a WO 95128630 PCTtUS95/04638 component of the analyzer is moved or changed. Another problem encountered with the use of fixed deployments of discrete photodetectors is that the number and complexity of detectors used increases the cost of the analyzer and increases the chance for malfunction. Solid-state photodetectors provide a current signal which is proportional to the light intensity f~lling on the photodetector. Thus, great care must be used in m~.~cllring the low current resulting from low intensity light.
The most significant problem with prior art analyzers using fixed deployments of discrete photodetectors is the limited number of detector elements used. These analyzers typically employ 16 to 32 detector elemen~c, although somemay use as many as 126 elements. In any case, the number used directly limits the resolution (number of unknown independent variables) obtainable in the size distribution. An approximation used by prior devices to overcome this limitation is to assume that a particular functional form, such as a G~llscian distribution, can be used to describe the particle size distribution of a sample. In this way, the number of unknown independent variables is reduced to the two parameters necessary to define the Gal~cci~n curve. Unfortunately, most samples are poorly described by a ~,.llcsian curve, and the validity of such a result is problematic at best. Sometimes size resolution is enhanced by limiting the analyzer to a narrow range of particle sizes, but this technique limits the general utility of the analyzer to determine particle size distributions across a broad variety of sizes.
Other prior art devices use photomultipliers as the light detector, such as described in U.S. Patent Nos. 4,676,641 and 4,781,460, issued to Bott.
Multiple photomultipliers can be used at different angles to the incident beam, or a single photomultiplier can be used and moved through an angle relative to the incident beam to collect data at different scattering angles. The physical size of a photomultiplier (in general, larger that a discrete silicon photodetector) causes problerns since a high angular resolution cannot be achieved without masking off a portion of the light entrance window. The m~cking limits the light entering the photomultiplier and thereby lengthens the exposure time required to obtain sufficient data. In addition, the size of a photomultiplier prohibits the side-by-side mounting of multiple photomultipliers to cover adjacent angle classes. It is therefore necessary to move the photomultiplier to many angular positions to getdata, further lengthening the data acquisition time and adding to the complexity of the analyzer. During long data acquisition runs, the particle size characteristics of the sample may change, creating problems for accurate data analysis. Like silicon - 21 8778~
~ WO 95/28630 PCI/US95/04638 photodetectors, photomultipliers provide a current signal which is proportional to the light intensity falling on the photomultiplier. Thus, where the intensity is low, the current is low and care must be exercised in reading the current.
A problem common to all of the prior art particle size analyzers is 5 that they must be mechanically or manually ~lignecl Frequently, the ali~nment procedure must be perforrned between data acquisition runs for different samples.
Thus prior art analyzers require operator monitoring and intervention on a regular basis, making lln~tten~ed or automatic operation problematic.
Another problem common to all of prior art analyzers is that their 10 angular resolution is controlled by varying the detector size, by masking of the detector, or by changing other mechanical or opto-mechanical aspects of the devices, generally in the design stage. These techniques of controlling angular resolution imply that the analyzer is not easily re-configured to change the resolution which may be desired for particular experimental needs. Prior art 15 analyzers tend to be configured by the manufacturer for an assumed amount of angular resolution at the various sc~ttçring angles provided by the analyzer and no variation is possible.
Prior art analyzers have had particular problems when analyzing particle samples that consist of two or more groups of distinct but nearly identical 20 sizes. This situation causes difficulties in the inversion process unless a very high angular resolution of the scattering data is available. Where sufficiently high resolution is not available, the inversion analysis must be constrained to look for assumed functional fits (i.e., Gallcsi~n, bi-modal or multi-modal Gaussian, etc.) to the experimental data with theoretical size values close to the size values to be 25 determined: The lack of sufficient angular resolution in prior art analyzers has led to the necessity of operator input, in the form of an educated guess as to the make-up of the particle mix or selection of functional constraints, to resolve the two or more groups of particles in the particle size distribution.
Thus, a need exists for a particle size analyzer capable of resolving 30 several hundred angle classes which can be used in varying analytical conditions without physical realignment of the analyzer or guidance from the operator as to the nature of the particle mix under investigation, and which, when compared to the prior art, produces both scattering intensity data over a larger angular range with greatly increased angular resolution and particle size distributions over a larger

3~ range of particle sizes with greatly increased size resolution.

wo 95/28630 2 1 8 7 7 8 9 p~US95/04638 SUMMARY OF THE INVENTION

The present invention solves the problems of the prior art described 5 above. Furthermore, the present invention achieves a precision and resolving power in particle size distributions that is unavailable using prior art devices. These advances are achieved by using a light detector compri~ing a two-dimensional array of small photosensitive elements, called pixels. Generally described, the invention provides a method and apparatus for obtaining particle size data for a group of 10 dispersed particles, according to which the particles are illl~min~t-od with a dose of light in a collim~t~.A beam from a light source so as to scatter light of the beam, and at least a portion of the light interacting with the particles is detected with a two-dimensional array of functionally equivalent photosensitive pixels. The functionally equivalent aspect of the pixels allows the analyzer to dynamically 15 configure and re-configure at least a portion of the pixels into a variable number of data collection areas. The nature of the pixel array makes it possible for output data from the pixels to be received by a processor configured to determine from the output data the location at which an unsc~tt~red center of the beam intersects the array. Thus, no precision mechanical ~lignmPnt of the light source and the detector 20 is required prior to operation of the analyzer. Furthermore, the ability of the analyzer to determine the unscattered bearn center allows the analyzer to classify each of at least a portion of the pixels to data collection areas according to a function of the geometric relationship that the pixel bears to the beam center.
The pixels are functionally equivalent in the sense that each pixel is 25 equally suitable for m~cllring the intensity of light scattered in any direction by the dispersed particles. Each of the pixels preferably is capable of individually and independently providing a measure of the light falling on it. The pixels preferably are not discrete components, but are manufactured as an integrated electrical device.
Preferably, the pixels are deployed such that the pixel array forms a surface and 30 such that the location of the pixel can be inferred from its identity.
The pixels can be of varying sizes. The pixels preferably are densely arranged, meaning that the pixels are of small size and the pixel spacing is not significantly larger than the pixel size. Commercially available densely arranged pixel arrays have pixel spacings from about .007 mm to .060 mm in 35 planar arrays, and the photosensitive area of the pixel array is more than two-thirds ~ WO 9S/28630 PCI'/US9S/04638 of the smallest contiguous area cont~ining the pixels. For high resolution and rapid measurement time, the pixel size is preferably small, on the order of 0.02 mrn square, and the number of pixels is preferably large, on the order of an array of 1,000 by 1,000 or larger, with the pixel spacing being not much larger than the pixel size. Thus, instead of 126 or fewer independent angular measurements of - scattered light intensity, as in the best prior art in~ le,l~, implem~nt~tions of the invention can provide as many as a million or more independent measurements.
The manufacturer of a prior art particle size analyzer which employs 126 light detectors has published literature containing the statement that this analyzer uses "the theoretical maximum number of detectors (126)." Thus, in contradiction to the teachings of the prior art, the present invention has greatly exceeded the "theoretical maximum".
Since each pixel's electric output signal (also called output data) can be read separately, extremely good geometric resolution can be achieved. By mounting the array at an applol,.iate distance from the scattering particles and by the preferred use of a lens or lenses, the array's superior geometric resolutiontranslates into superior angular resolution. To control the reading, storing andprocessing of the large amount of scattering data produced by the invention, electronic proceccing is used.
The two-dimensional array of photosensitive elements may be of several types. One type is a charged-coupled device ("CCD"). A CCD is an array of photosensitive pixels, preferably in perpendicular rows and columns, each of which converts incident light into an electric charge proportional to the total arnount of light falling on the pixel since the last reset comrnand provided to the CCD. The electric charge is made available as an output si~nal of the CCD on a row or column basis when a read command is given to the CCD. The readout of a CCD normally drains each pixel of its charge and is, in that case, a destructive readout.
CCD's have been extensively used, e.g., in video cameras, where their geometric resolution provides a good irnaging capability. Others have suggested the use of a CCD as the light detector in a particle size analyzer.
However, CCD's do not have a wide dynamic range; typically, they are capable of measuring light intensity only in a range of ~56 or 4,096 to 1. A particle size analyzer must be capable of handling light intensity variations spanning eight orders of magnitude. Furthermore, CCD's have par~cular electronic responses, such as "blooming", discussed below, which are not present in the detectors used in the prior art. These factors mitig~te against simply substituting a CCD unit for the light detectors in the prior art devices.
Another type of array suitable for use in the invention is a charge injection device ("CID"). A CID is a device sirnilar to a CCD, but its pixel structure and array architecture perrnit selective readout of a subsection of the pixel array. A
CID also provides non-destructive readout and pixel charge control, which farilit~ s control of the blooming phenomenon exhibited by CCD's.
Other pixel structures and array architectures have been reported in the literature, including a Charge Modulated Device ("CMD"). The CMD is an MOS image sensor, preferably with a rectangular grid of pixels, where each pixel is a light sensitive MOS transistor characterized by a high optical gain and a non-destructive readout operation. CMD's are described in the article A New MOS
Phototransistor Operating in a Non-Destructive Readout Mode, Japanese Journal of Applied Physics, Vol. 24 (1985), pp. L323-L325, and a later article by Nakamura et al., A New MOS Image Sensor Operating in a Non-Destructive Readout Mode, IDEM Vol 86, pp. 353-356, which articles are incorporated by reference. The CMD is an example of an active-pixel sensor ("APS"), where each pixel's output is individually amplified or buffered. Other APS devices include a Bulk Charge Modulated Device ("BCMD"), with a hexagonal packing format; APS
devices with static induction transistors; and a Base Stored Image Sensor, as reported in the article Active-Pixel Sensors Challenge CCDs, Laser Focus World, June 1993, which article is incorporated by reference. Hybrid infrared image sensors are photosensitive pixel arrays that are commercially available. All of these devices are suitable for use in the invention.
Yet another type of a photosensitive pixel array is an integrated array of silicon photodetectors. These arrays may contain configurations of 128 x 128 pixels or 256 x 256 pixels with a .06 rnm center-to-center pixel spacing in both the horizontal and vertical directions. The electronic circuitry associated with these devises preferably integrates the photodetector current for each pixel. In this case, each pixel's output is an electric charge proportional to the total amount of light falling on the pixel since the last reset comrnand, as in a CCD.
For simplicity in the specification and claims below, the term "pixel array" will be used herein to refer to any device whose structure includes a two-dimensional array of small, closely arranged photosensitive elements configured as an integrated electrical device and which provides an electric signal responsive to wo ss/28630 1 3 2 1 8 7 7 8 9 pCT~S95/o4638 the light falling on the photosensitive elements. Other than the invention described and claimed herein, the inventors are unaware of any su~ces~ful attempt to design or build a light scattering particle size analyzer using a pixel array, as broadly defined herein.
S The present invention, however, has solved the problem of using a pixel array in a particle size analyzer to measure the scattered light intensity. In the preferred embodiment, a single CCD is used to measure the scattered light intensity throughout all angular regions of interest. The invention compensates for the CCD's low dynamic range by employing a number of novel techniques. The techniques fall into two categories: recognizing and ignoring those pixels whosedynamic range is exceeded, and controlling the intensity and duration of the light source to ensure that the entire angular range of interest is measured. The net effect of these techniques is to extend the dynamic range of the CCD to that required by a particle size analyzer.
One technique employed by the preferred embodiment of the present invention to extend the dynamic range of the CCD uses the fact that each pixel of a CCD measures the time integral of the light intensity falling on it. Thus, extremely high intensity light can be effectively measured if the CCD is exposed to the light for only an extremely short period of time. Conversely, very low levels of lightintensity can be measured by exposing the CCD for a longer period of time. The exposure time of the CCD is controlled by switching the light source on and off or by deflecting or stopping the light source beam before it strikes the sample, effectively creating light pulses of varying duration. Typically the analyzer uses shorter exposure times for scattering data taken at forward angles and longer exposure times for scattering data taken at larger angles. Generally, in producing a single particle size distribution, multiple exposures of varying times are utilized in obtaining scattering intensity data which span a wide range of intensity values.Therefore, for effective analysis where there are differing exposure times, the CCD
output signals for the differing times must be normalized, or scaled, to an exposure time standard. The invention recognizes the effect of different exposure times and provides the correct norrn~li7.ing factors for adjusting the CCD output data.
Another technique used by the preferred embodiment of the invention to ensure that the dynamic range of the CCD is not exceeded also uses the intensity-integrating characteristic of the CCD. The invention directly controls the intensity of the light source so as to reduce or increase the amount of scattered light ~ w0 95l28630 2 1 8 7 7 8 9 pcr/us95/04638 - falling on the CCD, as desired. The combination of controlling both the intensity of the light source and the time of the exposure leads to the concept of a light"dose", which is the product of the intensity of the light source and the time that the light source is on. By controlling the light dose, the invention can ensure that the S amount of light scattered at a particular angle or region on the CCD is within the CCD's dynamic measurement range. The invention also uses the amount of the light dose for an exposure to determine automatically the correct factors to norn~li7e, or to scale, the measurements of scattered light taken during different exposures.
10Another technique to keep within the dynamic range of the CCD
used in the preferred embodiment of the invention is to control the number of sc~tte~ing particles, placing more particles in the incident beam to increase the intensity of scattered light and placing fewer particles in the beam for less intensity.
This may be accomplished by using sample cells to hold the scattering particles.15 Preferably, the particles are dispersed in a fluid, such as water which is contained in the sample cell. The number of scattering particles in the incident beam can be varied by varying the concentration of the particles in the fluid or by changing the angle of the scattering cell relative to the incident beam. Alternatively, the number of particles can be varied by using sample cells of differing widths measured in a 20 direction along the beam. The invention determines the correct norm~li7.ing factors to adjust the CCD output signals for multiple exposures using differing numbers of scattering particles in the incident beam. No realignment of the analyzer is requlred.
Another technique to keep within the dynamic range of the CCD is 25 to employ a filter interposed between the light source and the sample cell. The filter reduces the light intensity of light passing through it, typically by several orders of magnitude. In effect, the filter extends the dynarnic range of the light source and permits greater flexibility in pro~ -g light doses.
If the dynamic range of any pixels in the CCD is exceeded, the 30 phenomenon known as "blooming" can occur. Blooming occurs after a pixel becomes saturated with charge and its charge begins to "bleed", or discharge, into adjacent pixels. This phenomenon affects the ability of a CCD detector to be used successfully in a light scattering particle size analyzer. Blooming is a particular problem at small scattering angles, where very high light intensity gradients can 35 cause some pixels to be oversaturated before other nearby pixels register any ~_ WO 95128630 PCI~/US95/04638 measurable intensity. Blooming in such situations obscures important scattering patterns which occur at small angles. Certain commercially available CCD's, suchas the Kodak KAF-1300L, incol~ol~te anti-blooming protection which keeps each pixel from discharging into adjacent pixels for a limited rate of overcharging of the pixel. However, anti-blooming protection cannot protect against all blooming that would occur in a particle siæ analyær. The~Gfo~G, the invention inchlcles additional methods of addressing the blooming phenomena.
With the ability to control and adjust, or normalize, for differing beam intensities and exposure times, and with the ability to process individually each pixel of scattered light intensity data, it becomes possible to use a single pixel array, even one with a fairly low dynamic range such as a CCD, for all angular regions of interest. In the preferred embodiment, the use of a single pixel array minimi7es the expense of manufacturing the particle size analyær. When a single pixel array is used, it is preferable to provide for changing the relative anglebetween the pixel array and the incident beam so that sc~ttering intensity data can be obtained over a wide range of scattering angles. This is accomplished by providing a movable pixel array for moving through an angle relative to the incident beam, or, preferably, by providing a movable light source for moving through an angle relative to the optic axis.
Since in the preferred embodiment of the present invention the incident beam and the pixel array are not in a fixed orientation with respect to each other, provision is made to automatically locate the relative position of the pixel array. As a first provision, the invention automatically senses when the beam impinges directly on the pixel array and detPrmin~s the location on the pixel array of the beam center. When the light beam does not fall on the pixel array, a second provision is made to locate automatically the position of the pixel array. The movements of the light source or of the pixel array from or until the time the beam strikes the pixel array are recorded and are used to determine the relative angle between the light beam and the optic axis. In this manner, the light scattered through the entire range of scaKering angles, from 0 to 180, can be measured with the present invention. The deterrnination of the location of beam center is veryaccurate, reproducibly locating beam center to within one pixel on the pixel array.
The desirability of reproducibility in a particle size analyzer is discussed in the Coulter Corporation Technical Monograph, "LS Series Reproducibility," which monograph is incorporated by reference.

