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Claims  |
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What is claimed is:
1. A device to determine the complex amplitude A.sub.s (r,z) of a signal wave coming from an object illuminated by an illumination wave, the device comprising:
detection means for detecting waves optoelectronically;
means for generating two mutually coherent waves including said illumination wave and a reference wave, the two mutually coherent waves having a phase difference .phi..sub.i (t) that is a function of time;
filtering means, positioned between the object and the detection means, for limiting to a given elementary angular field the signal wave coming from the object;
means for inducing an interference, on the detection means, between the reference wave and said signal wave coming from the object and limited to said elementary angular field, the detection means enabling a temporal sampling of the interference
pattern, resulting in an acquisition of a number N of interferograms I.sub.i (r,t), N being greater than or equal to 2, each interferogram corresponding to a distinct phase difference between the signal wave and the reference wave incident on said
detection means;
processing means for calculating, based on said interferograms, the complex amplitude A.sub.s (r,z) of said signal wave coming from the object and limited to said elementary angular field, resulting in an elementary digital hologram; and
means to sweep through a set of elementary angular fields resulting in a set of elementary digital holograms, said processing means being configured to combine said set of elementary holograms to obtain a digital hologram of the object.
2. A device according to claim 1, wherein:
N is at least 3; and
said processing means is configured to calculate the complex amplitude A.sub.s (r,z) of the signal wave from a linear combination of said interferograms.
3. A device according to claim 2, wherein:
N is equal to 4,
said N interferograms I.sub.i (r,t) correspond to distinct phase differences substantially equal to 0, .pi./2, .pi., 3.pi./2 corresponding respectively to I.sub.1 (r,t), I.sub.2 (r,t), I.sub.3 (r,t), I.sub.4 (r,t), and
said processing means is configured to calculate the in-phase part of the complex amplitude A.sub.s (r,z.sub.0) from the difference I.sub.1 (r,t)-I.sub.3 (r,t), and to calculate the in-quadrature part from the difference I.sub.4 (r,t)-I.sub.2
(r,t).
4. A device according to any one of the preceding claims, wherein said means for generating is configured to generate the reference and illumination waves having said phase difference .phi..sub.i (t) variable in stages as a periodic function of
the time, and equal to N distinct values successively.
5. A device according to one of the claims 1 to 3, wherein said means for generating is configured to generate the reference and illumination waves being offset in frequency by an offset frequency, the interference between the reference wave and
the signal wave coming from the object resulting in an interferogram I(r,t) modulated as a function of time, having a sine modulation at said offset frequency.
6. A device according to claim 1, wherein the means for generating comprise a coherent source emitting an emission wave and two acousto-optical modulators, working at predetermined frequencies on opposite orders of diffraction, in order to form
the illumination wave and the reference wave from said emission wave, wherein said emission wave and said reference wave are offset by an offset frequency.
7. A device according to claim 6, wherein
the first acousto-optical modulator intercepts the emission wave, transmits a part of the emission wave to form the illumination wave and generates a first wave offset in frequency with reference to the emission wave, by a first frequency
variation,
the second acousto-optical modulator intercepts said first frequency-offset wave and generates a second wave offset in frequency, with respect to the first wave, by a second frequency variation equal to the difference between said offset
frequency and the first frequency variation, the second wave forming the reference wave having, with reference to the illumination wave, a frequency offset equal to said offset frequency.
8. A device according to claim 1, wherein the means for generating comprises two independent laser sources phase-locked by an electronic automatic control loop and configured to generate said illumination and reference waves having said phase
difference .phi..sub.i (t).
9. A device according to claim 1, further comprising:
means to carry out apparent rotations of the object about a direction normal to a plane of the detection means, each apparent position of the object resulting in an elementary digital hologram, and
wherein said processing means is configured to combine said elementary holograms to obtain a high-resolution digital hologram of the object.
10. A device according to claim 1, wherein the detection means comprises a detector comprising a set of elementary detectors and having an integration time, an acquisition rate, and an acquisition frequency, the detector integrating said
interferograms I.sub.i (r,t) during the integration time to give N averaged interferograms I.sub.i (r,t) at said acquisition rate, corresponding to N distinct values of the phase difference between the signal wave and the reference wave, the processing
means being configured to compute a digital hologram of the object from said averaged interferograms.
