FOURIER DOMAIN LOW-COHERENCE INTERFEROMETRY FOR LIGHT SCATTERING SPECTROSCOPY APPARATUS AND METHOD
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to an apparatus and method for obtaining depth-resolved
spectra for the purpose of determining structure by measuring elastic scattering properties.
More particularly, Fourier domain, low-coherence interferometry techniques are applied to light
scattering spectroscopy. This approach permits the viewing and recovery of depth-resolved
structures, as well as obtaining spectroscopic information about scattered light as a function of
depth.
2. Background of the Related Art
Accurately measuring small objects or other physical phenomena is a goal that is pursued
in many diverse fields of scientific endeavor. For example, in the study of cellular biology and
cellular structures, light scattering spectroscopy (LSS) has received much attention recently as a
means for probing cellular morphology and the diagnosing of dysplasia. The disclosures of the
following references are incorporated by reference in their entirety:
Backman, V., V. Gopal, M. Kalashnikov, K. Badizadegan, R. Gurjar, A. Wax, I.
Georgakoudi, M. Mueller, C.W. Boone, R.R. Dasari, and M.S. Feld, IEEE J. Sel. Top.
Quantum Electron., 7(6): p. 887-893 (2001); Mourant .R., M. Canpolat, C. Brocker, O.
Esponda-Ramos, T.M. Johnson, A. Matanock, K. Stetter, and J.P. Freyer, J. Biomed.
Opt, 5(2): p. 131-137 (2000); Wax, A., C. Yang, V. Backman, K. Badizadegan, C.W.
Boone, R.R. Dasari, and M.S. Feld, Biophysical Journal, 82: p. 2256-2264 (2002);
Georgakoudi, I., E.E. Sheets, M.G. Miiller, V. Backman, C.P. Crum, K. Badizadegan,
R.R. Dasari, and M.S. Feld, Am J Obstet Gynecol, 186: p. 374-382 (2002); Backman, V.,
M.B. Wallace, L.T. Perelman, J.T. Arendt, R. Gurjar, M.G. Muller, Q. Zhang, G. Zonios,
E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, J.M. Crawford, M.
Fitzmaurice, S. Kabani, H.S. Levin, M. Seiler, R.R. Dasari, I. Itzkan, J. Van Dam, and
M.S. Feld, Nature, 406(6791): p. 35-36 (2000); Wax, A., C. Yang, M. Mueller, R. Nines,
C.W. Boone, V.E. Steele, G.D. Stoner, R.R. Dasari, and M.S. Feld, Cancer Res, (accepted
for publication).
The LSS technique examines variations in the elastic scattering properties of cell
organelles to infer their sizes and other dimensional information. In order to measure cellular
features in tissues and other cellular structures, it is necessary to distinguish the singly scattered
light from diffuse light, which has been multiply scattered and no longer carries easily accessible
information about the scattering objects. This distinction or differentiation can be accomplished
in several ways, such as the application of a polarization grating, by restricting or limiting studies
and analysis to weakly scattering samples, or by using modeling to remove the diffuse
component (s).
As an alternative approach for selectively detecting singly scattered light from sub-surface
sites, low-coherence interferometry (LCI) has also been explored as a method of LSS.
Experimental results have shown that using a broadband light source and its second harmonic
allows the recovery of information about elastic scattering using LCI [7].
More recently, angle-resolved LCI (a/LCI) has demonstrated the capability of obtaining
structural information by examining the angular distribution of scattered light from the sample
or object under examination. The a/LCI technique has been successfully applied to measuring
cellular morphology and to diagnosing intraepitheUal neoplasia in an animal model of
carcinogenesis.
The above references are incorporated by reference herein where appropriate for
appropriate teachings of additional or alternative details, features and/or technical background.
SUMMARY OF THE INVENTION
The claimed exemplary embodiments of the present invention address some of the issues
presented above.
An object of the invention is to solve at least the above problems and/or disadvantages
and to provide at least the advantages described hereinafter.