21 8778~

An important feature of the present invention is a provision to divide the pixels of the pixel array into a number of data collection areas. One type of data collection area, called an angle class herein, is configured so as to have angular significance. This is desirable because the pixel array preferably employed subtends a fairly large angle at the optic center of the lens, typically on the order of five or six degrees. ~csi~nin~ the pixels to angle classes is performed under the control of the invention. The configuration of data collection areas is readily changed during the operation of the analyzer. Therefore, the ~c.ci~nment of pixels to angle classes can be multiply re-done to accommodate the different geometric shapes taken by the intersection of the cone of scattered light with the surface of the pixel array when the pixel array has different positions relative to the incident light beam. The division of the pixels into variable angle classes also permits the analyzer to achieve different angular resolutions at different stages of the analysis or at different sc~tt~o-ring angles. This means that the analyzer can decrease the angular resolution, where the resolution is not a critical factor, to shorten the analysis run time. The analyzer can also increase the angular resolution when resolution is important. The number and range of angular values represented by the angle classes is variable to accommodate varying angular resolution requirements. In setting up the angle classes, the present invention uses angular intervals varying from 0.0025 degrees for very small angles (less than 0.1 degree) to 0.1 degrees for large arlgles (greater than 3.2 degrees).
The ~ccignmtqnt of pixels to angle classes is carried out by use of well-known trigonometric relationships. Each pixel is assigned to an angle classbased on the angle at which the incident light beam must be scattered to strike the pixel. To achieve higher resolution at small angles, fractions of the pixel area may be ~ccignPd to adjacent angle classes when an angle class boundary falls across the pixel. The zlcci~nmt-nt is simplified by use of the virtual coordinate system which treats all sc~tterin~ as origin~3ting from the optic center of the lens.
To calculate the angle at which the incident beam must be scattered to strike the pixel, first the angle is calculated which is subtended at the optic center of the lens by the distance in the focal plane from the focal point to the pixelAppropriate corrections are made for any refraction which occurs in the scattered ray. This angle is the scattering angle if the light beam is coincident with the optic axis (beam angle = 0). If the light beam makes an angle with respect to the optic axis (beam angle > 0), then the bearn angle (corrected for refraction effects) must be 21 8778q geometrically combined with the previously calculated angle to determine the scattering angle, and hence the angle class to which the pixel belongs.
The preferred embodiment of the present invention combines norm~li7~rl output values from all of the pixels in the same angular region so that the average intensity of light falling in a given angle class may be determined. The norn:~li7e~1 combination technique is extended to include contributions from thesame angle class from multiple exposures arising from use of the light detector in different angular relations to the incident beam or from use of the light detector in the same angular relation to the incident beam for dirrelellt light doses.
In general, each exposure will have valid intensity data for only a subset of the full range of angles necessary to produce the particle size distribution.
Usually, the pixels in angle classes for angles smaller than the usable angles will be overexposed (saturated), and the pixels in angle classes for angles larger than the usable angles will be underexposed. Valid intensity data for these angle classesmust be obtained by taking longer or shorter exposures, or by varying the intensity of the incident light beam.
The ability of the present invention to locate the center of the incident light beam means that there is no mechanical ~lignment required in the normal operation of the apparatus. On the other hand, certain characterization adjustments are required to interpret the pixel array output values properly. For example, a particular pixel may provide either no or an anomalous output with respect to the amount of light falling on it. The present invention can determine when a pixel is not operating within proper operating limits, and a "bad pixel map"
is maintained to identify and compensate for such pixels. Additionally, certain pixel arrays are known to provide non-zero pixel output values even when no light is falling on the pixel array. The non-zero output values are a result of thermal effects in the pixel and increase linearly with time. Therefore, the electric charge acc-lm~ ting in a particular pixel with no light on the pixel can be expressed as the product of a "dark current" value characteristic of that pixel and the length of time since the last reset of the pixel array. The increase in pixel output with time due to this effect is sometimes called "dark current buildup". The present invention determines the dark current values for each pixel of the pixel array in order tocompensate for this effect.
Preferably, the c~mponents of the present invention include a light source, a CCD, and a converging lens. The particles to be investigated are positioned such that the light from the light source is scattered by the particles, and the converging lens is positioned to focus a portion of the scattered light onto the CCD. A lens used in this manner is somPtim~s called a Fourier transfomm lens. Inorder to facilitate different configurations of the analyzer, the lens can be a zoom 5 lens. The analyzer includes a processor and data storage memory configured to receive and reduce pixel output data from the CCD. The CCD output data provides a measure of the intensity of light that is scattered at an angle relative to the beam.
Preferably, the CCD provides antiblooming protection up to a predetermined intensity of light incident on the CCD, regardless of exposure time.
The light source is preferably a laser and is preferably movably mounted in the analyzer such that the angle between the beam emitted from said laser source and the axis of the lens may be varied. Altematively, the CCD and the lens may be movably mounted for movement together, such that the angle between the beam emitted from the laser source and the axis of the lens may be varied. The particles may be dispersed in a sample cell. The sample cell has a cell width in a direction along the axis of the lens and may have an adjustable cell mount capable of receiving a plurality of sample cells of differing cell widths.
Before the particle size analyzer is used for analytical work, the CCD preferably is characterized by uniformly ilhlmin:~ting it with laser light doses at a number of different light intensities. The bad pixel map, as discussed above, is created at this time. In addition, the dark current buildup of each pixel of the CCD
is determined as a function of time, so that the output data for each pixel can be modifled based on the dark current function and the duration of each exposure.
Finally, an output function for each pixel, relative to incident dose intensity, is determined so that the output data for each pixel may be modified based on the output function and the amount of light dose used in each exposure. The output function corrects for any variation in sensitivity or offsets which may be present in a given pixel's response to light. Once the CCD has been characterized, pixel-by-pixel, the analyzer is ready for use to ~eterrnine particle sizes.
A typical preferred operation of the analyzer to obtain particle size data involves dispersing the particles under investigation, exposing them to a dose from a collimated light beam so as to scatter a portion of the light, passing a portion of the scattered light through the lens, detecting a portion of the light passing through the lens with a pixel array, and reading the output data from the pixels into a memory device. The results of the first dose are analyzed to determine if `--WO 95/28630 PCT/US95/04638 additional doses are required to get readings within the dynamic range of the pixels for all angles desired for obtaining a good particle size distribution. If additional doses are required, the siz,es of additional doses are dete. .l ~ .d by varying either or both the length and illlensily of the pulse of light from the laser source.
S If the scattered light intensity in the region of interest cannot be brought within the dyn:~mic range of the pixels by adjusting the dose of the incident light beam, then the sample container may be replaced with another sample container having a dirr~ t width or the concentration of the .c~mpling particles may be changed and, without physical re~lignmP.nt of the laser source, the lens, or the array of pixels, the operational steps set forth above can repeated.
During a series of exposures at the same position of the light source relative to the optic axis, the beam center is dc-termined by projecting the unscattered beam onto the pixel array, reading the output data from a number of pixels into a memory device, defining an area of pixels where the magnitude of the output data is the highest, and determining a bearn center located at the center coordinates of the area. If the l-n.cc~ttered beam does not fall on any pixels in the pixel array, the direction of the beam relative to the optic axis is recorded as the beam angle for later use in computing scattering angles. After the beam center or beam angle is determined, the pixels of the pixel array are assigned to a number of predefinedangle classes. This is accomplished by determining the scattering angle for eachpixel, as described above, and assigning the pixel to the class, or fractionally to the classes, to which it belongs.
For a given dose of light from the light source, scattered light intensity data is read from the pixels into a memory device and intensity values for a number of angle classes are determined. This procedure may be repeated if necessary for a number of different doses. If desired, the light source can be moved to a new angular orientation with respect to the beam axis and additional intensity values obtained for the same or additional angle classes. Finally, for each angle class, a composite intensity value is deterrnined based on the combination of all of the exposures and scaled to compensate for differences in illurnination characteristics during each of the exposures. The composite relative intensity values, recorded as a function of angle class, are then fit to a combination of theoretical intensity-versus-angle data sets using an inversion technique to obtain the particle size distribution.

~,~, WO 95/28630 2 o PCI/US95/04638 Thus, it is an object of the invention to provide particle volume fraction data versus particle size for a spectrum of particle sizes with improved particle size resolution.
It is a further object of the present invention to provide a particle size S analyzer capable of determining particle size distributions for samples with particle sizes ranging from less than 0.1 rnic,ollleter to 1000 micrometers or more, without re-~lignm~nt or m-~ch~ni~:~l adjustmPnt of the analyzer.
It is a further object of the invention to provide a particle size analyzer which will resolve particle sizes over the size range from 0.1 micrometer 10to 1000 micrometers to better than 6% of the particle size being considered, automatically without operator input as to the nature of the mixture of particles.
It is a further object of the invention to provide scattering intensity data versus scattering angle for a plurality of total light doses and incident beam angles, with automatic norm~li7~tion of the intensity data.
15It is a further object of the invention to provide a particle size analyzer capable of effectively using a CC~, a CID, or other types of two-tlimt n~ional arrays of photosensitive elements for detecting and measuring scattered light intensity to obtain high angular resolution of the intensity data.
It is a further object of the present invention to provide a particle size 20 distribution analyzer which can automatically determine regions on a two-dimensional array of pixels corresponding to variable angle classes relative to the beam direction.
It is a further object of the present invention to provide a method of determining the center of a light source beam that is incident on a two-dimensional 25 array of pixels.
It is a further object of the present invention to provide a method of classifying various pixels in a two dimensional array into angle classes.
It is a further object of the present invention to provide a method of combining intensity data from a two-dimensional array of pixels, taken during 30 multiple exposures, to obtain one composite intensity data profile for a given scattering pattern.
It is a further object of the present invention to provide a particle size distribution analyzer in which. intensity data from like angle classes can be combined from different exposures using different incident beam intensities and 35 incident bearn angles.

2 l It is a further object of the present invention to provide an apparatus capable of scattering light onto a two-r~im.qncional array of pixels from multiple incidto.nt angles with multiple beam i~ s-It is a further object of the present invention to provide a particle size distribution analyzer which can use a converging lens capable of having different focal lengths and not require re-alignment of the analyzer components when the focal length of the lens is changed.
The present invention meets these objects and overcomes the drawbacks of the prior art, as will be apparent from the detailed description of the embo-lim~.nts that follow.

BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a plan view diagram of a particle size distribution analyzer depicting components of an embodiment of the present invention.
FIG. 2 is a simplified diagram of an embodiment of the invention depicting a plan view of a light source, sample cell, and lens, combined with an elevationview of a CCD to show the concept of angle classes.
FIG. 3 depicts the elements of FIG. 2 with the light beam directed to an area off the CCD.
FIG. 4 depicts the elements of FIG. 2 with the light beam directed so that the CCD will receive b~kcc~ .nng from the sarnple.
FIGS. 4A4F are plan view schematics showing the relative orientations of the light source, sample cell, lens and CCD for beam angles of 0, 45, 90, 90, 135, and 180, respectively.
FIG. 5 depicts the components of an embodiment of the invention which provide the capability of suspçn-ling the sample in a fluid in a sample cell.
FIG. 6 is a polar diagram of log intensity of scattered light as a function of angle predicted as by the Mie theory for 2 micrometer polystyrene spheres.
FIG. 7 is a polar diagram of log intensity of scattered light as a function of angle as predicted by the Mie theory for 10 micrometer polystyrene spheres.
FIG. 8 shows the intensity recorded by the pixels near beam center in an exposure taken to ~letennine beam center.
FIG. 9 shows the assignment of the pixels near beam center to their respective angle classes.

~,, WO 95n86302 2 Pcrlus95lo4638 FIG.10 shows the CCD image of scattered light for an exposure time of 0.010 second.
FIG. 11 shows pixel output values obtained by an embodiment of the invention for a 0.010 second exposure.
5FIG. 12 shows a graph of intensity versus angle for a 0.010 second exposure as obtained by an embo-lim~o-nt of the invention.
FIG. 13 shows the CCD image of scattered light for an exposure time of 0.164 second.
FIG. 14 shows pixel output values obtained by an embodiment of the 10invention for a 0.164 second exposure.
FIG. 15 shows a graph of intensity versus angle for a 0.164 second exposure as obtained by an embodiment of the invention.
FIG. 16 shows the CCD image of scattered light for an exposure time of 0.655 second.
15FIG. 17 shows pixel output values obtained by an embodiment of the invention for a 0.655 second exposure.
FIG. 18 shows a graph of intensity versus angle for a 0.655 second exposure as obtained by an embodiment of the invention.
FIG. 19 shows the composite intensity-versus-angle data set from the 20exposures shown in FIG.10 through 18.
FIG. 20 shows intensity-versus-angle data points as circles and a curve fit to this data using a series of theoretical Mie curves for dirrel~nt size spheres.
FIG. 21 shows the particle size distribution obtained by an embodiment of the invention for 108 micrometer polystyrene spheres in water.
25FIG. 22 shows the intensity-versus-angle data obtained by an embodiment of the invention for a mixture of particle sizes.
FIG. 23 shows the particle size distribution obtained by an embodiment of the invention for a mixture of particle sizes.
FIGS. 24A, 24B, 24C are oblique projections showing representative axes, 30angles, and ~lict~nce~ used in the calculation of the scattering angle.
FIGS. 25A, 25B, 25C, and 25D comprise a flow chart for the routine CCD
CHARAC-l ~RIZATION in an embodiment of the invention.
FIG. 26 is a flow chart for the routine LASER CHARACTERIZATION in an embodirnent of the invention.

