WO2015052252A1

WO2015052252A1 - Optical interferometer comprising a stationary mirror and a dynamically usable movable mirror, and method for controlling the spacing separating the mirrors of the interferometer

Info

Publication number: WO2015052252A1
Application number: PCT/EP2014/071570
Authority: WO
Inventors: Vincent Ragot
Original assignee: Sagem Defense Securite
Priority date: 2013-10-08
Filing date: 2014-10-08
Publication date: 2015-04-16
Also published as: FR3011643B1; FR3011643A1

Abstract

Interferometer comprising a holder on which a stationary mirror (1) and a movable mirror (2) are mounted parallel to each other, and means for adjusting a spacing separating the mirrors from each other, characterized in that the movable mirror is connected to the holder by elastic suspending means (4) and in that the means for adjusting the spacing separating the mirrors comprise at least three pairs of facing electrodes (5) that are connected to a control unit arranged to supply the electrodes so that they form electrostatic actuators and detectors and keep the movable mirror in position by placing the suspending means under stress. Method for adjusting such an interferometer.

Description

OPTICAL INTERFEROMETER WITH FIXED MIRROR AND MOBILE MIRROR, DYNAMICALLY USEABLE AND METHOD OF SERVICING

INTERFEROMETER MIRROR CLEARANCE

The present invention relates to an optical interferometer that can be used dynamically and to a method for controlling such an interferometer.

A Fabry-Perot interferometer comprises two blades (commonly called mirrors) having partially reflecting flat faces extending facing one another and opposed anti-reflective coated faces. The mirrors are mounted in a support to extend parallel to each other maintaining a spacing between them. A cavity is thus formed between the two mirrors in such a way that when a stream read ^¬ bituminous materials through this cavity, it will undergo multiple reflections on mirrors. At each meeting of the luminous flux with one of the mirrors, a portion of the light flux is reflected by the mirror and part of the light flux passes through the mirror ^¬ nous giving rise to a figure of multiple beam interference which consists of concentric rings . Fabry-Perot interferometers are used, for example, for separating or filtering the wavelengths of light flux by ex ^¬ plotting the portion of the luminous flux passing through the mirror.

The characteristics of the Fabry - Perot interferometer depend on the spacing and parallelism of the mirrors, as well as their reflection coefficient. The spacing of the mirrors and the angle of incidence of the luminous flux determine the resonance frequency of the interferometer. The reflection coefficient determines its fineness. The parallelism of the mirrors has a significant impact on the performance of the interferometer.

It is known to pre-set the spacing of the mirrors in order to be able to use the interferometer over a predetermined resonant frequency range. One of the mirrors is for this purpose mounted mobile on the support which is provided with micrometric screws arranged to drive the movable mirror relative to the fixed mirror and thus to vary the spacing of the mirrors.

It may be interesting to use

1 'interferometer dynamically, for example to spectrally ex ^¬ a spectral image in real time. It is then necessary to vary the analysis wavelength rapidly: the fine adjustment of the parallelism of the interferometer is then extremely complex, if not impossible, so that one seeks to move the mirrors while keeping their parallelism. To this end, one of the mirrors is generally mounted on a guiding sup ^¬ port extremely accurate, relatively expensive, bulky and low dynamic performance.

It is also known to use several interferometers housed in the same optics and tuned to different frequencies. This solution is however expensive, bulky and has a low resolution relati ^¬ tively.

An object of the invention is to provide a means for facilitating the dynamic use of Fabry-Perot type interferometers.

For this purpose, there is provided, according to the invention, an interferometer comprising a support on which are mounted a fixed mirror and a movable mirror extending parallel to one another, and means for controlling a spacing mirrors in relation to each other. The movable mirror is connected to the support by elastic suspension means. The servo-control means comprise at least three pairs of facing electrodes which are connected to a control unit arranged to feed the electrodes so that they form actuators and electrostatic detectors for holding the moving mirror in position. placing under con ^¬ constraint the suspension means. Thus, it is possible to detect the air gap between electrodes and thus the spacing between the mirrors and to modify this spacing by driving the electrodes so that they generate an electrostatic force displacing the mobile mirror by putting under stress the suspension means . The movable mirror is then maintained in a position determined by the equilibrium between the electrostatic force and the elastic restoring force generated by the suspension means. When the moving mirror is subjected to external forces, the electrostatic force is determined to also compensate for these forces if necessary.

The invention also relates to a method for controlling electrostatic transducers for adjusting the position of a mobile mirror with respect to a mobile mirror of an optical interferometer, the mobile mirror being connected by elastic suspension means to a support of which the fixed mirror is secured, the method comprising the steps of:

determining an air gap of each transducer by a capacitive measurement,

- estimate a spacing of the mirrors by calculating an average of the determined gaps,

determining and applying a control voltage for each transducer to generate an electrostatic force that puts the suspension means under stress so as to modify the estimated spacing by keeping the mirrors parallel to one another.