In one exemplary embodiment of the present invention, an apparatus comprises a first
receiver that receives a first reference light and outputs a second reference light. A second
receiver that receives a first sample light and outputs a second sample light and wherein the
second sample light contains light scattered from a sample when at least a portion of the first
sample light is scattered from a sample. A cross-correlator that receives and cross-correlates the
second reference light with the second sample light. The cross-correlator may be a spatial
cross-correlator.
In another exemplary embodiment of the present invention, a reference arm receives a first
reference light and outputs a second reference light. A sample receives a first sample light and
outputs a second sample light and wherein the second sample light contains light scattered from
the sample when at least a portion of said first sample light is scattered from the sample. A
spatial cross-correlator receives and cross correlates the second reference light with the second
sample light. The spatial cross-correlator comprises a detector and a processing unit. The
detector outputs an interference term to the processing unit. The processing unit processes the
interference term to yield depth resolved cross-correlation reflection profiles of the sample. The
processing unit first appUes a Gaussian window and then a Fourier transform transforms the
interference term to yield depth resolved cross-correlation reflection profiles of the sample. The
Fourier transform obtains an axial spatial cross-correlation between a signal field(s) and a
reference field(s). A Ught source outputs Ught, which contains the first sample Ught and the first
reference Ught.
In another exemplary embodiment of the present invention, a method comprises receiving
a first reference Ught and outputting a second reference Ught. A first sample Ught is received and
a second sample Ught is output. The second sample Ught contains Ught scattered from a sample
when at least a portion of the first sample Ught is scattered from a sample along with the
reception and cross correlation of the second reference Ught with the second sample Ught.
In another exemplary embodiment, a method comprises receiving Ught and spUtting at least
a portion of the Ught into reference Ught and sample Ught. At least a portion of said reference
Ught is reflected from a reference surface to yield reflected reference Ught. At least a portion of
the sample Ught is scattered from a sample to yield scattered sample Ught, and the scattered
sample and the reflected reference Ught are mixed. Information is recovered about the scattered
sample Ught. The mixing comprises detecting an intensity of the scattered sample Ught and the
reflected reference Ught. Recovering information comprises extracting an interference term
from a total intensity. Recovering information can further comprise applying a mathematical
operator to the interference term to recover the spectral information about the scattered sample
Ught at a particular depth to yield depth resolved cross-correlation reflection points of the
sample. The mathematical operator used is preferably a Gaussian window.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention wiU be described in detail with reference to the foUowing drawings in
which Uke reference numerals refer to like elements wherein:
Figure 1 A is a diagram of an exemplary embodiment of an fLCI system;
Figure IB is a diagram of another exemplary embodiment of an fLCI system using fiber
optic coupUng;
Figure 2 is a diagram illustrating exemplary properties of a white Ught source;
Figure 3 is a diagram of an exemplary axial spatial cross-correlation function for a
coversUp sample;
Figure 4 is a diagram of exemplary spectra obtained for front and back surfaces of a
coverglass sample when no microspheres are present;
Figure 5 is a diagram of exemplary spectra obtained for front and back surfaces of a
coverglass sample when microspheres are present;
Figure 6 is a diagram of exemplary ratios of spectra in Figures 4 and 5 iUustrating
scattering efficiency of spheres for front and back surface reflections;
Figure 7 is a diagram of a generaUzed version of the system shown in Figure 1;
Figure 8 is a block diagram of an exemplary embodiment of a method in accordance with
the present invention; and
Figure 9 is a block diagram of another exemplary embodiment of a method in accordance
with the present invention.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
In the foUowing detailed description of the various exemplary embodiments, reference is
made to the accompanying drawings that show, by way of iUustration, specific embodiments in
which the invention may be practiced. In the drawings, Uke numerals describe substantiaUy
similar components throughout the several views. These embodiments are described in
sufficient detail to enable those skiUed in the art to practice the invention. Other embodiments
may be utiUzed without departing from the scope of the present invention. Moreover, it is to be
understood that various embodiments of the invention, although different, are not necessarily
mutuaUy exclusive. For example, a particular feature, structure, or characteristic described in one
embodiment may be included within other embodiments. Therefore, the foUowing detailed
description is not to be taken in a limiting sense. The scope of the present invention is
deUneated by the claims, along with the fuU scope of equivalents to which such claims are
entitled.