`-- WO 95/28630 PCT/US95/04638 FIG. 27 is a flow chart for the routine VALIDATE AND CORRECT
PIXEL DATA in an embodiment of the invention.
FIG. 28 is a flow chart for the routine MEASURE BEAM INTENSITY
AND ALIGNMENT in an embodiment of the invention.
S FIGS. 29A and 29B compri.ce a flow chart for the routine LOCATE OPTIC
AXIS in an embodiment of the invention.
FIG. 30 is a flow chart for the routine CALCULATE OPTIC AXIS
COORDINATES in an embodiment of the invention.
FIG. 31 is a flow chart for the routine CLASSIFY PIXELS TO ANGLE
CLASSES FOR A BEAM ANGLE in an embodiment of the invention.
FIG. 32 is a flow chart for the routine CALCULATE SCATTERING
ANGLE in an embodiment of the invention.
FIGS. 33A and 33B comprise a flow chart for the routine MAP PIXEL
DATA TO ANGLE CLASSES in an embodiment of the invention.
FIG. 34 is a flow chart for the routine COLLECT DATA in an embodiment of the invention.
FIG. 35 is a flow chart for the routine SAMPLE ANALYSIS in an embodiment of the invention.
FIG. 36 is a perspective view of the collimator, filter, and sample cell assemblies in an embodiment of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring now to the drawings, in which like numerals refer to like parts throughout the several views, FIG. 1 shows a plan view diagram of a particle size analyzer 10 depicting the components of an embodiment of the present invention.
The principle components of this embodiment include a laser 11 in a beam assembly 21 to provide a collirnated beam 22 of light to a sarnple of particles 38 contained in a sample cell 31. The particles 38 scatter light and the scattered rays 33 are focused in converging rays 43 on a CCD 51 by a converging field lens 41.
The CCD records the intensity of the scattered rays 33 and provides data to a digital signal processor 71. The digital signal processor 71 processes the data from the CCD S1 and provides intensity-versus-angle data sets to a work station 91 for analysis. The analysis results in particle size information and plots which are output on a display screen 92 and a printer 93. The automatic features of the particle size analyzer 10 are under the control of a control processor 81, which can 21 8778~

rotate the beam assembly 21 about the sample cell 31 and the sample cell 31 about its own axis, control the loading and dilution of the particles 38 in the sample cell 31, operate the laser 11 to make exposures, and in general control all of the m~-~h~nic~l operational features of the analyzer.
The laser 11 can be a solid state device, operating at an output wavelength of approximately 685 nm and nominal output power of 10 milliwatts, such as the Toshiba model TOLD 9l40. The fact that the laser 11 produces coherent light is not important to the operation of the invention. Any source of light of minim~l spread in wavelength may be used in the invention. Although different types of laser sources can be used in the present invention, the laser 11 preferably is a diode or solid state laser. It is also possible to use a helium/neon type laser source. If so, it is not necessary to use the fiber optics 20 described below, and a beam expander may be used to produce the collimated bearn 22. A variable wavelength laser source could also be used.
The laser 11 is operated by a pulsed current source 14 providing control over the power and duration of the pulse, such as the "Laser Diode Driver"
marketed by Seastar Optics, Inc., or a similar device by Oz Optics. The current source 14 provides drive current power to the laser 11 in pulses varying in duration from 1 microsecond to 10 seconds and in current from 0 to 50 milliamperes. The current source 14 can vary the drive current in steps of 0.1 milliamperes, repeatable to within 0.03 milli~mperes. The power output of the laser 11 is a function of the drive current supplied by the current source 14.
The laser 11 is housed in a laser source assembly 12 which also contains a Peltier effect cooling device 16 for cooling the laser 11 to better control and stabilize the wavelength. The laser 11 preferably operates below room temperature, in a temperature range of 50 to 70 degrees Fahrenheit. A heat sink 18 preferably surrounds the laser 11 in order to absorb heat created during the operation of the laser 11. A tempe-atule sensor 13 measures the temperature of the laser.
A portion of the light emitted by the laser may be split by a beam splitter (not shown) and received by a photodiode (not shown). The photodiode provides a direct reading of the duration and intensity of the pulse of light from the laser 11, and hence provides a signal proportional to the light dose ~lministered to the sample cell 31. By splitting approximately half of the light to the photodiode and half to the sample cell 31, the photodiode signal can represent an accurate measure '-- WO 95/28630 PCI~/US95/04638 of the dose a(lministered to the sample cell 31. When this beam splitter technique is used, the actual amount of light dose delivered to the sample in the sample cell 31 can be used to detçrmine the proper inter-dose norm~li7.ing factors, rather than a calculated amount of light dose determined from the light source control 5 par~m~ter.c Fiber optics 20 are used to carry the beam emitted from the laser source assembly 12. The fiber optics 20 are attached to the laser 11 in a conventional manner. The other end of the fiber optics 20 is attached to a lens holder 28. The fiber optics 20 are preferably a single mode fiber which produces a conical exit10 beam 24 with a G~lcci~n intensity distribution. The exit beam is directed toward a collim~ting lens 25 held by the lens holder 28. Light em~n~fing from the collim~ting lens 25 is a highly collim~ted beam 22 (parallel rays of light), the rays of which are preferably parallel to within 0.1 milliradian. The collimated beam is preferably circular in cross-section and approximately 10-lS mrn in diamet~r. The laser source assembly 12, the fiber optics 20, and lens holder 28 may be housed together in the beam assembly 21. Alternatively, the laser source assembly 12 may be mounted remotely and the light directed to the collim~ting lens 25 or, generally, any type of collimator 225, by the fiber optics 20.
The term "collim~ted beam" used herein refers to essentially parallel rays of 20 light however generated. Examples are, without limitation, a beam made parallel by a lacer, a beam made parallel by a collim~ting lens or mirror regardless of the source of the light, and a beam origin~ting effectively at infinity with respect to an optical system.
In order to adjust the incident angle of the collimated beam 22, the preferred 25 embodiment also includes a rotation device 5 which is used to rotate the beamassembly 21 to various different beam angles with respect to the optic axis of the field lens 41. The center of rotation should be within the volume of the sample cell 31 containing the particles 38, and preferably at the center of the dispersed particles 38. The rotation device can be a rotation stage, or a goniometer platform, 30 such as those manufactured by New England Affiliated Technologies, or any comparable rotation device. Rotation is controlled by the control processor 81. To avoid vignetting errors when the beam assembly is rotated, the entire volume of the collimated beam 22 inside the sample cell 31 must encounter the same concentration of particles 38 that are present when the beam angle is norninally35 zero.

A filter assembly 201 may be interposed between the collimator 225 and the sample cell 31 to control the intensity of light reaching the sample cell. As shown in Figure 36, the filter assembly 201 is composed of a glass wedge 202 held in a filter mount 205, which is movably attached to a linear motion rail 206.
A drive screw 209 threaded through an arm of the filter mount 205 may be rotatedby a drive motor 208 to move the filter assembly up and down. Other mPch~nicm.c for movement, such as a solenoid or other translation mech~nicm, may also be used. An upper limit switch 215 and a lower lirnit switch (not shown) may be used to control the position of the filter assembly 201. The limit switches, linear motion rail 206, and a collimator mount 228 holding the collimator 225 may all be mounted on a positioning arm 211.
The glass wedge 202 should have a clear section 203 and one or more filter sections arranged vertically on the wedge. In Figure 36, a single filter section 204 is shown. When the filter assembly 201 is positioned so that the collimated beam 22 passes through the clear section 203, the beam is not tliminiched in intensity, except for reflections of the beam from the surfaces of the glass wedge 202. The wedge shape is chosen so that reflections (both interior and exterior) are not directed toward the sarnple cell 31 or the CCD 51. When the filter assembly 201 is positioned so that the collimated beam 22 passes through a filter section204, the intensity of the collimated beam 22 is ~liminiched by the optical density of the filter. A preferred optical density of the filter is four, which reduces theintensity of the collimate~ bearn 22 by a factor of 10,000. By using a clear section 203 and a filter section 204 on the same glass wedge, the deflection of the collimate~l beam 22 due to refraction is the sarne for both sections.
The filter material in the filter section 204 may be of any type, such as a metallic neutral density filter or a dialectic interference filter. The filter preferably should be thin and flat, such as that produced by a vacuum deposition, to minimi7e any displacement of the bearn center between the filter-in and filter-out conditions of the analyzer. In effect, the filter extends the dynamic range of the laser 11 and permits greater flexibility in prograrnIning light doses.
The sample cell 31 is a container including two glass windows 36, each of which is approximately 1.5 mm in thickness. The glass windows preferably have an anti-reflection coating. In addition, the surfaces of the glass windows may be angled so that reflections are not directed toward the sample cell 31 or the CCD 51.
In the preferred embodiment, one sample cell 31 is sufficient for determining particle sizes in the range 0.1 rnicrometers to 1000 micrometers. However, more than one sample cell 31 may be used if desired. The sample cell 31 is mounted inan adjustable frame 35 which can receive cells of a variety of widths. The two glass windows 36 are preferably spaced farther apart when analyzing larger S particles and closer together when analyzing smaller particles. It will be understood that a smaller path length between windows is desired for small partlcles to minimi7t-. the possibility of a light ray interacting with more than one particle.
However, when the particles are larger, a longer path length is needed to provide enough particles for scattering without too high a concentration in the suspension.
The present invention allows the user to change sarnple cell width with little or no re~lignm~nt needed.
The particles 38 may be delivered to the sarnple cell 31 and m~int~ined in suspension by any apparatus known in the art. An example of such an apparatus isan autosampler as shown in U.S. Patent No. 4,920,550, which patent is incorporated herein by reference. The autosampler uses a liquid 39 to disperse the particles 38. A fluid interface circuit between the sarnple cell 31 and the autosampling device is described below with reference to FIG. 5. Alternatively, the scattering particles 38 can be dispersed in the scattçring region by jets of air or other gasses, as is known in the art.
The sample cell 31 is positioned so that the entire cross section of the collimated beam 22 passes through the scattering region in the sample cell 31.
Some of the light rays in the collimated beam 22 strike the particles 38 in the sample cell 31. The remainder of the light rays in the collimated beam 22 pass through the sarnple cell 31 without interacting with the particles 38 to form anlln.cc~ttered beam 32. The choice of a suitable suspending and dispersing liquid 39 is affected by the size, density and chemical composition of the particles. The two windows 36 are aligned close to each other so that each light ray (not pictured)from the collimated bearn 22 preferably strikes not more than one particle 38 dispersed in the liquid 39. In determining the particle size distribution of theparticles 38, the refractive index of the air and of the liquid 39 through which the scattered rays 33 travel is taken into account in the interpretation of laser beam intensity data.
After traveling through the liquid 39 and interacting with the particles 38, at least a portion of the scattered rays 33 pass through the field lens 41. The field lens 41 is of the converging type and is positioned such that its distance to the ._ WO 95/28630 PCI/US95/04638 CCD 51 is equal to its focal length and its distance to the sample cell 31 is much less than its focal length. ~t this position, scattered rays 33 which are parallel to each other, and which pass through the field lens 41, are directed in convergingrays 43 toward the same point on the CCD 51. The field lens 41 thus operates as S a Fourier transform lens. Converging rays 42 from the un~c~ttered beam 32 strike the CCD at a beam center 50. To avoid vign~ttin~ errors, all light scattered at an angle for which scattered light intensity data is being taken must reach the field lens 41 and be focused to a point on the CCD 51. Preferably, the field lens has a focal length of about 200 mm and is about 50 millimPt~rs in rli,.m~-ter.
The converging field lens 41 can be a single lens or multiple lenses may be used in combination with each other or separately. Generally, a long focal length lens (up to 2 meters) is most efficient for measuring the particle size distribution of larger particles (up to 4000 micrometers). On the other hand, a shorter focal length (as little as 35 mm) is more efficient in measuring smaller particles (down to l15 micrometer). For particles smaller than 1 micrometer in size, the apparatus should be capable of measuring scattering intensity at scattering angles up through 36 degrees. To accomplish this, a shorter focal length lens can be used with a larger CCD 51 or with multiple smaller. CCD's 51. Alternatively, a preferred option is to move the orientation of the beam assembly 21 such that scattering angles larger 20 than that subtended by the CCD 51 can be measured by using a series of exposures, each at a different beam angle.
The field lens 41 may be a zoom lens, of the type well-known in the camera art. The use of a zoom lens provides for ch~nging the effective focal length of the field lens 41 without replacing the lens itself. The zoom lens is 25 advantageous when used in combination with the CCD 51 because, as described in detail below, no ~lignm.o.nt of the lens is needed to position the beam center 50 on the CCD 51.
Although an apparatus according to the present invention is most versatile when it incorpQrates a zoom lens or lens of a multiple focal lengths, an advantage 30 of the present invention is that a wide range of data can be obtained using a single field lens 41 in conjunction with the other improvements described herein.
The CCD 51 receives converging rays 42 and 43 from the field lens 41.
The CCD is located in the focal surface of the field lens 41. For good positional resolution, the CCD 51 preferably has on the order of l000 rows and 1000 35 columns. Preferably, the CCD is the model KAF-1300L CCD manufactured by `-- WO 95128630 PCI`/US95/04638 Eastman Kodak. This CCD has 1024 rows and 1296 colurnns of pixels 55, the rows being perpendicular to the columns. Each of the pixels 55 is square with sides approximately .016 mm in length. The pixel-to-pixel spacing is 0.016 mm inboth the horizontal and vertical directions and each pixel subtends an angle of about S 0.004 degrees when used with the preferred 200 mm focal length field lens 41.
The size of the pixels is such that there are between 15,000 and 30,000 plxels in each angle class for sC~3ttering angles greater than about 1.0 degree, where the light intensity is low compared to that for forward angles. Averaging the output data from this number of pixels enables the analyzer 10 to provide an excellent signal-to-noise ratio. The overall size of the pixel area of the CCD 51 is 20.7 mm wideby 16.4 mm high. In conjunction with the preferred 200 mm focal length field lens 41, the CCD 51 subtends approximately 6 degrees when viewed from the field lens 41. The CCD may be oriented such that its surface is perpendicular to the optic axis of the field lens 41. Alternatively, the CCD may mounted at a slight lS angle to the optic axis of the field lens 41 to minimi7.e reflections of the scattered light back into the sample cell 31. Care should be taken so that the surface of the CCD 51 lies as close to the focal surface of the field lens 41 as is possible.
The CCD 51 may equipped with a conventional temperature control mechanism (not shown) in order to regulate the te~ ;lature of the CCD 51. By regulating the temperature of the CCD 51, the "dark current" effects can be ",h~i.,.;,t~l In addition, the CCD 51 preferably has anti-blooming protection, such as that afforded by the model KAF-1300L CCD.
The analyzer 10 may also use a photodiode array, such as the EG&G
Reticon model RA0128A or model RA1662N in place of the CCD 51. The model RA0128A has 128 rows and 128 columns of pixels, spaced 0.060 mm center-to-center in both the row and column directions. The model RA1662N has a 16X62 matrix of pixels, spaced 0.100 mm center-to-center in both the row and column directions. In each model, each photodiode integrates the photocurrent from the time of the last reset signal. However, for both models, resolution is less thanobtained by the Kodak model KAF-1300L CCD.
The CCD 51, in conjunction with its associated conventional electronics (not shown), provides a measurement of the light intensity falling on each pixel55. The CCD 51 is used with a standard analog-to-digital converter (not shown) which is well-known in the art. The preferred embodiment uses a 12-bit analog-to-digital converter which is capable of conver~ing intensity data to values which range WO 95/28630 PCT/US95tO4638 from 0 to 4095 for each pixel 55. Other bit size analog-to-digital converters may be used; for instance, an 8-bit analog-to-digital converter would provide the intensity values for each pixel 55 ranging from 0 to 255.
It should be noted that the methods of determining beam center and of classifying pixels to angle classes, described below, are facilitated if the pixel array contains regularly spaced pixels, such as, for example, pixels placed on a rectangular or hexagonal grid.
All interior surf~ces of the analyzer should be positioned, coated, covered, or otherwise treated to minimi7.e reflections and to direct any reflections that do occur away from the sample cell 31 and the CCD 51. This treatment ensures that the light received by the CCD 51 is light scattered by the sample in the sample cell 31 from illumin~ting light origin~tin~ only in the collim~te-l beam 22.
The CCD 51 operates under control of the control processor 81 by means of control line 85 and passes its data to the digital signal processor 71 via data line 57. The digital signal processor 71 is programmed with software and configured to reduce the pixel intensity data measured by the CCD 51 to obtain and normalize the intensity of scattered light at various scattering angles. The digital signal processor 71 preferably also contains the ability, given the pixel intensity data available, to determine the pixel location of beam center 50 on the CCD 51, to classify pixels into a variety of angle regions on the CCD 51 based in part on each pixel's distance from the beam center 50, to combine intensity data for different exposure times and laser beam intensity values in order to formulate a composite set of intensity-versus-angle data, and to reclassify pixels to angle regions when the incident angle of the collim~te.d bearn 22 is changed. The digital signal processor 71 preferably is a Texas Instrument TMS 320 or similar processor.
The digital signal processor 71 passes the intensity-versus-angle data to the control processor 81 via data line 78. The control processor 81 is preferably a Motorola 68040 or similar processor wnich can directly address random access memory in excess of one gigabyte. The control processor 81 controls the loading of the particles in the sample cell and the orientation of the sample cell by control line 83. The control processor 81 controls the operation of the laser 11 and thebeam angle of the beam assembly 21 by control line 82. The control processor 81 passes the intensity-versus-angle data to the work station 91 via data line 89. The work station 91 may be an IBM PC or compatible which can analyze the intensity-versus-angle scattering data to deterrnine particle size.