11. A device according to claim 10, wherein the means for generating is configured to generate the reference and illumination waves being offset in frequency by an offset frequency substantially equal to the acquisition frequency divided by N.
12. A device according to claim 10, wherein the means for generating is configured to generate the reference and illumination waves being offset in frequency by an offset frequency substantially equal to the sum of a vibration frequency of said
object and f.sub.im /N, where f.sub.im is said acquisition frequency of said detector.
13. A device according to one of the claims 10 to 12, wherein:
said filtering means for limiting to a given elementary angular field the signal wave coming from the object comprises a filtering hole positioned in the intermediate focal plane of an afocal device intercepting the signal wave coming from the
object and formed by two objectives, the filtering hole being substantially centered on the axis of the objective located nearest to the detector; and
said means to sweep through a set of elementary angular fields comprise means to shift the filtering hole, the objective positioned facing the detector and the detector jointly and fixedly with respect to one another, in a plane perpendicular to
the direction of the axes of the objectives.
14. A device according to claim 10, wherein the means for generating is configured to generate the reference and illumination waves being offset in frequency by an offset frequency substantially equal to the sum of one of the harmonics of a
vibration frequency of said object and f.sub.im /N where f.sub.im is said acquisition frequency of said detector.
15. A device according to claim 14 wherein:
said filtering means for limiting to a given elementary angular field the signal wave coming from the object comprises a filtering hole positioned in the intermediate focal plane of an afocal device intercepting the signal wave coming from the
object and formed by two objectives, the filtering hole being substantially centered on the axis of the objective located nearest to the detector; and
said means to sweep through a set of elementary angular fields comprise means to shift the filtering hole, the objective positioned facing the detector and the detector jointly and fixedly with respect to one another, in a plane perpendicular to
the direction of the axes of the objectives.
16. A device according to claim 1, wherein:
the means for generating is configured to generate the reference and illumination waves being offset in frequency by an offset frequency,
the detection means is configured to synchronously detect the interferograms I.sub.i (r,t) at a frequency substantially equal to the offset frequency, and
wherein the processing means is directly provided by an electronic circuitry of said detection means.
17. A device according to claim 1, wherein the means for generating comprises a laser source for the emission of a wave enabling the formation, from said emission wave, of the illumination wave and the reference wave,
the object is illuminated in reflection, and
the device further comprises means for sweeping through the wavelength of the emission wave, enabling removal of ambiguities on the absolute value of the phase of the measured complex amplitude of the signal wave.
18. A system of 3D mapping of an object comprising the device according to claim 1, further comprising computation means configured to compute:
on the basis of the complex amplitude of the signal wave coming from the object and measured substantially on the plane of the detection means, the complex amplitude of the signal wave coming from the object in any plane of a free space included
between the object and the detector,
on the basis of said complex amplitude, with the object illumination wave being known, the coordinates of points of the object in said any plane, said points being at the origin of a scattering of the illumination wave. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to a digital holography device, for example used for the 3D mapping of objects, and especially moving objects, for example under vibration, and also for the measurement of optical components or the study of scattering media.
2. Description of the Prior Art
Conventional holography, invented by Dennis Gabor in 1948, underwent development particularly in the 1960s with the appearance of lasers. It is a method by which it is possible to reconstruct a 3D image of any object from a recording made on a
photographic plate called a hologram, without the assistance of any objective. Today, the applications of conventional holography are numerous. A real 3D image that is obtained during restitution gives an impressive effect of relief. It is thus
possible to obtain beautiful holograms of art objects, even fairly big ones. In science and industry, holographic interferometry enables the study of changes in the shape of a variety of elements, under different forces, such as for example the study of
fluid flows in wind tunnels.
FIGS. 1A and 1B show the recording and restitution of a conventional hologram of a source point OBJ. During the recording (FIG. 1A) a recording is made, on a photographic plate HOLO, of the variations in intensity due to the interferences of a
reference wave WREF, for example a plane wave, with a coherent wave WS scattered by the object. After development according to ordinary methods of photography, the photographic plate constitutes the hologram. During the restitution (FIG. 1B), the
hologram HOLO is illuminated by the reference wave WREF and produces two waves of diffractive light, one wave WOBJ that reconstitutes a virtual 3D image of the object and one conjugate wave WCONJ that forms a real image of the object point OJB, which is
a parasitic image to be eliminated. One way to separate the diffractive waves then consists of the use of a thick material as the holographic emulsion. Thus, a so-called volume hologram is made in which the interferences occur throughout the thickness
of the material. At restitution, the diffraction obeys the Bragg condition and only the object wave is diffracted.