The contents of the foUowing references are incorporated by reference in their entirety:
Wojtkowski, M., A. Kowalczyk, R. Leitgeb, and A.F. Fercher, Opt. Lett, 27(16): p. 1415-1417
(2002); Wojtkowski, M., R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A.F. Fercher, J.
Biomed. Opt., 7(3): p. 457-463 (2002); Leitgeb, R., M. Wojtkowski, A. Kowalczyk, C.K.
Hitzenberger, M. Sticker, and A.F. Fercher, Opt. Lett., 25(11): p. 820-822 (2000).
In general, spectral radar makes use of techniques where depth-resolved structural
information is recovered by applying a Fourier transform to the spectrum of two mixed fields.
In fLCI, the aforementioned approach used in spectral radar appUcations is extended to recover
not only depth-resolved structure, but also to obtain spectroscopic information about scattered
Ught as a function of depth. The capabilities of fLCI enable extracting the size of polystyrene
beads in a sub-surface layer based on their Ught scattering spectrum. The apparatus and method j according to exemplary embodiments of the invention can be appUed to many different areas.
One such area of appUcation is to recover nuclear morphology of sub-surface ceU layers.
One exemplary embodiment of the fLCI scheme is shown in Figure 1A. White Ught
from a Tungsten Ught source 100 (e.g. 6.5 W, Ocean Optics™) is coupled into a multimode fiber
101 (e.g. 200 μm core diameter). The output of the fiber 101 is collimated by an achromatic lens
102 to produce a beam 104 (e.g. a pencil beam 5 mm in diameter). The beam 104 is then
forwarded to an fLCI system 10.
This iUumination scheme achieves Kohler illumination in that the fiber acts as a field
stop, resulting in the proper aUgnment of incident or iUuminating Ught and thereby achieving
critical iUumination of the sample. In the fLCI system 10, the white Ught beam is spUt by the
beamspUtter 106 (BS) into a reference beam 105 and an input beam 107 to the sample 108. The
Ught scattered by the sample 108 is recombined at the BS 106 with Ught reflected by the
reference mirror 114 (M).
The reference beam 105 in conjunction with the reference mirror 114 forms a portion of
a reference arm that receives a first reference Ught and outputs a second reference Ught. The
input beam 107 and the sample 108 form a portion of a sample arm that receives a first sample
Ught and outputs a second sample Ught.
Those sldUed in the art wiU appreciate that the Ught beam can be spUt into a pluraUty of
reference beams and input beams (e.g. N reference beams and N input beams) without departing
from the spirit and scope of the present invention. Further, the spUtting of the beams may be
accompUshed with a beamspUtter or a fiber spUtter in the case of an optical fiber implementation
of and exemplary embodiment of the present invention.
In the exemplary embodiment of the present invention shown in Figure 1A, the
combined beam is coupled into a multimode fiber 113 by an aspheric lens 110. Again, other
coupUng mechanisms or lens types and configurations may be used without departing from the
spirit and scope of the present invention. The output of the fiber coincides with the input sUt of
a miniature spectrograph 112 (e.g. USB2000, Ocean Optics™), where the Ught is spectraUy
dispersed and detected.
The detected signal is Unearly related to the intensity as a function of wavelength I(λ),
which can be related to the signal and reference fields (Es, Er) as:
<J(λ)>=<|^(λ)|2)+<|Je(λ)|2>+2R£<J5(λ)^λ)>cos^ (1)
where φ is the phase difference between the two fields and <•••) denotes an ensemble average.
The interference term is extracted by measuring the intensity of the signal and reference beams
independently and subtracting them from the total intensity.
The axial spatial cross-correlation function, TSR(Z) between the sample and reference
fields is obtained by rescaUng the wavelength spectrum into a wavenumber (k = 2π/λ) spectrum
then Fourier transforming:
This term is labeled as an axial spatial cross-correlation as it is related to the temporal or
longitudinal coherence of the two fields.