3 l FIG. 2 shows a plan view diagrarn of the particle size distribution analyzer 10 with a view of the CCD 51 rotated 90 such that the face of the CCD S1 is displayed (as in an elevation view). This orientation of the CCD 51 shows rows and columns of the pixels 55 and a point representing the beam center 50.
Although the operation of the ap~alaLus 10 does not depend in general on where the beam center 50 is located on the CCD 51, it is generally preferable to locate the CCD 51 such that the beam center 50 is located near one edge of the CCD 51 when the beam assembly 21 is approximately at zero degrees relative to the opticaxis of the field lens 41. This location provides data for the maximum range of sc~llr~ g angles (up to approxirnately 5 degrees) before rotating the beam assembly 21 to obtain data at larger sc~ttçring angles (if necessary). The location of bearn center 50 should be chosen so that the CCD 51 may contain several angle classes corresponding to very small sc~ttPring angles, each comprising the entire circular annulus about beam center 50. FIG. 2 also illustrates the concept of angle classlS when beam center 50 lies on the CCD 51. Circular arcs provide class boundaries 54 centered on the beam center 50 and divide the CCD 51 into angle classes 56.
Each circular annulus is an angle class and corresponds to a particular scattering angle; the larger the circle, the larger the scattering angle.
In FIG. 3, the particle size distribution analyzer 10 is again shown with the CCD 51 rotated 90 such that the face of the CCD 51 is displayed. The beam assembly 21 as shown in FIG. 3 is aligned so that the collimated beam 22 makes apositive angle with respect to the optic axis of the field lens 41. The beam center 50 is now off the CCD 51, In this configuration, the CCD 51 receives light scattered at larger angles than when the collim~tP~ beam 22 is aligned with the optic axis of the field lens 41. To assign a pixel 55 of the CCD 51 to an angle class 56 when the beam center 50 is off the CCD 51, the scattering angle corresponding tothe pixel 55 must be deterrninP-l, as explained in detail below, from the location of the pixel 55 and the amount of the beam angle. Obtaining scattering intensity data at different beam angles is accomplished by rotating the lens 41 and CCD 51 together or, preferably, by rotating the beam assembly 21 a known angular distance between selected exposures.
For a CCD 51 which subtends an angle of approximately S to 6 degrees, it is possible to cover the entire range of scattering angles (0 through 180 degrees) by stepping the beam assembly 21 with the rotation device 5 in beam angle increments of S degrees, from 0 to 175 degrees. Generally, the exposures taken with the beam 21 8778q _ W O 95/28630 PC~rrUS95/04638 center 50 located off the CCD 51 are longer than exposures taken when the beam center 50 is located on the CCD 51 because sc~ft-o-nn~ intensity is less for larger sc~ttenn~ angles. A longer exposure is needed to collect enough light to provide a measurable illlellsily at these larger s~ttenng angles.
FIG. 4 shows another plan view diagram of the particle size distribution analyzer 10, again with a view of the CCD 51 rotated 90 to show the face of theCCD 51. In the configuration of FIG. 4, the beam assembly 21 has been rotated a positive angle of approximately 135 degrees to a "back sc~ttenng" position. Backscattering is a terrn used whenever the scattering angle is more than 90 degrees.
10 Back scattering may be useful when analyzing the particle size distribution of extremely small particles, typically particles smaller than one micrometer in size.
When positioning the beam assembly 21 in a back-scattenng position, the CCD 51 measures bearn intensity of the light scattered by the dispersed particles 38 back toward the light source.
When rotating the beam assembly 21 to beam angles larger than approximately 45, it is preferable to also rotate the sample cell 31 by an amount approxirnately equal to one-half the bearn angle. Rotation of the sample cell isabout an axis passing through the dispersed particles 38 norrnal to the optic axis of the lens 41 and is controlled by the control processor 81. Preferably, the axis of 20 rotation passes through the center of the dispersed particles 38. FIGS. 4A through 4F illustrate the relative orientations of the beam assembly 21, sample cell 31, lens 41 and CCD 51 for beam angles of oo, 45, 90O, 90c (again), 135, and 180.
FIG. 4D shows an alternate orientation of the sample cell 31 compared with that shown in FIG. 4C, and orients the sample cell 31 for collecting back scattering 25 data. To provide for the extreme b~kscattering angle of 180, as shown in FIG.
4F, the sample cell 31 is removed and mounted a distance away from the CCD 51.
A half-silvered mirror 61 is placed at a 45-de~ree angle in the adjustable frame 35 to provide partial reflection of the collim:lted bearn 22 and partial transmittance of the scattered rays 33.
A fluid circuit 100 for supplying the cell 31 with dispersed sample is shown in FIG. 5. A reservoir 102 for holding sample particles and dispersing fluid is connected via a non-pulsatile pump 103 along a fluid line 104 to an inlet 105 of the sample cell 31. The pump is operated in response to commands received from the control processor 81 to deliver pure liquid or dispersed sample to 35 the cell 31. ~n outlet 106 of the cell 31 leads along a return line 107 back to the 2 1 877~9 ~3 reservoir 102. A container 108 of dispersing fluid is connected to the reservoir102 via line 110, which includes a valve 111. In the embodiment shown, flow from the container 108 into the reservoir 102 is by gravity. A flow cell with anultrasonic probe 115 is positioned in the line 104 to disperse the sample particles in the dispersing fluid.
Sample particles may be inserted m~nll~lly into the reservoir 102, such as from a syringe or beaker, or automatically from an autosampler 120. Those skilled in the art will understand that typical autosarnplers are programmed to deliver a series of samples to an analyzer according to a preset schedule, and in response to signals received from the analyzer. The autosampler 120 shown in FIG. 5 includes its own pump, and is connected to the reservoir 102 by a line 122 including a valve 123. A rinse liquid supply 125 is provided and is connected tothe line 122 by a line 126 including a valve 128, between the autosampler 120 and the valve 123.
The reservoir 102 preferably includes a pair of level sensors, a full level sensor 117 and a low (primed) level sensor 118, connected to the control processor 81. These sensors can be monitored for the purpose of controlling the filling or draining of the reservoir 102, and for providing alarrns if insufficient fluid is present for analysis to begin or continue. An overflow line 138 also protects against overfilling of the reservoir 102. The overflow line leads to a waste receptacle 136. The pump 103 also can be operated to pump fluid from the reservoir 102 into the waste receptacle 136 along a waste line 139 including a valve 140. A fluid presence (empty) sensor 142 in the line 139 monitors whether any fluid remains in the system above the sensor 142.
The valves 111, 123, 128, and 140 can be manually operated, or solenoid operated by the control processor 81. The fluid circuit 100 operates during sample analysis in the manner described below in connection with FIG.35.
To operate the particle size analyzer 10, the responses of the CCD 51 and the laser 11 are characterized as explained in detail below. For each beam angle at which the analyzer is to be operated, baseline data for the analyzer 10 is obtained by collecting light intensity data with no particles 38 in the sample cell 31. The baseline data are stored for later subtraction from the scattering intensity data. For each analysis with particles present 38, a number of exposures are made at varying bearn doses to obtain scattering intensity data. The beam doses (a function of the laser drive current and exposure time) are selected so as to obtain scattering -21 877~9 __ WO 95/28630 . PCI/US95/04638 intensity data within the dynamic range of the CCD 51 for each of the angle classes 56 of interest for the given beam angle. When all exposures are made, the scattering intensity data from each exposure are norm~li7e~1 and the data from all exposures are combined to provide a composite intensity-versus-angle data set.
The intensity-versus-angle data set is then subject to a m~th~m~tical inversion process to extract the particle size distribution.

Example 1 Before describing the process of the invention in detail, it will be helpful to 10 illustrate the process with a specific example. In this example, the analyzer uses a CCD which comprises an array of 1024 rows and 1296 colurnns of pixels in a rectangular array. Each pixel is 0.016 mm square. The CCD uses an 8-bit analog-to-digital converter, so that the digital output for each pixel varies from 0 to 255.
The CCD is positioned in the focal plane of a 200 mm focal length converging lens 15 and subtends an angle of about 6 degrees when viewed from the optic center of the lens. The analyzer is aligned so that the beam strikes the CCD in the upper leftcorner. The light source of the analyzer is a laser, emitting light with a wavelength of 673.4 nm. The sample is comprised of 108 micrometer diameter polystyrene spheres dispersed in water.
FIG. 6 shows a polar diagram of the log of the intensity of the scattered light from 2 micrometer polystyrene spheres as a function of the angle of the scattered light relative to the direction of the incident beam, as computed by Mie theory. The first miniml-m in the intensity distribution occurs at about 15 degrees relative to the beam angle. FIG. 7 shows another polar diagram of the log of theintensity of the scattered light, in this instance from 10 micrometer polystyrene spheres. Relative to the distribution for 2 micrometer spheres, the intensity distribution is compressed in the forward direction, and the first minimum in the distribution occurs at about 4 degrees. From this comparison, it is apparent that the intensity distribution for the 108 micrometer spheres of this example will be even more compressed in the forward direction. Indeed, Mie theory predicts that the first minimllm will be at about 0.5 degrees, with intensity variations of over 100 to 1 between 0 and 1.0 degrees. To measure accurately the extreme intensity variations in this interval, a series of three exposures are made, with exposure times of 0.010 second, 0.164 second, and 0.655 second. The example shows the data collected from the CCD for the three exposures and how these data are normalizedand combined to the extract particle size illfollllaLion.
Each time the laser light source illl-min~tes the sample, scattered light falls on the CCD. Data from the CCD represents a measurement of the intensity distribution, or patterns of the scattered light falling on the CCD for each exposure conducted during an analysis. The process of reducing the scattered light patterns to particle size data involves two basic parts:
cing the CCD pixel data to intensity-versus-angle data, and 2. Fitting this experimental intensity-versus-angle data to a combination of theoretical intensity-versus-angle data sets from a given theory (such as Mie theory or Fraunhofer theory) for different particle sizes.
The first step is to locate the center of the beam on the CCD. This is done by locating the area of maximum intensity. FIG. 8 shows the output recorded for each of the relevant pixels in an exposure taken to determine beam center. The ",ini",~ size rectangle is identified which contains all pixels with intensity above a threshold (in this case 50). The center coordinate is determined by averaging the center coordinates of each pixel in the rectangle, weighted by the square of theintensities in those pixels. The center coordinate for each pixel is its row andcolumn numbers plus 0.5. Beam center for this example is row 130.9 and column 136.7.
Light scattered by spherical particles will be symmetric about the beam center and vary with angle from the beam. When the beam angle is zero, the cone of scattered light for each angle relative to the beam intersects the CCD plane in a circle concentric about beam center. The light striking the CCD in the annular region between two such concentric circles is the light scattered between the corresponding angles. Thus to identify the light intensity scattered in each of a series of angular intervals, the CCD irnage must be mapped into a series of concentric rings around the beam center. When the beam angle is not zero, the C(~D image must be mapped to a more general conic section.
The average intensity for each angular interval is the average intensity of the pixels in its annular ring on the CCD. For each angle the radial distance from beam center on the CCD is calculated. The equation, correcting for refraction exiting a waterf1lled cell, is:
Radial distance = F *tan(arcsin(sin(angle)* Nfluid/Nair)) where F = focal length of the field lens (200 mrn.), Nfluid and Nair are the refractive indices of water (1.33) and air (1.00), respectively. Refraction by the glass of the cell window cancels out. If the fluid suspending the sample particles is not water, the refractive index of the fluid is used.
FIG. 9 contains, for each pixel, the index of the angle class cont~ining the innermost corner of the pixel. The fraction of the pixel's area which falls in that inner angle class is calculated; the rem~inder of the pixel's area is assigned to the next angle class farther out. The angles are at intervals of 0.0025 degrees.
Using this classification of CCD pixels into angle classes, any CCD
exposure made with the same ~ nm~nt of the light source relative to the CCD can be reduced to intensity-versus-angle data. This reduction is accomplished by averaging the intensity readings for all included pixels in an angle region, weighting partially included pixels by the fraction of area included.
The next problem is to classify, for each exposure, the data from each pixel into an angle class. Each exposure may contain some pixels that are underexposedor overexposed. Therefore, each pixel is checked and the output is ignored if itfalls below minimllm or above maximum value (4 and 254 respectively in the case of an 8-bit analog-to-digital converter.) Thus, pixels with output values between the ",il~i",~.l. and the m~ximllm are used in d~ -g the average intensity for anangle class. If too many pixels in an angle class are out of range, or too few pixels fall in that class, the intensity data for that class is considered invalid and not used for further calculations.
In general, each exposure will have valid intensity data for only a subset of the full range of angle classes. Usually, angles smaller than the usable angles will be overexposed, and angles larger than the usable angles will be underexposed.
Valid intensity data for these angular ranges must be obtained by taking longer or shorter exposures, or by varying the intensity of the incident light beam.
FIGS. 10 through 18 show a series of three exposures of increasing exposure times taken of 108 micrometer diameter polystyrene spheres in water.
Three figures for each exposure are shown:
(1) the CCD image of the scattered light (for compactness, only one quadrant of the image is shown); (2) a selected representation of digital pixel output values for the image shown in the previous figure; and (3) a graph of intensity versus angle, derived by classifying the pixels into angle classes using the correspondence shown in FIG. 9.