However, while excellent-quality images can be reconstituted through a very high resolution of the photographic emulsions, there is no direct access to the information registered. This limits the applications of conventional holography to
qualitative observations. It is not possible for example to make a 3D mapping of an object or have access to quantitative measurements of the photometry parameters. To overcome this drawback and obtain information that can be quantitatively exploited,
new techniques of holography have appeared. These techniques replace the photographic film by a 2D optoelectronic detector, for example a CCD camera. In digital holography devices, the interferences between the reference wave and a wave scattered by
the object (the signal wave) are recorded in the plane of the detector. These two waves have come from the same laser source in order to meet the conditions of coherence. The acquisition of the interference signal by the detector makes it possible to
digitize the information and determine sampled values of the phase and amplitude of the scattered wave. These data elements may then be exploited to obtain quantitative results on the object.
However, just as in conventional holography on thin films, the field pattern of the computed signal wave simultaneously shows the desired order, namely the zero order, and a parasitic conjugate order. There is therefore a degree of indeterminacy
in the complex amplitude of the scattered wave that is to be determined. This indeterminacy has repercussions on the quality of the results obtained by this technique. For example, the mapping of the object to be established will be determined with
lack of precision.
The digital holography device according to the invention enables the full and extremely precise determination of the complex amplitude of the wave scattered by the object. This full determination is furthermore very well suited to the study of
vibrating objects for example.
SUMMARY OF THE INVENTION
For this purpose, the invention relates to a device used to determine the complex amplitude A.sub.s (r,z) of a signal wave coming from an object illuminated by a known illumination wave, the device comprising means of optoelectronic detection and
furthermore comprising:
means for the generation of two mutually coherent waves, the object illuminating wave and a known reference wave, the two waves having a known phase difference .phi..sub.i (t) that is a function of time,
means to obtain interference, on the detection means, between the reference wave and the signal wave coming from the object, the detection means enabling a temporal sampling of the interference pattern resulting in the acquisition of a given
number N of interferograms I.sub.i (r,t), N being greater than or equal to 2, each interferogram corresponding to a distinct phase difference between the signal wave and the reference wave that are incident on the detection means,
processing means making it possible, on the basis of said interferograms, to determine a digital hologram of the object corresponding to the expression, in a given plane .PI.(z), of the complex amplitude A.sub.s (r,z) of the signal wave coming
from the object.
BRIEF DESCRIPTION OF THE DRAWINGS
The advantages and characteristics of the invention shall appear from the following description, illustrated by the appended figures, of which:
FIGS. 1A and 1B are drawings that illustrate the recording and restitution of a conventional hologram (already commented upon);
FIG. 2 is a drawing of an exemplary device according to the invention;
FIGS. 3A and 3B are graphs giving a view, as a function of time, of the value of the phase difference according to two examples;
FIG. 4 is a drawing illustrating means of the device, according to a variant;
FIG. 5 is a drawing illustrating another exemplary embodiment of the device according to the invention.
MORE DETAILED DESCRIPTION
FIG. 2 is a drawing of a first exemplary digital holography device according to the invention. It is sought to determine the complex amplitude A.sub.s (r,z) of the signal wave WS.sub.2 coming from the object or <<device under test>>
DUT when it is illuminated by a known illumination wave WS.sub.1 having a given axis (zz'), for example a plane wave. The term `digital hologram of the object` herein refers to the expression of the complex amplitude A.sub.s (r,z) in a given plane
.PI.(z) perpendicular to the axis (zz') of the illumination wave of the object, where z is the coordinate of the plane .PI.(z) on the axis zz', taken with reference to an arbitrary reference, and r is the position vector of a point occurring in said
plane. The object DUT is for example a light-scattering object for which it is sought to establish a mapping, namely a surface or volume image. Or it is an optical system for which it is sought to measure the aberrations. Unlike the prior art devices,
the complex amplitude of the signal wave is determined without ambiguity on the value of the phase and is specially well applied to the study of vibrating objects.