Another exemplary embodiment of an fLCI scheme is shown in Figure IB. In this
exemplary embodiment, fiber optic cable is used to connect the various components. Those
skilled in the art wiU appreciate that other optical coupUng mechanisms, or combinations
thereof, may be used to connect the components without departing from the spirit and scope of
the present invention.
In Figure IB, white Ught from a Tungsten Ught source 120 is coupled into a multimode
fiber 122 and the white Ught beam in the multimode fiber is spUt by the fiber spUtter (FS) 124
into a reference fiber 125 and an sample fiber 127 to the sample 130. The fiber spUtter 124 is
used to spUt Ught from one optical fiber source into multiple sources.
The reference Ught in reference fiber 125, in conjunction with a lens 126 (preferably an
aspheric lens) and the reference mirror 128, forms a portion of a reference arm that receives a
first reference Ught and outputs a second reference Ught SpecificaUy, reference Ught in reference
fiber 125 is directed to the reference mirror 128 by lens 126, and the reference Ught reflected by
the reference mirror 128 (second reference Ught) is coupled back into the reference fiber 125
with lens 126. The sample Ught in sample fiber 127 and the sample 130 form a portion of a
sample arm that receives a first sample Ught and outputs a second sample Ught. SpecificaUy,
sample Ught in sample fiber 127 is directed to the sample 130 by lens 131 (preferably as aspheric
lens), and at least a portion of the sample Ught scattered by the sample 130 is coupled into the
sample fiber 127 by lens 131. In the exemplary embodiment shown in Figure IB, the sample
130 is preferably spaced from lens 131 by a distance approximately equal to the focal length of
lens 131.
At least a portion of the reflected reference Ught in reference fiber 125 and at least a
portion of the scattered sample Ught on sample fiber 127 are coupled into a detector fiber 133 by
the FS 124.
The output of detector fiber 133 coincides with the input of a miniature spectrograph
132, where the Ught is spectraUy dispersed and detected.
Figure 2 iUustrates some of the properties of a white Ught source. Figure 2(a) iUustrates
an autocorrelation function showing a coherence length (lc = 1.2 μm). Figure 2(a) shows the
cross-correlation between the signal and reference fields when the sample is a mirror, and this
mirror is identical to the reference mirror (M). In this exemplary scenario, the fields are identical
and the autocorrelation is given by the transform of the incident field spectrum, modeled as a
Gaussian spectrum with center wavenumber ko = 10.3 μnr1 and 1/e width Δkι/e = 2.04 μm-1
(Figure 2 (b)).
Figure 2(b) shows an exemplary spectrum of Ught source that can be used in accordance
with the present invention.
From this autocorrelation, the coherence length of the field, h — 1.21 μm is determined.
This is sUghtly larger than the calculated width of k = 2/Δkι/e = 0.98 μm, with any discrepancy
most Ukely attributed to uncompensated dispersion effects. Note that rescaUng the field into
wavenumber space is a nonUnear process which can skew the spectrum if not properly executed
[13].
In data processing, a fitting algorithm is appUed (e.g. a cubic spUne fit) to the rescaled
wavenumber spectrum and then resampled (e.g. resample with even spacing). The resampled
spectrum is then Fourier transformed to yield the spatial correlation of the sample. Those skilled
in the art wiU appreciate that other frequency based algorithms or combinations of algorithms
can be used in place of the Fourier transform to yield spatial correlation. One example of a
software tool that can be used to accompUsh this processing in real time or near real time is to
use Lab View ™ software.
In one exemplary embodiment of the present invention, the sample consists of a glass
coversUp (e.g., thickness, d ~ 200 μm) with polystyrene beads which have been dried from
suspension onto the back surface (1.55 μm mean diameter, 3% variance). Thus, the field
scattered by the sample can be expressed as:
In equation 3, Ejr0nt and Eback denote the field scattered by the front and back surfaces of
the coversUp, and δz is the difference between the path length of the reference beam and that of
the Ught reflected from the front surface and n the index of refraction of the glass. The effect
of the microspheres wiU appear in the Eback term as the beads are smaU and attached closely to
the back surface. Upon substituting equation 3 into equation 2, a two peak distribution with the
width of the peaks given by the coherence length of the source is obtained.