W 095/28630 PCTnUS95104638 FIG. 10 shows the CCD image of light scattered by 108 rLucrometer diameter polystyrene spheres in water, with an exposure time of 0.010 second.
Exposures of short duration such as this will saturate the pixels of the CCD in a small area around beam center and provide measurable outputs as the radial S rli~t~nres from beam center to the pixels increase. The CCD pixel output values for the 0.010 second exposure is given by FIG. 11. The number of the pixel row is given in the left-most column of FIG. 11 and the number of the pixel column is given in the top row. This figure is for the pixel area around the beam center at row 130.9 and column 136.7. The pixels close to beam center exhibit the saturation value of 255, but the pixels in colurnns 141 and higher begin to show measurableintensity less than 255. The intensity of the peak of the second ring (not visible in FIG. 10.) is just above an underexposure cutoff threshold value of 4 counts and is beyond the set of rows and columns shown in FIG. 11 FIG. 12 shows a graph of intensity versus angle for the 0.010 second exposure. Classes inside of approximately 0.11 degrees are overexposed (pixel output values of 255) and excluded, and classes outside Qf approximately 0.55 degrees are underexposed (pixel values of 4 or less) and excluded. The valley between 0.34 degrees and 0.42 degrees is also underexposed and will need a longer exposure to adequately characterize it. The peak of the second scattering ring at about 0.5 degrees is just over the underexposure cutoff..
FIG. 13 shows the CCD image of light scattered by 108 micrometer diameter polystyrene spheres in water, with an exposure time of 0.164 second.
For the 0.164 second exposure, a portion of the pixel output values are given byF~G. 14. This figure is for the pixel area corresponding to a scattering angle of approximately 0.3 degrees. In this area, as shown in FIG. 15, the intensity is dropping from the saturation value of 255 counts to approximately 50 counts.
FIG. 15 shows a graph of intensity versus angle for the 0.164 second exposure.
The dramatic drop in intensity just beyond 0.3 degrees is evident. The valley between 0.34 degrees and 0.42 degrees, mi~ing from the previous exposure, is 30 now adequately characterized. The second, third, and fourth scattering rings (peaks in the intensity versus angle graph) are all on scale in this exposure. Classes inside of approximately 0.3 degrees are overexposed and excluded, and classes outside of approximately 1.5 degrees are underexposed and excluded.
FIG. 16 shows the CCD image of light scattered by 108 micrometer 35 diameter polystyrene spheres in water with an exposure time of 0.655 second. For _ WO 95/28630 PCI/US95/04638 the 0.655 second exposure, a portion of the pixel output values is given by FIG.17. FIG. 18 shows a graph of intensity versus angle for the 0.655 second exposure. The valley between the first and second rings is on scale, but everything below this and the peak of the second ring is overexposed and excluded. The third through the seventh rings between 0.6 degrees and 2 degrees are on scale.
The next step is to combine the intensity-versus-angle data from multiple exposures into a composite, more complete data set. Intensity values for different exposures must be scaled to account for the differences in exposure time and incident beam intensity. This is done either using predetermined scaling values based on knowledge of exposure time and beam intensity, or by determining an average scaling factor between pairs of exposures to match intensity values for overlapping portions of the valid data range. The latter is done by identifying all classes for which both exposures have valid intensity data, then computing the average ratio between intensities from the two exposures for the corresponding classes. The average is weighted by the product of the number of pixels includedin a class for each of the two exposures.
The composite data set is then produced by multiplying the intensity data for each exposure by that exposure's scaling factor, and averaging all the valid intensity data for an angle class from the different exposures. The average is weighted by the number of pixels contributing from each exposure. FIG. 19 shows the resulting composite data set from the exposures shown in FIG. 10 through 18.
A baseline intensity-versus-angle data set (not shown), derived from exposures taken with no sample particles in the system, is scaled and subtractedfrom the sample intensity-versus-angle data. This step elimin~tes intensity data due to the lln.cc~ttered portion of the light beam and other stray light in the system.
Finally, the particle size distribution is determined from the composite intensity-versus-angle data. FIG. 20 shows two sets of data. The intensity-versus-angle points from the composite data set are shown as circles; also shown is the curve representing the non-negative least-squares ("NNLS") fit to this data using a series of theoretical Mie curves for different size spheres.
FIG. 21 shows the particle size distribution obtained by the analyzer for 108 micrometer polystyrene spheres in water. The position of the single peak indicates particles having a size of 108 micrometers.

~ wo gs/28630 Pcrlus9S/04638 ;~9 Example 2 An analysis similar to that described for Example 1 was run for a mi~lul~ of polypropylene powder in water. FIG. 22 shows the intensity-versus-angle data and FIG. 23 shows the particle size distribution obtained by the analyzer for this mixture. The position of the two peaks indicates the presence and relative proportions of the two particle sizes of 300 micrometers and 600 micrometers.

Detailed Description of Operation The sequence of operation described in the above examples is carried out under the control of computer programs residing in the control processor 81, thedigital signal processor 71, and the work station 91. In general, the control processor controls all of the mechanical aspects of the analyzer, such as the rotation of the beam assembly 21 and the operation of the fluid circuit 100, and controls the operation of the laser 11 and CCD 51 and the flow of data through the analyzer.
The digital signal processor 71 processes all of the data from the CCD 51 to produce intensity-versus-angle data sets. The work station 91 processes the intensity-versus-angle data sets to produce volume fraction versus size data sets (particle size distributions). The operation of the routines which comprise these computer programs is described below.
Certain conventions are used in the description below of the steps carried out during the operation of the routines. Names of procedures implemented by subroutines are indicated by ALL CAPS. Names of program constants or variables that are referred to frequently are defined once and indicated by Initial Caps.
Frequently the constant and variable names are RunTogether. Where values are given for program constants, it is assumed the CCD uses a 12-bit analog-to-digital converter.
Certain common geometric and optical functions will be used throughout the remainder of this specification. These functions represent simple transformations involving Snell's Law for the refraction of light and the relation between an angle and the distance subtended by the angle in the focal plane of the lens. These functions and their definitions are as follows:

FluidFromAir(angle) = arcsin(sin(angle) * Nair / Nfluid) AirFromFluid~angle) = arcsin(sin(angle) * Nfluid / Nair) DistanceFromAngle(angle,FocalLength) = tan(angle) * FocalLength 4o AngleFromDistance(tlict~nre FocalLength) = arctan(-lict~nre / FocalLength) where:

Nair = refractive index of air = 1.00 Nfluid = refractive index of suspending fluid (1.33 for water) 1. CCD and Laser Char~rteri7~tion A characterization of the CCD and of the laser used in the analyzer provides a way to correct for vagaries in the control or response characteristics of these two components of the analyzer. CCD characterization is performed upon in.ct~ tion of a CCD in an instrument. It defines the response of the particular CCD to differing intensities of light at the wavelength provided by the laser, and to differing integration times. CCD characterization provides the means to interpret CCD dataas a linear function of the Total Light Dose delivered during an exposure.
Laser characterization is performed upon installation of a laser or any laser subsystem optical or electronic component, or any change to the operating temperature of the laser. It requires that a valid CCD characterization has previously been completed.
Routine CCD CHARACTERIZATION is shown in FIGS. 25A-25D. The first step in the routine, shown in blocks 1-10 of FIG. 25A, is to identify bad pixels. Bad pixels are pixels that have a dark current accumulation rate higher than a predetermined limit, or that do not respond linearly to light with sensitivity within a predetermined limit of the average sensitivity of other pixels. Bad pixels areidentified during the course of deter~nin~tion of dark current rates and the response and offset of each pixel as described below. Bad pixels are marked in an array in the processor storage referred to as the Bad Pixel Map and are excluded from use in all further analysis.
The analyzer performs its own independent dark current analysis in a subroutine DETERMINE DARK CURRENT RATES (blocks 1-4 of FIG. 25A).
Thus, if the CCD in use has columns of dark current pixels, such as columns 1280to 1295 on the Kodak KAF-1300L, those columns are excluded from use in all operations. To determine the dark current values, the CCD is caused to integrateover each of a set of predetermined Exposure Times (0.1 to 10 seconds) without turning on the laser. As shown in blocks 1-4 of FIG. 25A, for each exposure, the ~ WO gsn8630 PCI/US95104638 intensity value for each pixel is divided by the Exposure Time to give the norrn~li7e(1 intensity for this pixel. As shown in blocks 5-10, when all exposures are complete, the normalized intensity values for all of the exposures are averaged for each pixel and the standard deviation is computed. If the average is greater than S the predetermint~l maximum dark current rate (preferably, about 100 counts/second for a 12-bit analog-to-digital converter), the pixel is marked as bad in the Bad Pixel Map. If the standard deviation is greater than the predetermined maximum dark current standard deviation (preferably, about 5 counts/second), the pixel is marked as bad in the Bad Pixel Map. Otherwise, the average is saved in array Dark[i,j] as 10 the dark current rate for this pixel, where i is the row of the pixel and j is the column of the pixel.
The next step in CCD characterization is to determine the CCD response and offset. The CCD response is determined by measuring the response of each pixel to a uniform light intensity for varying amounts of time, correcting for dark current, 15 and computing the pixel sensitivity to light. For the purpose of reducing requirements for co~ uler memory and compuLation time, square patches of pixels called N x N pixel areas may be averaged and characteriæd together.
Determining CCD response and offset is shown in blocks 11-32 of FIGS.
25B and 25C. The sample cell 31 is replaced with a uniform diffuser (not shown).20 The diffuser can be constructed from foam core poster board, covered with an opaque black mask with a 15 mm to 30 mm diameter circular aperture. It scatters all the incident light from the laser so that the light exiting the diffuser is of approximately equal intensity (within 0.1 %) at all angles captured by the field lens and focused on the CCD. This causes all pixels on the CCD receive approximately 25 equal light i~ iLies.
The subroutine CHECK LASER TEMPERATURE CONTROL is executed at block 11. This ~L~rou~ e is described below. The laser is rotated to the nominal Beam Center Location Angle. The nominal Beam Center Location Angle is chosen so that, in the absence of the diffuser, (l) the unscattered beam 32 will strike the 30 CCD, (2) the primary reflected light from the CCD is directed away from the field lens and into a light trap (not shown), and (3) light scattered at angles from 0degrees to at least 4.7 degrees will fall on the CCD. The nominal Beam Center Location Angle is preferably a negative angle of 4.6 degrees with respect to theoptic axis. The laser is set to the maximum analysis Laser Drive Current. The 35 CCD is exposed to the laser for a predetermined series of Exposures Times. The ~ _ W O 95/28630 PC~rrUS9S/04638 Exposure Times are chosen such that the range of usable pixel intensity values is adequately covered. For each exposure, the Total Light Dose ~lmini.ctered and the Exposure Time are recorded. For each pixel not marked as bad, if the pixel intensity value is below the predeterrnined miniml-m raw pixel value (4 to 16 for a 12-bit analog-to-digital converter) or above the m~illlulll raw pixel value (4094 for a 12-bit analog-to-digital converter), this reading is invalid and excluded from use in subsequent average calculations. Whether invalidated or not, the dark currentrate for this pixel multiplied by the Exposure Time, is subtracted from the intensity reading and the difference is kept as the corrected intensity for this pixel.
The average corrected intensity is computed for all pixels with valid corrected intensities for this exposure, and the result is kept as the CCD average intensity for this exposure.
As shown in blocks 20-23, another loop is executed through all of the pixels. For each pixel not marked as bad, if the corrected intensity value (whether valid or invalid) is different from the CCD average intensity by more than the predetermined maximum response variation factor ("MRVF", 0.1 to 0.5) and by more than the predetermined maximum response variation counts ("MRVC", 1 to 5 counts), the pixel is marked as bad in the Bad Pixel Map.
As shown in blocks 24-28, for each N x N pixel area, where N (l to 4 pixels) is the predetermined CCD response pixel area size, the average correctedintensity is computed for all pixels in the area with valid corrected intensities, and is kept as the area average intensity for this pixel area and for this exposure.
As shown in blocks 29-32, when all exposures are complete, for each pixel area, the slope and intercept of a line are computed from a least squares fit to the data for area average intensity versus Total Light Dose. For each pixel in the pixel area, the slope and intercept of the line is kept as the Response[i,j] and Offset[i,j], respectively, of the CCD for the pixel at row i and colurnn j.
This completes determination of the CCD response and offset. At this point the laser is located at the nominal Beam Center Location Angle. The next step is to deterrnine the actual Beam Center Location Angle, as shown in blocks 33-40 of FIG. 25D.
To deterrnine the Beam Center Location Angle, the sample cell or diffuser, if either is present, is removed. The subroutine CHECK LASER TEMPERATURE
CONTROL is executed. Optic Axis (as distinguished by initial caps from "optic axis") is the point where the optic axis of the field lens 41 intersects the CCD. The ;~ WO 95128630 PCT/US95/04638 Optic Axis is nominally at the same location as the focal point of the field lens 41, although for any location subtending less than 4 degrees at the optic center of the field lens 41, 90% of the pixels will be correctly assigned for every angle class.
The subroutine LOCATE OPTIC AXIS is executed. The coordinates of Beam S Center (Bx,By) are detf~mined from the coordinates of the Optic Axis (Ox,Oy) and the current Beam Center Location Angle as follows:

Bx = Ox - DistanceFromAngle(BeamCenterLocationAngle,FocalLength) /
PixelWidth By=Oy The Bad Pixel Map is checked for any bad pixels too close to Beam Center by scanning the rectangle of pixels within minimum bad pixel to beam center distance rows and columns of Beam Center. The minimum bad pixel to beam 15 center distance is a predefined program constant, typically 32 pixels. If any bad pixels are found, the steps shown in blocks 35-37 are repeated with other possible Bearn Center Location Angles, starting at the nominal Beam Center Location Angleand alternately checking smaller and larger angles varying by the minim-lm settable beam angle increment (a program constant, preferably 0.01 degrees), until a Beam20 Center Location Angle is found with no bad pixels within the minimum bad pixel to beam center distance of Beam Center. If no such angle is found between the minimum Beam Center Location Angle and the maximum Bearn Center Location Angle, an error condition, "Unable to Locate Valid Beam Center Location Angle,"
is reported. Both the minimum Beam Center Location Angle and the maximum 25 Beam Center Location Angle, program constants, are chosen so that the three conditions specified above for the norninal Beam Center Location Angle are met.
Subroutine CHECK LASER TEMPERATURE CONTROL (not shown) is called above, and is executed at any time that the laser is to be used. This subroutine checks the laser temperature sensor 13. The sensor is on if the laser30 temperature is within an acceptable range, preferably within 0.1 degrees, of the predetermined laser operating temperature (between 50 and 70 degrees Fahrenheit for the Toshiba model TOLD 9140). If the sensor is off, a laser temperature error is indicated. Checking continues until the sensor is on, then processing returns to the calling routine.

~_ W095128630 4 ¢ PCT/~S95/04638 This completes the process to detPrmine Beam Center Location Angle and routine CCD CHARACTERIZATION. The next step is to execute the routine LASER CHARACTERIZATION.
Routine LASER CHARACTERIZATION is shown in FIG. 26. This routine characterizes laser output versus drive current and time. The sample cell and/or diffuser are removed from the system, and a beam expander lens (not shown) is inserted at the location of the sample cell. The beam expander lens is an additional lens, which causes a slight defocusing of the collim~tPd beam at the CCD, so that its diameter is approximately 50% of the width of the CCD (or approximately 8 mm.). This allows a more accurate quantification of the total beam intensity using the CCD. Subroutine CHECK LASER TEMPERATURE
CONTROL is executed, followed by the subroutine LOCATE OPTIC AXIS (FIG.
3.1) using the laser characterization angle (about negative 2.3 degrees) as the Beam Center Location Angle. Starting with the minimnm settable laser drive current (aprogram con.ct~nt, about 0.1 milli:~mp) and increasing by the minimllm settable laser drive current increment (a program constant, preferably about 0.1 milli~mp), thelaser intensity is ~letçrminP~l as a function of Exposure Time for a given Laser Drive Current as follows:
As shown by blocks 4-15 of FIG. 26 for each Exposure Time from the minimum Exposure Time (a program constant, about 1 microsecond) to the maximum Exposure Time (a program constant, about 10 seconds), take an exposure, call subroutine VALIDATE AND CORRECT PIXEL DATA (FIG. 2.1), and sum the pixel values in the rectangle centered on Beam Center and including all pixels within the laser output quantification distance of Beam Center (a programconstant, about 256 to 384 pixels). Save this sum as the Total Light Dose for the specified Laser Drive Current and Exposure Time. Discard data points having no pixel values above the minimum laser output pixel value (a program constant, 4 to 16 counts), and data points having any pixel values above the maximum laser output pixel value (a program constant, about 4094 counts). Terminate data collection for a Laser Drive Current when an exposure is taken having a pixel value in the rectangle which exceeds the maximum laser output pixel value.
When a Laser Drive Current is reached for which the minimum number of laser output points (a program constant, 3 to 5 points) cannot be taken due to exceeding the maximum laser output pixel value, insert the filter section 204 into the optical path. A filter correction scaling factor may be computed by repeating WO 95/28630 PCI`IUS9S/04638 data collection for an earlier Laser Drive Current having enough valid data points and calcul~tin~ the least squares fit of Total Light Dose versus Exposure Time for each of the two data sets for this Laser Drive Current and taking the ratio of the two slopes. Other methods of determining a filter correction scaling factor will be a~a Gnt to those skilled in the art. Scale all data taken with this filter by its filter correction. Continue as before with successively higher Laser Drive Currents until the maximum Laser Drive Current is reached. If necessary, substitute additional sl-ccessively optically denser filters (not shown) as above and obtain and use the filter correction for each to scale data. This completes the deterrnination of Laser Intensity as a function of Exposure Time and Laser Drive Current.
The Total Light Dose values associated with each Laser Drive Current and Exposure Time may be kept individually in a table for use in scaling data taken at the same current and time. Alternatively, the data may be fit to a function or to a series of functions and those functions may be used to compute Total Light Dose for any Laser Drive Current and Exposure TiIne. This completes routine LASER
CHARACTERIZATION .