This method makes it possible to control the resonance frequency of the interferometer.

Other features and advantages of the invention will emerge on reading the following description of a particular non-limiting embodiment of the invention.

Reference will be made to the accompanying drawings, among which :

- Figure 1 is a schematic bottom view of an interferometer according to the invention;

FIG. 2 is a schematic side view of this interferometer;

FIG. 3 is a diagram of the electro- ^mechanical circuit of the means for adjusting the spacing of the mirrors;

FIG. 4 is a timing diagram showing the control and detection cycles;

FIG. 5 is a timing diagram detailing the detection cycle;

FIG. 6 is a schematic view of a virtual machine equivalent to the means for adjusting the spacing of the mirrors.

With reference to the figures, the interferometer of the invention is a Fabry-Perot type interferometer comprising two diopters or mirrors 1, 2 which, in a manner known per se, are partially reflective and have a relatively high reflection coefficient. The mirrors 1, 2 are mounted in a support 3 to extend parallel to each other. The mirror 1 is fixed relative to the support 3. The mirror 2 is movable relative to the support 3 and is connected to the support 3 by resilient suspension means 4 essentially characterized by their mechanical stiffness K. The mirrors 1 and 2 are spaced apart from each other. a distance e which is mechanically adjusted but which can be slightly dynamically modified, as will be described later, so as to allow a variation of the resonance frequency of the interferometer.

The mirrors 1, 2 are provided with at least three, here four pairs of electrodes facing one another. The electrodes of each pair of electrodes 5 are formed of a metal layer deposited directly on the mirror 1 and the mirror 2 respectively.

One of the electrodes of each of the four pairs of electrodes 5 is connected to digi converter ^¬ America / analog 21, 1 bit, and the other electrode is connected to an input of a charge amplifier 22. There is a digital-to-analog converter 21 by pair of electrodes 5. The charge amplifier 22 is common to all pairs of electrodes 5.

A capacitor C _ref is connected in parallel pairs of electrodes 5. The capacitor C _ref has elec trode ^¬ connected to a fifth converter Numé ^¬ America / analog 21, 1 bit, and an electrode connected to the input of the charge amplifier 22. The capacitor C _ref makes it possible to calibrate and / or compensate in real time the gain errors due to the electronics in order to reduce the relative instabilities of the air gap to the relative instabilities of the capacitor C _ref .

Each digital-to-analog converter 21 is produced by means of analog switches allowing the application of either a zero voltage or a common reference voltage V _ref as a function of a command E originating from the control unit. 10 (the output voltage of the digital-to-analog converters is denoted V in FIG. 3, with an index 1 to 4 for each of the pairs of electrodes 5 and with an index 5 for the capacitance C _ref ).

The charge amplifier 22 is looped by a capacitor C _b and measures the load variations caused by the voltages Vi to V ₅ .

The charge amplifier 22 has an output (providing a signal yi) connected to a filter 23 (providing a signal y2), which is an anti-aliasing filter which reduces the bandwidth of the signals before they are digitized by an analog / digital converter. 24 (providing a signal y). The digital-to-analog converters 21 and the analog / digital converter 24 are connected to a control unit 10 arranged to drive the electrodes so that they form four electrostatic transducers constituting alternately:

electrostatic detectors for estimating the air gap, and therefore the spacing e, and its anisotropies through the measurement of the capacitances at each pair of electrodes 5;

- Electrostatic actuators to control the adjustment of the gap, and therefore the gap e, by applying four control voltages.

The pairs 5 of facing electrodes connected to the control unit 10 thus form actuators and electrostatic detectors constituting means for adjusting the position of the moving mirror 2 with respect to the fixed mirror 1, and therefore constituting means for adjustment of the spacing e of the mirrors 1, 2, puts ^¬ as stress means suspensions 4.

The electrostatic transducers formed by the pairs of electrodes opposite are characterized by their respective surfaces and air gaps si and β _ί and are assimilated to capacitors planes of value:

where ε denotes the dielectric permittivity of the gas separating the mirrors 1, 2.

The method of the invention consists in controlling the spacing e of the mirrors 1, 2 which defines the resonance frequency of the optical interferometer while minimizing the defects of parallelism affecting the quality of the interferometer.

To ensure the parallelism between two planes, it suffices to have three transducers simul- 7

temporarily or sequentially the functions of detectors and actuators.

The embodiment shown here uses advan ^¬ tageusement four transducers instead of three to take advantage of symmetry properties favorable to the re ^¬ duction of gain between transducers anisotropics.