In order to obtain spectroscopic information, a Gaussian window is appUed to the
interference term before performing the Fourier transform operation. Those skiUed in the art
wiU appreciate that other probabilistic windowing methodologies may be appUed without
departing from the spirit and scope of the invention. This makes it possible to recover spectral
information about Ught scattered at a particular depth.
The windowed interference term takes the form:
The proper sizing of a windowed interference term can faciUtate the processing
operation. For example, by selecting a relatively narrow window (Akw smaU) compared to the
features of Es and Ek, we effectively obtain {Es(kw)E*r(kw)). In processing the data below, we
use Akw = 0.12 μm-1 which degrades the coherence length by a factor of 16.7. This exemplary
window setting enables the scattering at 50 different wavenumbers over the 6 μm-1 span of
usable spectrum.
In Figure 3, an axial spatial cross-correlation function for a coversUp sample is showed
according to one embodiment of the invention. Figures 3(a) and (b) shows the depth resolved
cross-correlation reflection profiles of the coversUp sample before and after the processing
operations. In Figure 3(a), a high resolution scan with arrows indicating a peak corresponding to
each glass surface is shown. In Figure 3(b), a low resolution scan is obtained from the scan in
Figure 3(a) is shown by using a Gaussian window.
Note that the correlation function is symmetric about z = 0, resulting in a superposed
mirror image of the scan. Since these are represented as cross-correlation functions, the plots
are symmetric about z = 0. Thus the front surface reflection for z>0 is paired with the back
surface reflection for z<0, and vice versa.
In Figure 3(a), the reflection from the coversUp introduces dispersion relative to the
reflection from the reference arm, generating multiple peaks in the reflection profile. When the
spectroscopic window is appUed, only a single peak is seen for each surface, however several
dropouts appear due to aUasing of the signal.
To obtain the spectrum of the scattered Ught, we repeatedly apply the Gaussian window
and increase the center wavenumber by 0.12 μm between successive appUcations. As
mentioned above, Ak& = 0.12 μnr1 is used to degrade the coherence length by a factor of 16.7.
This results in the generation of a spectroscopic depth-resolved reflection profile.
Figures 4 (a) and (b) show the spectrum obtained for Ught scattered from the front (a)
and back (b) surfaces of a coverglass sample respectively, when no microspheres are present.
The reflection from the front surface appears as a sUghtly modulated version of the source
spectrum. The spectrum of the reflection from the rear surface however has been significantly
modified. Thus in equation 3, we now take
T(k) E
s(&), where T( )
represents the transmission through the coversUp.
In Figure 5, the spectra for Ught scattering obtained for front (a) and back (b) surfaces of
a coverglass sample when microspheres are present on the back surface of the coversUp are
shown in Figures 5 (a) and (b). It can be seen that the reflected spectrum from the front surface
has not changed significantly, as expected. However, the spectrum for the back surface is now
modulated. We can examine the scattering properties S k) of the microspheres by writing the
scattered field as EsphenJk) = S(k) T(k) Es(k) and taking the ratio Eφhem(k)/ Eback ) = S(k), which
is shown as a soUd Une in Figure 6(a). It can be seen from this ratio that the microspheres induce
a periodic modulation of the spectrum.
In Figure 6 (a), a ratio of the spectra found in Figure 4 and Figure 5 is shown. This
illustrates the scattering efficiency of spheres for front (represented by the dashed line) and back
(represented by the soUd Une) surface reflections. In Figure 6(b), a correlation function obtained
from ratio of back surface reflections is shown. The peak occurs at the round trip optical path
through individual microspheres, permitting the size of the spheres to be determined with sub-
wavelength accuracy.
For comparison, the same ratio for the front surface reflections (dashed Une in Figure
6(a)) shows only a smaU Unear variation. Taking the Fourier transform of S(k) yields a clear
correlation peak (Figure 6(b)), at a physical distance of z= 5.24 μm. This can be related to the
optical path length through the sphere by z = 2«/with the index of the microspheres n = 1.59.