2. Process Raw Pixel Data Raw pixel data is received by the digital signal processor 71 from the CCD
at completion of any exposure. Several subroutines, described below, are used toprocess raw pixel data at various points in the process. In the following, "pixel[i,j]" refers to the pixel at row i, column j of the CCD, and "Pixel[i,j]" refers to the numerical data received from pixel[i,j].
The subroutine VALIDATE AND CORRECT PIXEL DATA is shown in FIG. 27. For the raw data Pixel[i,j], if pixel[i,j] is marked on the Bad Pixel Map, the pixel data is invalidated. If-the value of Pixel[i,j] is above the predetermined m~ximllm raw pixel value (about 4094 counts), the pixel data is invalidated and proce~ing continues with the next pixel. If the value of Pixel[i,j] is below thepredeterrnined miniml]m raw pixel value (4 to 16 counts), the pixel data is invalidated and, as shown in block 11, processing continues with the next pixel. If pixel[i,j] is adjacent to a pixel whose raw data value is greater than the maximum raw pixel value, the pixel data Pixel[i,j] is invalidated and processing continues with the next pixel. The 8 nearest neighbors of pixel[i,j] are considered adjacent.
If the pixel is not bad, the dark current is subtracted as shown in block 7 for this pixel based on exposure time and the CCD Offset:

_ WO 95/28630 4 6 PCT/US95/04638 Pixel[i,j] = Pixel[i,j] - Dark[i,j] x ExposureTime - Offset[i,j].
Proces~ing continues with the next pixel. Completion of all the pixels completesthe ~ubl~u ille VALIDATE AND CORRECT PIXEL DATA.
The subroutine SCALE PIXEL DATA BY TOTAL LIGHT DOSE (not S shown) norrn~li7es the pixel data to account for differences in laser drive currents and exposure times. For each pixel with valid data, each pixel value is divided by the Total Light Dose for this exposure as determined in block 6 of FIG. 26 and proce~ing returns to the calling routine.
The subroutine ADD PIXEL DATA TO AGGREGATE PIXEL DATA (not shown) combines pixel data from different exposures and keeps track of the number of exposures. For each pixel[i,j] with valid data, Pixel[i,j] is added toAggregatePixelData[i,j] an array to sum Pixel [i,j] values for multiple exposures.
AggregatePixelExposureCount[i,j] an array to record a count of the number of exposures, is incremented by 1 and processing returns to the calling routine.
The subroutine CORRECT AGGREGATE PIXEL DATA (not shown) adjusts the pixel data to conform to the linear form determined during CCD
Characterization. For each AggregatePixelData[i,j], the following computation ismade CorrectedAggregatePixelData[i,j] = AggregatePixelData[i,j] / Response[i,j]

and proce~ing returns to the calling routine.

3. Measure Beam Intensity and Alignment Several routines are provided to measure the intensity of the light source beam and to calibrate its alignment relative to the optic axis of the lens. As shown in FIG. 28, to calibrate the location of the optic axis, suspending fluid is circulated through the cell, with no sample present. Subroutine LOCATE OPTIC AXIS is executed. As shown in blocks 3 and 4 of FIG. 28, if the newly computed Optic Axis differs from the currently saved small angle Optic Axis by more than the predetermined small angle Optic Axis threshold (0.1 to 1 pixel), subroutine CLASSIFY PIXELS TO ANGLE CLASSES is executed for the Beam Center Location Angle. As shown in blocks 5-7, if the newly computed Optic Axis differsfrom the currently saved large angle Optic Axis by more than the predetermined large angle Optic Axis threshold (0.5 to 5 pi~els), subroutine CLASSIFY PIXELS

21 8778q '_ WO 95/28630 PCT/US95/04638 TO ANGLE is executed for all other analysis Beam Angles, and subroutine CALCULATE PROJECTION CORRECTION (described below) is called. To measure the intensity of the light source beam, subroutine MEASURE BEAM
INTENSITY (described below) is called.
S Subroutine LOCATE OPTIC AXIS is shown in F~G. 29A and 29B. The steps of this subroutine are as follows: Rotate the laser to the Beam Center Location Angle. As shown in blocks 2-4 of FIG. 29A, take an exposure at the lastrecorded beam center Laser Drive Current and beam center Exposure Time. For a new system, these are the default beam center Laser Drive Current (preferably, 4 to 7 milli~mps), and the default beam center Exposure Time (preferably, about 10 microseconds). Call subroutine VALIDATE AND CORRECT PIXEL DATA. Call subroutine CALCULATE OPTIC AXIS COORDINATES (FIG. 30). Retain the pixel data from the beam center rectangle located in this process.
As shown in blocks 7 and 8, if no beam center rectangle is found or if no pixel value in the beam center rectangle is greater than or equal to the predetermined minimllm beam center value (1000 to 2000 for a 12 bit A/D converter), change to the next higher analysis Exposure Time and repeat from block 4. If the next higher analysis Exposure Time is above the maximum beam center Exposure Time (preferably, about 100 microseconds), use the next higher analysis Laser Drive Current and the default beam center Exposure Time. If the highest analysis LaserDrive Current was already in use, indicate a "Beam Detection Underrange Error"
and end the procedure.
As shown in blocks 12-14 of FIGS. 29A and 29B, if any pixel in the beam center rectangle has a data value above the predetermined maximum beam center value (3000 to 4094 for 12 bit A/D converter), change to the next lower analysisExposure Time and repeat from block 4. If the lowest analysis Exposure Time was already in use, use the next lower analysis Laser Drive Current and the default beam center Exposure Time. If the lowest analysis Laser Drive Current was already in use, indicate a "Beam Detection Overrange Error" and end the procedure.
Continue until the maximum pixel value in the beam center rectangle is between the minimum Beam Center value and the maximum Beam Center value If the new Optic Axis x coordinate (NewOx) differs from the previous value (OldOx) by more than the maximum Optic Axis x deviation (a program constant, 1 to 3 pixels), compute the corresponding angular displacement ~_"WO 95/28630 PCI/US95/04638

4~

A = AngleFromDistance((NewOx - OldOx) x PixelWidth, FocalLength), correct the Beam Angle by adding A to the current rotation position, and repeat the subroutine from the beginning Otherwise, record the current Laser Drive Current and Exposure Time as the beam center Laser Drive Current and the beam center Exposure Time. This completes subroutine LOCATE OPTIC AXIS; processing returns to the calling routine.
Subroutine CALCULATE OPTIC AXIS COORDINATES is shown in FIG. 30. The steps of this routine are as follows: Scan the rows and columns of pixels, and determine the bollnd~n~s of the minimllm rectangle containing all pixels with values above the Beam Center threshold (preferably, 500 to 1000 counts).
Compute the weighted average of the coordinates of the pixels in the rectangle, where the coordinates of the pixel at row i, colurnn j are (i + 0.5, j + 0.5), and the weighting factor for each pixel is the square of the pixel intensity value. The weighted average column or y coordinate is the y coordinate of Optic Axis, Oy.
The weighted average row or x coordinate is corrected for the Beam Center Location Angle and pixel width to produce the x coordinate of Optic Axis, Ox:

Ox = AverageRow + DistanceFromAngle(BeamCenterLocationAngle, Foc~lT P.~h) / PixelWidth This completes subroutine CALCULATE OPTIC AXIS; processing returns to the calling routine.
Subroutine CLASSIFY PIXELS TO ANGLE FOR A BEAM ANGLE is shown in FIG. 31. Scattering angle classes are intervals between fixed scattering angles. All light scattered at angles within one angle interval is treated as light scattered at the corresponding angle class. This is a means of treating the continuous phenomenon of sc~ttçr~ng intensity versus angle as a discrete problemof scattering intensity-versus-angle class. Angle classes may cover variable intervals, such as varying in width from 0.0025 degrees for very small angles (less than 0.1 degrees), increasing in width for larger angles up to a width of 0.1 degrees for the largest angles (greater than 3.2 degrees). One example of angle classes is given by the following table:

Table Of An~le Classes 2 1 877~9 Angular Resolution Angle Range Number of Angles (degrees) (degrees) 0.0025 0.0 - 0.1 40 0.005 0.1 - 0.2 20 0.01 0.2 - 0.4 20 0.02 0.4 - 0.8 20 0.04 0.8- 1.6 20 0.08 1.6 - 3.2 20 0.1 3.2 - 180 10/degree Each pixel of the CCD is assigned to a scattering angle class based on the angle at which the incident light beam must be scattered in the cell to strike the pixel. Thus, a re-assignment of the pixel must be done for any change in the geometric configuration of the lens or the CCD and at any time the Beam Angle changes. To achieve higher resolution at small angles, fractions of pixel area are assigned to different angle classes when an angle class boundary falls across the pixel. The scattering angle classes are arranged in an array according to increasing angle. Pixels in an angle class are contiguous in the sense that nearest neighbors of a pixel are in the same angle class until a class boundary 54 is reached.
A.~.signment of a pixel to an angle class is signified by the corresponding index into the single--limen.sional angle class arrays; this index is stored in a two-dimensional pixel-to-angle-class array InClass.
For a given Beam Angle, InClass[i,j] will contain the index of the smallest scattering angle class to which any portion of pixel[i,j]'s area is assigned. The pixel-fraction-in-class array InFrac[i,j] will contain the fraction of the total area of pixel[i,j] which is assigned to that angle class. The remainder of pixel[i,j]'s area is assigned to the next larger scatteripg angle class. NormClass[m] is an array associated with the scattering angle classes used to count the number of pixels included in each class In the following, the row and column coordina~es i and j are taken to be the coordinates of the lower left corner of pixel[i,j] as seen facing the CCD from the direction of the field lens and sample cell. The arrays InClass, InFrac, and NorrnClass are set to zero. As shown in blocks 1 and 2 of FIG. 31, for each pixel[i,j] not marked bad in the Bad Pixel Map, subroutine CALCULATE
SCA'l'l'~RING ANGLE (FIG. 32, described below) is called for the pixel's center coordinates, (i + 0.5, j + 0.5). If the scattering angle is greater that the predetermined fractional pixel angle threshold (preferably, 0.2 to 0.8 degrees), the class-indication index m is set to the index of the smallest angle class whose upper limit is greater than or equal to the scattering angle.

l . Set InClass[i,j] = m.
2 . Set InFrac[i,j] = 1.
3 . Add 1 to NormClass[m].

As shown in blocks 3, 5, and 6, if the scattering angle is less than or equal to the fractional pixel angle threshold, subroutine CALCULATE SCATTERING
ANGLE is called for the center coordinates of each of the pixel's quadrants, (i + 0.25, j + 0.25), (i + 0.25, j + 0.75), (i + 0.75, j + 0.25), and (i + 0.75, j + 0 75). Index m is set to the index of the smallest angle class whose upper limit is greater than or equal to the minimllm of the four scattering angles:

l . Set InClass[i,j] = m.
20 2. Fo~r each of the four quadrant scattcring angles, if the scattering angle is smaller than the upper limit for class m, add 0.25 to InFrac[i,j].
3. Add InFrac[i,j] to NormClass[m].
4. Add 1 - InFrac[i,j] to NormClass[m+1].

As shown in blocks 9-12, when a~ignment of pixels is completed, pixel ~c~ignm~nts are removed if they are to classes that contain only a small number of pixels near the edge of the CCD (not including the small angle classes near BeamCenter at the Beam Center Location Angle). These classes will have better data at the next larger Beam Angle. The array NormClass is inspected to determine the angle class mMax containing the maximum number of pixels assigned to any class.
For each angle class m (if the given Beam Angle is the Beam Center Location Angle, only classes with index m greater than mMax are tested), if NormClass[m] < (NormClass[mMax] * MinimllmRelativeClassSize) --` WO 95/28630 PCI/US95/04638

5 l then each pixel[i,j] ~csigne~l to class m is deassigned so that it is assigned to no class:

InClass[i,j] = <INVALID>
S NorrnClass[m] = 0.

The value for the minimllm relative class size is a program constant, preferablybetween 0.2 and 0.5. This completes subroutine CLASSIFICATION OF PIXELS
TO ANGLES for a Beam Angle; processing returns to the calling routine.
Subroutine CALCULATE PROJECTION CORRECTION (not shown) corrects for the reduction in intensity at each pixel of the CCD where the pixel is not located at a dict~n(~e from the optic center of the lens equal to the focal length of the lens or is not in an area perpendicular to the line connecting the pixel with the optic center of the lens. For the former correction, for each pixel, the correction iscalculated for projection of intensity from a sphere of radius FocalLength to the focal plane:

Ox = x or row coordinate of Optic Axis Oy = y or column coordinate of Optic Axis PixelWidth = pixel width in mm PixelHeight = pixel height in rnm R = distance from center of pixel to Optic Axis in mm =
(((i + 0.5 - Ox) x PixelWidth)^ 2 + ((j + 0.5 - Oy) x PixelHeight)^ 2 ) ^ lt2 A = angle of a vector from lens center to the pixel, relative to the Optic Axis = AngleFromDistance(R / Foc~lT ength,FocaLength) B = correction for difference in area from rectangle tangent to sphere at angle A to rectangle parallel to focal plane = 1 / cos(A) C = correction for decrease in intensity with distance from source = (FocalLength / (FocalLength x cos(A))) A 2 = 1 / cos(A) ^ 2 21 8778q `-- W095/28630 5 2 PCT/US95/04638 P = total correction for projection = B x C = l / cos(A) ^ 3 The value P is saved in the two-dimensional array Projection[i,j] for pixel at row i, column j. This completes subroutine CALCULATE PROJECTION
5 CORRECTION; procec~ing returns to the calling routine.
Subroutine CALCULATE SCAl-rERING ANGLE is shown in FIG. 32.
In this subroutine, coordinates x, y, and z represent the following:

1. x = horizontal axis in the focal plane of the field lens (parallel to rows on the CCD) 2. y = vertical axis in the focal plane of the field lens (parallel to columns on the CCD) 3. z = optic axis (normal to the focal plane or CCD, and usually to the cell windows) This coordinate system, some of the intermediate values computed by this subroutine, and the scattering angle aScat computed by this subroutine are shown in FIGS. 24A, 24B, and 24C. When the field lens 41 is used in the analyzer 10, the coordinate system is a virtual system based on the spatial Fourier transform provided by the field lens 41.
As shown in FIG. 24A and in block 1 of FIG. 32, given row and column coordinates for a point on the CCD (i.e., in the focal plane of the field lens), the distance from that point to the Optic Axis is computed in millimeters:

1. xAir = (row - Ox) * PixelWidth 2. yAir = (column - Oy) * PixelHeight 3. rAir = ( xAir A 2 ~ yAir ^ 2 ) ^ 1/2 The angle from the normal to the focal plane (and, generally, to the cell window) is calculated. This is the angle of scattered light, after exiting the cell, that would strike the given point on the CCD:

aAir = AngleFromDistance(rAir,FocalLength) Once the angle aAir is computed, the coordinate system in air of FIG. 24A can bedropped in favor of an analogous coordinate system in fluid as shown in FIGS.