Thus, the capacity measurement of the four ^trans¬ ductors provides redundant information that allows the estimation of the three quantities of interest, namely:

the average gap, equal to the distance e, obtained by calculating an average of the air gaps of the pairs of electrodes 5,

the roll (or the degree of rotation of the mirror 2 around a predetermined axis A1, which is here called roll axis),

the pitch (or the degree of rotation of the mirror 2 about a predetermined axis A2 which is here called the pitch axis).

The pairs of electrodes 5 are here arranged at the vertices of a square and the axes A1 and A2 extend along the diagonals of this square so that two pairs of electrodes 5 are on the axis Al and two pairs of electrodes 5 are on the axis A2. The roll will therefore be equal to the difference between the air gaps of the pairs of electrodes 5 located on the axis A2 and the pitch will be equal to the difference between the air gaps of the pairs of electrodes 5 located on the axis A1.

Incidentally, the redundancy can be used to partially estimate the curvature of the moving mirror 2, the fixed mirror 1 being assumed to be plane.

The application of four adequate control voltages applied to the four transducers generates an electrostatic force allowing the adjustment of the three quantities of interest. The electrostatic force, which is only attractive, must be sufficient to under constraint the suspension means 4 so as to be able to counter the effect of the accelerations and forces ^¬ venerational applied to the device regardless of the direction thereof.

Finally, to minimize gain anisotropies and to simplify the electronic scheme, an all-or-nothing control strategy is used. This operating mode assumes that the air gap modulation caused by the applied voltages is low. This property is obtained thanks to the strong amor ^¬ tissement caused by the gas film separating the mirrors 1, 2 which naturally filters the high frequency components of the applied voltages as accelerations ^¬ rations. This reduces the regulator bandwidth to a few Hertz.

The control unit 10 (associated with an oscillator not shown) is a digital circuit which sequences the operations in time and performs all the calculations.

The operation is periodically clocked at a frequency F _e said real-time frequency according to the timing diagram of FIG. 4.

With regard to the actuation, each command T _ci is characterized by its duty cycle ηι at the cycle time T _e which determines its average efficiency:

The "frequency" and the number of "periods" (arbitrarily set at 2 on the timing diagram) of the excitation signal are adjustment variables allowing optimization of the signal-to-noise ratio.

By neglecting the bandwidth limitations of the electronics, the product of the gains of the antireflection filter 23 and the analog / digital converter 24 can be likened to a gain denoted by:

where R (the reset signal of the charge amplifier 22) is 0 or 1, where Qo denotes the amount of charge injected by the switch of the digital-to-analog converters 21 during its opening, where y ₀ is the offset of the 22 + filter amplifier + 23 + analog / digital converter 24.

As regards the detection, the system is clocked by a so-called high oversampling clock characterized by its period T _s . To simplify the chro ^¬ nogramme of Figure 5, the temporal quantization related to T _s is not shown: for example the timing diagram of Figure 5 shows only the envelope of the digital signals associated with analog signals of the timing diagram of Figure 4 (period T _d ).

The reduced durations characterizing the timing are noted:

To easily manage the timings, it is preferable to choose a sufficiently large oversampling frequency in front of the real-time frequency (typically T _s = 10 s and T _e = 10 ms). The output y of the analog / digital converter 24 is demultiplexed, demodulated and accumulated in the same operation by the control unit 10 to obtain the signal ydmi:

Born

1

d, = -1, 0 or + 1

The accumulation is reset at each real time period by the reset signal R of the charge amplifier 22.

The high and low durations of the excitation being chosen equal so as to reject the biases Q ₀ and yo during the demodulation, we obtain (with i varying from 1 to 4 for the transducers): ydm, = m - - Î - V _ref

ydm ₅ = m -? - - C _re V _ref

To overcome the uncertainties related to a, C _b and V _ref , just calculate the ratio: ydm; ε - If C _ref

The estimate of the gap depends thus only:

the dielectric permittivity ε of the gas separating the mirrors,

- surfaces If mirrors,

- the reference capacity C _ref .

Moreover, the differential errors are only affected by the surface anisotropies of the electrodes.

The four transducers observed perpendicular to the mirror are numbered from 1 to 4 in the clockwise direction. The observation and control vectors are then formed in the following manner, ei (with i varying from 1 to 4) designating the estimated gaps for each of the four transducers:

e =

In order to better control the gain anisotropies between the different transducers of the same mirror, the solution adopted uses four symmetrical detectors / actuators.

This hyperstatic solution can lead to unbearable stress on the mirror.

This problem is solved by simply bringing the four-input and four-output physical system back to a three-input, three-output virtual system that is better suited as needed.

For this, the servocontrol is performed according to the block diagram of FIG.

It then returns to matrices A and B to reduce the apparent size of the system.

The matrix A is chosen so that the output vector consists of:

- the average air gap (index m).

- roll (index r).

pitching (index t).