The diameter of the microspheres to be / = 1.65 μm +/- 0.33 μm, with the uncertainty given by
the correlation pixel size. Thus with fLCI, we are able to determine the size of the microspheres
with sub-wavelength accuracy, even exceeding the resolution achievable with this white Ught
source and related art LCI imaging.
There are many appUcations of the various exemplary embodiments of the present
invention. One exemplary appUcation of fLCI is in determining the size of ceU organelles, in
particular the ceU nucleus, in epitheUal tissues. In biological media, for example, the relative
refractive indices are lower for organeUes compared to microspheres and thus, smaUer scattering
signals are expected. The use of a higher power Ught source wiU permit the smaUer signals to be
detected. Other examples include detection of sub-surface defects in manufactured parts,
including fabricated integrated circuits, detection of airborne aerosols, such as nerve agents or
biotoxins, and detection of exposure to such aerosols by examining epitheUal tissues within the
respiratory tract.
AdditionaUy, the larger the size of the nucleus (compared to the microspheres in this
experiment), the higher the frequency modulation of the spectrum. Those skilled in the art wiU
appreciate that higher frequency oscillations are detected at a lower efficiency in Fourier
transform spectroscopy techniques. Therefore, in order to detect these higher frequency
osciUations, a higher resolution spectrograph is used.
Figure 7 iUustrates a generaUzed embodiment of the fLCI system shown in Figure 1 and
discussed in greater detail above. In Figure 7, a Ught source 700 (e.g. a multi-wavelength Ught) is
coupled into an fLCI system 702. Within the fLCI system 702, a sample portion 704 and a
reference portion 706 are located. The sample portion 704 includes a Ught beam and Ught
scattered from a sample. For example, the sample portion 704 may include a sample holder, a
free space optical arm, or an optical fiber. The reference portion 706 includes a Ught beam and
Ught that is reflected from a reference. For example, the reference portion 706 may include an
optical mirror. A cross-correlator 708 receives and cross-correlates Ught from the sample with
Ught from the reference.
Figure 8 illustrates another exemplary embodiment of the present invention. In Figure 8,
a method is disclosed where a first reference Ught is received 800 and a second reference Ught is
output 802. A first sample Ught is received 804 and a second sample Ught is output 806. The
second sample Ught contains Ught scattered from a sample when at least a portion of the first
sample Ught is scattered from a sample. The second reference Ught with the second sample Ught
are received and cross-correlated 808.
Figure 9 iUustrates another exemplary embodiment of the present invention. In Figure 9,
a method is disclosed where Ught is received 900 from a sample that has been iUuminated. At
least a portion of the Ught is spUt into reference Ught and sample Ught 902. At least a portion of
said reference Ught is reflected from a reference surface to yield reflected reference Ught 904. At
least a portion of the sample Ught is scattered from a sample to yield scattered sample Ught 906.
The scattered sample Ught and the reflected reference Ught are mixed 908. Spectral information
is recovered about the scattered sample Ught 910.
The foregoing example iUustrates how the exemplary embodiments of the present
invention can be modified in various manners to improve performance in accordance with the
spirit and scope of the present invention.
From the foregoing detailed description, it should be apparent that fLCI can recover
structural information with sub-wavelength accuracy from sub-surface layers based on measuring
elastic scattering properties. The simpUcity of the system makes it an exceUent candidate for
probing ceUular morphology in tissue samples and may one day serve as the basis for a
biomedical diagnostic device.
The foregoing embodiments and advantages are merely exemplary and are not to be
construed as limiting the present invention. The present teaching can be readily appUed to other
types of apparatuses. The description of the present invention is intended to be iUustrative, and
not to limit the scope of the claims. Many alternatives, modifications, and variations wiU be
apparent to those skiUed in the art. In the claims, means-plus-function clauses are intended to
cover the structures described herein as performing the recited function and not only structural
equivalents but also equivalent structures.