- 21 8778q ~ WO 95/28630 PCT/US95/04638 24B and 24C. To move to the coordinate system in fluid, a correction is made forthe angle for refraction at the cell.window to get the angle in the cell:

aFluid = FluidFromAir(aAir) As shown in FIG. 24C and in block 4 of FIG. 32, a computation is made of the length of a vector at this angle projected a unit distance in the z direction onto a plane normal to the optic axis:

rFluid = DistanceFromAngle(aFluid,l) The x and y components of the vector are colllpuled:

xFluid = xAir * rFluid / rAir yFluid = yAir * rFluid / rAir As shown in FIG. 24B and in block S of FIG. 32, a computation is made of the length of a vector at the Beam Angle (corrected for refraction entering the cell) projected a unit ~ t~nre onto a plane normal to the optic axis:0 rBeam = DistanceFromAngle(FluidFromAir(Bea~lnAngle), 1 ) Since the Beam Angle lies in the xz plane, the x component is equal to the vector, and the y component is æro:5 xBeam = rBeam yBeam = 0 As shown in block 5 of FIG. 32, the beam vector components are added to the 30 pixel angle components to get the sc~tte~.-ing angle components:

xScat - xBeam + xFluid yScat = yBeam + yFluid _,. WO 95/28630 PCT/US95/04638 As shown in FIG. 24C, the x and y components are combined to get the length of avector at the scattering angle projected a unit distance onto a plane normal to the OptlC axls:

rScat = ( xScat ^ 2 + yScat ^ 2 ) ^ 1/2 Finally, the sc~ orin~ angle is computed:

aScat = AngleFromDistance(rScat,1) This completes subroutine CALCULATE SCATTERING ANGLE; processing returns to the calling routine.
It will be appreciated by those skilled in the art that modifications to the above method of calculating the scattering angle may be implemented, without 15 departing from the spirit of the invention. For example, for scattering angles not near 90 degrees, the distance a pixel 55 lies rel~tive to the center of the beam 22 in the plane of the pixel array may be used directly to calculate the scattering angle.
- For sc~ttering angles near 90 degrees, it may be mathematically more precise to calculate the sc~ ring angle with reference to a projection of the vector at the Beam 20 Angle in a direction other than the direction of the optic axis, since in this situation the beam 22 is roughly perpendicular to the optic axis (parallel to the plane of the pixel array). This alternative is preferred for Beam Angles near 90 degrees, because, at these angles, projections of the vector at the Beam Angle will extend large distances and will not intersect the plane of the pixel array at a calculable 25 distance from any given pixel.

Subroutine MEASURE BEAM INTENSITY (not shown) has the following steps: Take an exposure at the last recorded beam center Laser Drive Current andbeam center Exposure Time, and call subroutine VALIDATE AND CORRECT
30 PIXEL DATA. Call subroutine SCALE P~EL DATA by Total Light Dose. Sum the scaled pixel data for all pixels within the beam intensity rectangle size rectangle of pixels centered at Beam Center. This is the measured beam intensity. This completes subroutine MEASURE BEAM INTENSITY; processing returns to the calling routine.

4. Sample or Baseline Analysis Actual analysis involves the foregoing routines as well as three additional subroutines described as follows:
Subroutine CALCULATE BEAM TRANSMITTANCE FACTOR (not shown) c~lc-~ tes the tli.n~ csion coeffcient for the beam through the sample cell, using Beer's Law. PathLength is the length of the path of the incident beam through the cell at the current Beam Angle, relative to the path length when thebeam is perpendicular to the cell windows. The variable alphaC is the exponent coefficient of path length for calculating beam transmittance by Beer's Law.
Uncorrected Beam Tr~ncmitt~nce is the measured beam intensity divided by the baseline beam intensity.

p~thl P.ngth = 1 / cos(FluidFromAir(IncidentBeamAngle));
alphaC = log(UncorrectedBeamTransmittance) / p~thT ~.ngth;
BeamTr~n.cmitt~nceFactor = exp(alphaC).

This completes subroutine CALCULATE BEAM TRANSMl'l'l'ANCE FACTOR;
proceccing returns to the calling routine.

Subroutine MAP PIXEL DATA TO ANGLE CLASSES is shown in FIGS. 33A and 33B. The steps of this subroutine are as follows: Initialize the intensity-versus-angle-class data array, Intensity[m], to zero for the current incident Beam Angle. Initialize the PixelCountPerClass data array to zero. For each pixel[i,j] on the CCD, if the Aggregate Pixel Exposure Count is zero, skip to the next pixel. Otherwise, the average intensity is calculated for the readings in the CorrectedAggregatePixelData for this pixel, corrected for projection:

AveragePi~el~nten.city[i,j] = Projection[i,j] x CorrectedAggregatePixelData[i,j] / AggregatePixelExposureCount[i,j]
Let m be the angle class specified for pixel[i,j] by the pixel-to-angle class map InClass[i,j]. The following computations are made for the current incident Beam Angle:

35 1. Add AveragePixelIntensity[i,j] x InFrac[i,j] to Intensity[m].

21 8778q _,~ WO 95128630 PCI`/US95/04638 2. Add PixelFractionInClass[i,j] to PixelCountPerClass[m].
3. Add AveragePixelTnten~ity[i,;] x (1 - InFrac[i,j]) to Intensity[m+1].
4. Add (1 - InFrac[i,j]) to PixelCountPerClass[m+l].

5 Proces~ing continues with the next pixel.

As shown in blocks ll-lS of FIG. 33B, when all the pixels have been processed, compute the average intensity for each angle class m. Note that different values for ~inimllm Pixel Count Per Class may be used for small angles10 and large angles, to allow lower counts for small angles than for large angles. If PixelCountPerClass[m] is less than the predeterrnined minimllm pixel count per class, discard the data for class m. Otherwise, set Intensity[m] = Intensity[m] /
PixelCountPerClass[m]. If PixelCountPerClass is to be used as a weighting factorin further computation, it must be preserved in addition to the intensity data.
lS This completes the mapping of pixel data to angle classes for the current Beam Angle; processing returns to the calling rcutine.
The COLLECT DATA subroutine is shown in FIG. 34. A
predetermined schedule of analysis Beam Angles, analysis Laser Drive Currents, and analysis Exposure Times for each analysis Laser Drive Current are used for data collection. Analysis Beam Angles include the Beam Center Location Angle (0 to -S degrees) followed by angles from S degrees to 45 degrees in S degree increments. The analysis Laser Drive Currents are in the range of 0.1 milli~mps to 50 milli~mps. The analysis Exposure Times are in the range of 1 microsecond to 10 seconds.
The schedule is followed in order of increasing Beam Angle, increasing Laser Drive Current, and increasing Exposure Time for each Laser Drive Current. Termination of data collection at a Beam Angle is determined based on intensity data collected at that Beam Angle. Beginning Laser Drive Current and Exposure Time for each Beam Angle are based on the last values used at the previous Beam Angle. Termination of data collection occurs when sufficient data has been collected at the last Beam Angle, or when the maximum Laser Drive Current and Exposure Time have been reached without sufficient data being collected at the current Beam Angle, i.e. no further measurable Intensity data is available.
The following steps are executed to collect data:

21 8778~
~ WO 95~28630 PCTtUS95/04638 1. Reset the Aggregate Pixel Data array to zero (block 1 of FIG. 34). Begin the following steps with the last recorded beam center Laser Drive Current and beam center Exposure Time.
2. Take an exposure, call subroutines VALIDATE AND
S CORRECT PlXEL DATA, SCALE PIXEL DATA BY TOTAL LIGHT DOSE, and ADD PlXEL DATA TO AGGREGATE PIXEL DATA (blocks 2-5).
3 . Select a column of pixels (not a bad column) near the edge of the CCD farthest from Beam Center (such as column 5 if the current Beam Angle isthe Beam Center Location Angle, or column 1275 for other Beam Angles). Using the Aggregate Pixel Exposure Count array, compute the average number of exposures taken cont~ining valid readings for each pixel in the colurnn excluding bad pixels. If the average is greater than or equal to the predetermined optimumnumber of exposures (preferably, 3 to 5 exposures), sufficient data has been collected at this angle. Call subroutines CORRECT AGGREGATE PIXEL DATA
and MAP PIXEL DATA TO ANGLE CLASSES (blocks 6-11) and proceed to step 5 (block 13).
4. Change to the next higher analysis Exposure Time for the current analysis Laser Drive Current, if any. Otherwise, change to the next higher analysis Laser Drive Current and the lowest analysis Exposure Time for that analysis Laser Drive Current. If the highest analysis Laser Drive Current was already in use, call subroutines CORRECT AGGREGATE PIXEL DATA and MAP PIXEL DATA TO ANGLE CLASSES and proceed to step 6 (block 15).
Otherwise, repeat from step 2 (block 2).
5 . If the current analysis Beam Angle is the last, proceed to step

6 (block 15). Otherwise, move to the next analysis Beam Angle. Reset the analysis Laser Drive Current and analysis Exposure Time to the values used N
exposures earlier, where N is the predetermined optimum number of exposures (block 1). Repeat from step 1.
6. Move the laser back to the Beam Center Location Angle (block 15). Collection of the sample or baseline intensity-versus-angle class data set is complete.
Generally speaking, sample analysis consists of loading a sample, adjusting the concentration, resuspending the sample, measuring the beam transmittance, collecting intensity-versus-angle data, and rinsing. Three basic methods are possible, based on the means of sample loading. Manually started woss/28630 5 8 ~ us9~l04638 analysis involves explicit operator command to start. Autosampler analysis is started automatically based on an operator-entered schedule. Automatic sample sense is a mode in which the instrument circulates dispersant liquid and continually monitors beam tr~n~mitt~nce to detect when a sample has been poured into the 5 reservoir.
Referring to FIG. 35, sample analysis begins by calling the subroutines CHECK LASER TEMPERATURE CONTROL and DETERMINE
DARK CURRENT RATES. When these checks have been updated, a sample is loaded into the reservoir 102 and circulated through the sample cell 31. The l0 sample may be loaded in any of the three ways noted above. The probe 115 is operated as needed to assure that the particulate sample is dispersed in the dispersing fluid. If the sample is being delivered automatically from the autosampler 120, the valve 128 is closed and the valve 123 is opened to allow the alltos~mrler pump to deliver sample in a conventional manner to the reservoir 102.
Next, the concentration of sample in the dispersing fluid is checked and adjusted if necessary, as shown in block 4 of FIG. 35. For optimal signal-to-noise results with minim~l multiple scattering, the sample concentration should be adjusted by dilution or adding sample particles to cause a beam transrnittance of about 70% to 85% of the baseline beam intensity. Concentration adjustment can bedone m~nu~lly by adding sample or opening the valve 111 to allow fluid to flow into the reservoir 102. The processor is programmed to display for the operator a real time readout of beam tr~n~mitt~n~e relative to baseline beam intensity, so that the operator can add fluid or sample until the transmittance is within the desired range.
Alternately, an autodilution routine (not shown) can be run, according to which a signal representing the beam intensity divided by the baseline beam intensity is monitored by the processor. If this value is less than the minimllm optimal beam transmittance (for example 70%), the processor opens the valve 111 for a predetermined short interval to add fluid to the reservoir 102, diluting the sample and raising the transmittance. This process of monitoring and diluting is repeated until the transmittance is within the acceptable range If the level sensor 117 indicates that the reservoir 102 is full, the processor opens the drain valve 140 for a preset time to lower the level of fluid before adding fluid from the supply 108.

~- W095/28630 PCT~S95/04638 As shown in block 5, when the concentration of sample is properly adjusted, all the subroutines of MEASURE BEAM INTENSITY AND
ALIGNMENT (FIG. 28) are run to set up the angle classes on the CCD and measure the beam intensity. This procedure takes the place of m~-cll~.nical ~ nm~nt required for prior art analyzers, and assures that the angles ~cci~nPd to the intensity data from the CCD detector are accurate. Next the subroutine CALCULATE
BEAM TRANSMlTTANCE FACTOR is run using the measured beam intensity divided by the baseline beam intensity as the uncorrected beam tr~ncmitt~nce. The beam tr~ncmitt~nre factor obtained is saved for later use.
Now the system is ready to run the subroutine COLLECT DATA as described above, for the selected schedule of analysis Beam Angles, Laser Drive Currents, and Exposure Times. Sets of intensity-versus-angle data are obtained for further processing as described below.
After the data has been obtained, the system may be rinsed (block 8) prior to loading another sample. The valve 128 may be opened to allow rinse liquid from the container 125 to flow into the reservoir 102, and the drain valve 140 may be opened to drain the prior sample to waste. The sensor 142 provides a signal when draining is complete. Several cycles of draining and circulating rinse liquid may be condllcte~l to remove essentially all of the prior sample from the cell 31 and the reservoir 102. Furthermore, the rinse liquid may be provided via lines 126 and 122 to the autosampler 120 for rinsing procedures well known to those skilled in the art.
Baseline intensity data is obtained in a similar manner. Baseline data should be obtained at any time the sample cell 31 is m~nll~lly cleaned or replaced and otherwise on a periodic (once a day or once a week, depending on use) basis.First, the CHECK LASER TEMPERATURE CONTROL and DETERMINE
DARK CURRENT RATES subroutines are run. Then, the MEASURE BEAM
INTENSITY subroutine is run with no particulate sample in the fluid circulating through the cell 31, to record the Baseline Beam Intensity. Then this value for beam intensity is used in the COLLECT DATA subroutine in the absence of sample particles to obtain Baseline Intensity data for use below.