The matrix A then has the following form:

This makes it possible to go from the estimated physical gaps to the virtual gaps e _v : e "= A · e

An estimate of a distortion or curvature of the mirror can be obtained by adding to A a fourth line of the form [1 1 -1 -1]. Theoretically, the fourth compo ^¬ health of the virtual air gap e _v, denoted E _c must be natu ^¬ ACTUALLY near zero, as this corresponds to a con ^¬ minimum strain energy figuration.

The real system with four inputs and four outputs is to a large extent assimilable to four independent subsystems but identical to each other, the transfer matrix H (p) is then reduced to a scalar:

β = Η (ρ) · η

We then impose on the virtual system a behavior identical to that of the real system:

e _v = Η (ρ) · η _ν -> Α · β = Η (ρ) · η _ν → Β · Α · β = Η (ρ) · Β · η _ν = Η (ρ) · η

This requires:

1 0

0 1

B = I ■ A → B = A ^T · (A · A ^T V ¹ = B = - ·

- 1 0

0 -1

The numerical correctors C _m (z), C _r (z) and C _t (z) are clocked at T _e , they are synthesized according to the electromechanical characteristics of the physical system and the desired dynamics in closed loop.

The control voltages are determined by the control unit 10 from average air gap, roll and pitch instructions.

The control voltages of the transducers are preferably equal to the same reference voltage. The excitation of the capacitances by the same reference voltage contributes to the control of the gain anisotropy in detection.

The structure of the interferometer has not been detailed except for the parts thereof in connection with the invention. To improve the accuracy of 1 'interferometer, this structure is designed in a manner known per se to compensate at least in part the disturbances induced by:

- the thermal which involves long time constants, it intervenes in the quasi-static dimensioning.

- the mechanical vibrations which determine the need in terms of bandwidth.

the electromagnetic disturbances (the part of the electromagnetic disturbances against which the control unit 10 is impotent will be taken into account during the design of the interferometer by pre ^¬ for example shielding, short links ...).

Of course, the invention is not limited to the embodiments described but encompasses any variant within the scope of the invention as defined by the claims.

In particular, the adjustment means may comprise three, four or more transducers. The ac- tionneurs and detectors may be separate TRANSDUC ^¬ tors.

The transducers can be mounted directly on the mirrors or on integral parts thereof.

The transducers can be controlled in all or nothing or in continuous modulation.

Claims

1. Interferometer comprising a support (1) on which are mounted a fixed mirror and a movable mirror extending parallel to one another, and means for controlling a spacing of the mirrors relative to each other. the other, characterized in that the movable mirror is connected to the support by elastic suspension means ^¬ tick and in that the control means 1 spacing mirrors comprise at least three pairs of electrodes opposite which are connected to a control unit arranged to supply the electrodes so that they form actuators and elec ^¬ trostatic detectors to maintain in position the movable mirror by putting under stress the suspension means.

An interferometer according to claim 1, wherein three pairs of electrodes form the actuators and three pairs of electrodes form the detectors.

3. Interferometer according to claim 1, wherein the control unit is arranged to drive the three pairs of electrodes so that each of them alternately form one of the actuators and one of the detectors.

4. Interferometer according to claim 1, wherein the pairs of electrodes are four in number and are symmetrically arranged relative to the mirrors.

An interferometer according to claim 1, wherein one of the electrodes of each pair of electrodes is connected to a digital-to-analog converter and the other of the electrodes each pair of electrodes is connected to an input of a digital amplifier. This charge is common to all pairs of electrodes and is terminated by a capacitor, the charge amplifier having an output connected via an anti-aliasing filter to an analog-to-digital converter.

6. Interferometer according to claim 5, wherein a reference capacitor has a first elec ^¬ trode connected to a digital / analog converter and a second electrode connected to the input of the charge amplifier.

7. Interferometer according to claim 1, wherein the electrodes are each formed of a metal layer deposited directly on the mirror.

8. transducers control method ^¬ tatiques appliances for adjusting the position of a movable mirror with respect to a fixed mirror of an optical interferometer, the movable mirror being connected by means of elastic suspension to a support which is integral the fixed mirror, the method comprising the steps of:

determining an air gap of each transducer by a capacitive measurement,

- Determining and applying a control voltage for each transducer to generate an electrostatic force stressing the suspension means so as to modify the estimated spacing by keeping the mirrors parallel to each other.

The method of claim 8, wherein the control voltages are applied in all or nothing.

10. The method of claim 8, wherein the transducers are four in number corresponding to a real system hyperstatic four inputs and four outputs, and a servo transducers is performed by bringing the real system to a virtual system with three inputs and three outputs.

11. The method of claim 8, comprising the step of estimating a deformed mobile mirror from the determined gaps.

The method of claim 8, wherein the control voltages of the transducers are equal to the same reference voltage.