5. Aggregate Corrected Intensity versus Scattering Angle Calculation Certain subroutines are called, ultimately to obtain Aggregate-Corrected-Intensity-versus-Scattering-Angle data. For each incident Beam Angle, the ~_ WO 95/28630 PCI`/US9S/04638 .

subroutine CALCULATE REFLECTANCE and subroutine CALCULATE BEAM
PATH LENGTH AND BEAM TRANSMITTANCE are called. For each scattering angle with sample mtensity data and baseline intensity data at this incident beam angle, subroutine CORRECT SAMPLE INTENSITY FOR BASELINE
INTENSITY, BEAM TRANSMITTANCE, AND REFLECTANCE is called.
Subroutine COMBINE INTENSITY DATA FOR ALL INCIDENT BEAM
ANGLES is then called. These subroutines (not shown) will now be described.
Subroutine CALCULATE REFLECTANCE calculates the reflectance of the anti-reflection coated glass used for the cell windows. It is calculated as a function 10 of:

nl, refractive index of air (1.00) n2, refractive index of coating (1.362) n3, refractive index of fused silica glass (1.456) al, angle of incident bearn to window in radians h, thickness of coating (0.138 micrometers) pi = 3.14159 a2 = asin(nl * sin(al) / n2);
a3 = asin(nl * sin(al) / n3);
rl2p = (n2 * cos(al) - nl * cos(a2)) / (n2 * cos(al) + nl * cos(a2));
r23p = (n3 * cos(a2) - n2 * cos(a3)) / (n3 * cos(a2) + n2 * cos(a3));
rl2s = (nl * cos(al) - n2 * cos(a2)) / (nl * cos(al) + n2 * cos(a2));
r23s = (n2 * cos(a2) - n3 * cos(a3)) / (n2 * cos(a2) + n3 * cos(a3));
beta = 2. * pi * n2 * h * cos(a2);
rp = (rl2p * rl2p + r23p * r23p + 2. * rl2p * r23p * cos(2. * beta)) /
(1. + rl2p * rl2p * r23p * r23p + 2. * rl2p * r23p * cos(2. * beta));
rs = (rl2s * rl2s + r23s * r23s + 2. * rl2s * r23s * cos(2. * beta)) /
(1. + rl2s * rl2s * r23s * r23s + 2. * rl2s * r23s * cos(2. * beta));
Reflectance = (rp + rs) / 2.

(Reference: Melles Griot Optics Guide 5 pg. 4-13 and 4-14, Melles Griot Inc.) 6 l Subroutine CALCULATE BEAM PATH LENGTH AND BEAM
TRANSMlTTANCE (different from CALCULATE BEAM TRANSMll-rANCE
FACTOR described above) c~lr~ tes the following factors:

p~thT Pn~th = 1 / cos(FluidFromAir(Tn~ ntReamAngle));
alphaC = log(BeamT~ PFactor);
BeamTli-".~",i~ nce. = exp(alphaC * p~thT ~.ngth).

Subroutine CORRECT SAMPLE INTENSITY FOR BASELINE
INTENSlTY, BEAM TRANSMITTANCE, AND REFLECTANCE collects and applies the above calculated factors. BaselineThreshold is a predetermined number between 0 and 1 (normally 0.3 to 0.5) representing the maximum allowable fraction of total light measured that can be attributed to baseline without causing an unacceptable amount of noise in the rem~ining corrected sample intensity data.
If (BaselineIntensity *` BeamTransmittance > BaselineThreshold *
SampleTntçn.city), exclude this intensity-versus-angle data point from further use.
Otherwise, CorrectedSampleTntensity = (SampleTntencity - BaselineIntensity *
BeamTI~l-s,,li~ e) / ((1 - Reflectance) * (1 - BeamTransmittance)) Subroutine COMBINE INTENSITY DATA FROM ALL INCIDENT
BEAM ANGLES collects all the data from all the Incident Beam Angles into one Aggregate-Corrected-Intensity-versus-Scattering-Angle array. The steps of this routine are as follows: For each scattering angle, average the corrected sample intensity values for all incident Beam Angles having corrected sample intensity values at this scattering angle. If the PixelCountPerClass data was preserved insample or baseline data collection, use a weighted average for this step, weighting each corrected sample intensity value by the associated PixelCountPerClass. In this case, compute an Aggregate Pixel Count Per Class by summing the PixelCountPerClass values used in averaging for this class.

6. Mie Scattering Models Calculation 21 8778~
~_ wo 95/28630 Pcrlus95/04638 Mie Scattering Models Calculation is based on the algorithm shown in Absorption and Se~tterin~ of Light by Small Particles by Bohren and Hnffm:~n, Copyright 1983 by John Wiley & Sons, Ine. Modifieations to the algorithm are made to increase precision, remove calculation of backscattering angles, use a S predeterrnined array of sc~ttPrin~ angles, and optimize perform~n~e.
Size classes span the particle diameter range from 0.08 micrometers to 800 micrometers in a geometric progression. A resolution between 20 classes per decade and 100 classes per decade can be chosen based on computation time for particle size distribution calculation, computation time for Mie scattering models, and stability of particle size distribution results for multiple analyses.
The computed intensity for a given angle class is the integral of scattered light intensity versus angle over the angle interval. The number of points calculated within each angle class for use in the integration is determined based on frequency of change in intensity with angle for the current particle size.
The sc~tterin~ function for each size class may be the average of several Mie scattering curves for sizes sp~nnin~ the interval ~f the size class to account for high frequency features that change too rapidly with size to be characterized accurately by an individual curve for each class. Alternatively, the scattering function for each class may be the weighted average of several Mie scattering curves for sizes overlapping with the sizes used to compute the adjacent classes, with the weighting factors based on, for example, a (~ussi~n distribution about the class mean.
The final construction of the size class data should be determined based on stability and goodness of fit of particle size distribution results. A set of Fraunhofer sc~tterin~ data can also be provided for use when the refractive index of the sample is unknown, the sample is not of homogeneous composition, or for comparison with other data based on Fraunhofer scattering. Fraunhofer calculations may be substituted for Mie calculations f~r large particle sizes to reduce computation time.

7. Particle Size Distribution Calculation The technique for calculating particle size distribution from scattered intensity-versus-angle data is preferably a Non-Negative Least Squares deconvolution (NNLS) with regularization by weighted minimi7~tion of the function. The NNLS algorithm is presented in Solving Least Squares Problems by Lawson and Hanson, Copyright 1974 by Prentice-Hall, Inc. The regularization method is presented in The Solution of Adsorption Inte ral Equation by Means of ~~ WO 95/28630 PCT/US95/04638 the Regularization Method by M. v. Szombathely and P. Brauer, University of Leipzig, Dept. of ChPmictry, publi~hP-d in the Journal of Computational Chemistry, Vol. 13, No. 1, 17-32, Copyright 1992 by John Wiley & Sons, Inc.
The output data is preferably volume fraction per particle size class.
Intensity-versus-angle data used in the deconvolution may be trllnc~tecl at the small angle end based on location of an intensity l,la~illlulll. Large particle size classes may be excluded based on a ",il-i""~"~ number of valid intensity data points available in the angle region of the plilna.~ lobe of the theoretical scattering pattern for those sizes. Small particle size classes may be excluded based on a minimum decrease in the theoretical scattered light intensity from the miniml-m angle with valid intensity data to the maximum angle with valid intensity data. Small particle size classes may also be excluded based on the requirement to have at least as many valid input data points as output classes.
The kernel matrix may be normalized by the total extinction for each size over the range of angles included, so that minimi7~tion of error (least squares) and minimi7~tion of the function (regularization) bo~h evenly weight the response to all sizes. The problem may be transformed into a relative least squares problem by norm~li7:~tion of the kernel matrix and input vector by the input vector. The kernel matrix may be conditioned by weighting by a function of scattering angle, as described in Optimizing the Kernel for Laser Diffraction Particle Sizing by Y. C.
Agrawal and H. C. Pottsmith, Applied Optics Vol. 32, No. 22, 1 August 1993 and in Optimal Scaling of the Inverse Fraunhofer Diffraction Particle Sizing Problem:
the Linear System Produced by Ouadrature by E. D. Hirleman, Particle Characterization 4, 128-133 (1987). Alternatively, the kernel function may be conditioned by weighting by the Aggregate Pixel Count Per Class computed in the subroutine Combine Intensity Data from All Incident Beam Angles.
The threshold for deterrnining class inclusion in the NNLS algorithm may be determined based on convergence of the deconvolution for a variety of particle size distributions. If necessary to prevent spurious addition of large amounts of small particle sizes to a distribution based on scattered light at wide angles at intensities below the instrument noise level, a two stage deconvolution may be used. If so, the first deconvolution should have a high threshold for class inclusion and should be used to lirnit the range of classes eligible for use in the seconddeconvolution. The second deconvolution should have a lower threshold for class inclusion but should exclude classes outside the limits defined by the first -~_ W0 95/28630 PCT/US95/04638 deconvolution. This technique becomes necessary if the single stage inversion process is unstable, given the set of angle classes chosen and the particle sizedistribution resolution desired.
It is efficacious to limit the maximum allowable number of deconvolution iterations. The value for the m~ximllm may be determined based on the total number of size classes used.
While this invention has been described in detail with particular reference to . preferred embodiments thereof, it will be understood that variations and modifications can be made to these embo~limP-~t~ without departing from the spirit and scope of the invention as described herein and as defined in the appended clalms.

Claims (23)

We claim:

1. A method of obtaining particle size data for a group of dispersed particles, including the steps illuminating a plurality of dispersed particles with an exposure of light in a collimated beam from a light source so as to scatter rays of light of said beam; passing at least a portion of said rays scattered by said particles during said illuminating step through a lens such that rays parallel to one another are focused at one location in a focal surface of said lens; and reading output data from said array into a memory device, characterized by the step of:
detecting at least a portion of said rays passing through said lens with a two dimensional array of functionally equivalent photosensitive pixels positioned in the focal surface.

2. The method of Claim 1, wherein at least a portion of said array comprises densely arranged pixels.

3. The method of Claim 1, wherein said array comprises a charge coupled device.

4. The method of any preceding claim, further characterized by the steps of:
illuminating said dispersed particles with a plurality of distinct exposures of light from said light source;
varying in each of said exposures one or more characteristics of illumination of said particles;
reading output data from said pixels following each of said exposures into a memory device;
determining from said output data intensity values for selected angle classes into which said light has been scattered for each of said exposures; and determining for each angle class a composite intensity value based on all of said exposures and scaled to compensate for differences in illumination characteristics during each of said exposures.

5. The method of Claim 4, wherein said one or more illumination characteristics are selected from the group consisting of: duration of light dose, light source output level, path length through said particles.

6. The method of claim 4, wherein said step of determining composite intensity values comprises:
determining a scale factor between each of said exposures (n+1) and the preceding exposure (n, n 1) by:
(a) normalizing intensity values for each exposure by dividing the intensity value associated with each angle class by the number of pixels in the same angle class;
(b) for each angle class, dividing each normalized intensity value for exposure (n+1) by the normalized intensity value for the exposure (n); and (c) weighting the quotient by the number of pixels contributing; and (d) calculating a weighted average of said quotients to obtain said scale factor;
and for each angle class:
multiplying the intensity value for the first exposure by the scale factor and adding the product to the intensity value for the second exposure and averaging to obtain a composite intensity value; and for each successive exposure (n+1), multiplying the existing composite intensity value by the scale factor between exposures (n+1) and (n), and adding the product to the intensity value for exposure (n+1) and averaging to obtain a cumulative composite intensity value.

7. The method of any preceding claim, further characterized by the steps of:
prior to illuminating said dispersed particles, uniformly illuminating said array with light doses from said light source at a plurality of different dose sizes;

determining an output sensitivity function for each pixel relative to incident dose size; and following illumination of said dispersed particles, modifying said output data for each pixel based on said output function and the incident dose size of the light dose used in illuminating said dispersed particles.

8. The method of any preceding claim, wherein said scattering particles are in a first sample container having a first width in the direction of said beam; and further comprising the steps of replacing said first sample container with a second sample container having a second width; and repeating, without physicalrealignment of said light source, said lens, or said array, the steps of Claim 1.

9. The method of any of Claims 4 through 6, further characterized by, between two of said plurality of exposures, the step of changing the relative angle between the incident direction of said beam from said light source and an optic axis of said lens.

10. The method of Claim 9, comprising dispersing said particles in a sample container including a planar window in the path of said beam, and, in conjunction with the step of changing the incident angle of said beam, rotating said sample container about an axis passing through said dispersed particles normal to said optic axis to alter the angle at which said beam strikes said window.

11. The method of Claim 4, further characterized by the steps of:
assigning each of said pixels to one or more of said angle classes;
dividing each of a group of said pixels into fractions;
assigning each of said fractions of said pixels to the angle class in which said fraction is located;
multiplying the output data obtained for each pixel in a particular angle class by the fraction of said pixel located in said particular angle class to obtain a plurality of pixel output fractions;
and averaging together said pixel output fractions to obtain an average output value for said particular angle class.

12. The method of Claim 1, further comprising the steps of:
exposing said array to a first calibration dose of said light directed along the axis of said lens in the absence of said particles;
measuring a first amount of said first calibration dose striking a predetermined area around a center of said beam;
exposing said array to a second calibration dose of said light directed along the axis of said lens in the presence of said particles;
measuring a second amount of said second calibration dose striking said predetermined area around the center of said beam after passing through said particles;
dividing said second amount by said first amount to obtain a beam transmittance factor;
adjusting said beam transmittance factor responsive to the path length of said beam through said particles.

13. The method of any preceding claim, further characterized by the initial steps of:
selecting a beam center location angle of said light source measured relative to an optic axis of said lens, and determining the center of said beam relative to said array with said light source at said beam center location angle by the steps of:
projecting said beam onto said array with no particles present;
reading the output data from a plurality of pixels included in the array into a memory device;
defining an area of pixels where the magnitude of the output data is the highest; and determining a beam center located at the weighted average of the coordinates of pixels within said area.

14. An apparatus for determining particle size data, a light source capable of generating a collimated beam of light; a plurality of dispersed particles positioned such that at least a portion of light emitted from said light source is scattered by said particles; and a lens positioned to focus at least a portion of said scattered light onto a detector positioned in a focal surface of said lens, rays parallel to one another being focused at one location in the focal surface of said lens, characterized by:
said detector comprising a two dimensional array of functionally equivalent photosensitive pixels positioned in the path of at least a portion of said scattered light.

15. The apparatus of Claim 14, wherein said lens is a zoom lens.

16. The apparatus of Claim 14 or Claim 15, wherein said array comprises a charge coupled device.

17. The apparatus of Claim 14, wherein said CCD includes lateral overflow drains.

18. The apparatus of any of Claims 14 through 17, wherein said particles are dispersed in a sample cell having a cell width in a direction along the axis of said lens, and further comprising an adjustable cell mount capable of receiving a plurality of sample cells of differing cell widths.

19. The apparatus of Claim 14, further characterized by:
an exposure controller for operating said light source to illuminate said particles with a plurality of distinct exposures of said light beam, each differing in illumination characteristics;
a memory device connected to said CCD device to receive output data from said pixels following each of said exposures; and a processor configured (a) to determine from said output data intensity values for angle classes into which said light has been scattered for each of said exposures, and (b) to determine for each angle class a composite intensity value based on all of said exposures and scaled to compensate for differences in illumination characteristics during each of said exposures.

20. A method of obtaining particle size distribution data for a group of dispersed particles, including the steps of illuminating a plurality of dispersed particles with a dose of light in a collimated beam from a light source; detecting at least a portion of said light passing through said dispersed particles with a detector, and reading output data from said detector into a memory device, characterized by the steps of:
detecting said light passing through said dispersed particles with a two dimensional array of photosensitive pixels; and determining from said detected light the location at which an unscattered center of said beam intersects said array.

21. The method of Claim 20, further comprising the step of assigning pixels of said array to data collection areas defined responsive to the location at which an unscattered center of said beam intersects said array.

22. An apparatus for obtaining particle size data, including a light source; a particle dispersing device capable of positioning a plurality of dispersed particles in the path of a collimated beam of light emitted from said light source; and a positioned to detect at least a portion of said light passing through said dispersed particles, said detector providing output data responsive to said detected light;
characterized by:
said detector comprising a two dimensional array of photosensitive pixels; and a processor configured to receive output data from said array and to determine from said output data the location at which an unscattered center of said beam intersects said array.

23. The apparatus of Claim 22, wherein said processor is configured to determine the location at which an unscattered center of said beamintersects said array by defining an area of pixels where the magnitude of the output data is the highest, and determining center coordinates of said area.