For this purpose, the device according to the invention comprises means for the generation of two mutually coherent waves, the object illumination wave and a reference wave, the two waves having a known phase difference .phi..sub.i (t) that is a
function of time (t). Advantageously, the generation means of the device according to the invention comprise a coherent source LAS, for example a laser source, emitting an emission wave WEM, and two acousto-optical modulators AOM.sub.1 and AOM.sub.2,
working at predetermined frequencies on opposite orders of diffraction, in order to form the object illumination wave WS.sub.1 and the reference wave WREF from the emission wave WEM with the phase difference between the two waves .phi..sub.i (t). The
use of acousto-optical modulators makes it possible especially to obtain very high precision in setting up the phase difference .phi..sub.i (t). According to another variant, the illumination wave and the reference wave may be formed by two independent
laser sources that are phase-locked by an electronic automatic control loop. Exemplary modes of implementation of the phase shift between the waves shall be seen in greater detail here below.
The device furthermore comprises means BS, for example a separating plate in the case of FIG. 2, to bring about interference, on the detection means DET, between the reference wave WREF and the signal wave WS.sub.2 coming from the object. The
detection means DET in this example are formed by a mono-element detector shifted mechanically or, advantageously, they are formed by a set of elementary detectors distributed linearly or in matrix form and enabling image acquisition at a predetermined
rate f.sub.im and with a given integration time T.sub.int. The detector is for example, as shown in FIG. 2, a CCD matrix camera whose sensitive surface is substantially normal to the axis (zz') of the illumination wave.
According to the invention, the detection means enable a temporal sampling of the interference figure resulting in the acquisition of a given number N of interferograms I.sub.i (r,t), with N greater than or equal to 2, each corresponding to a
distinct phase difference between the signal wave and the reference wave that are incident on the detection means. In practice, it is advantageously possible to have N greater than or equal to 3 if it is desired, by computation, to cancel out the
measurement bias introduced by the detector. In the example of FIG. 2 which uses a detector having an integration time T.sub.int, for example a CCD camera, the interferogram I.sub.i (r,t) is averaged during the integration time, resulting in an averaged
interferogram I.sub.i (r) whose expression is given by: ##EQU1##
where t.sub.i is the instant of acquisition of the interferogram with an index i. Each averaged interferogram I.sub.i (r) corresponds to a value of the phase difference .phi..sub.i at the instant of acquisition t.sub.i. The device furthermore
comprises processing means which, on the basis of the averaged interferograms, can be used to determine a digital hologram of the object corresponding to the expression in a given plane .PI.(z), with a complex amplitude A.sub.s (r,z), of the signal wave
coming from the object. In the example of FIG. 2, the computations are performed for example by means of a microcomputer PC that is fast enough to carry out real-time computations. With the complex amplitude (A.sub.s (r,z.sub.0)) of the signal wave in
the plane of the detector being known, it is possible, by a standard operation of propagation, to determine the complex amplitude (A.sub.s (r,z)) of the signal wave at any point of the free space between the object and the detector.
According to one variant, the phase difference .phi..sub.i (t) is variable by stages as a function of time. It is periodic. Successively, during a period equal to the ratio N/f.sub.im, it takes N distinct values. This variant is illustrated by
FIG. 3A, which shows the value of the phase difference as a function of time. In this case, N is equal to four and the phase difference takes four distinct values equal to 0, .pi./2, .pi., 3.pi./2, for durations substantially equal to 1/f.sub.im.
According to a preferred variant, the reference wave WREF and the illumination wave WS.sub.1 show a frequency offset F.sub.0. The interference between the reference wave WREF and the signal wave WS.sub.2 coming from the object that results in an
interferogram I(r,t) modulated as a function of time, has a sine modulation at said frequency F.sub.0. Indeed, this variant makes it possible especially, as shall be explained hereinafter, to study vibrating objects by adjusting the offset frequency
F.sub.0 between the two waves.
For example, in the case of the study of a substantially immobile object, the offset frequency is substantially equal to the ratio .delta.f=f.sub.im /N between the acquisition frequency f.sub.im of the detector and the number N. This ratio, in
the case of a video camera for example, is a frequency with a low value (typically 10 Hz). In this case, the interferogram I(r,t) has a sine modulation, as a function of time, at said frequency .delta.f and the phase difference between the two waves is
linear by intervals as a function of time. This phase difference goes from 0 to 2.pi. on a time interval equal to 1/.delta.f, as shown in FIG. 3B. By synchronizing, for example, the acquisition of the detector with the frequency of modulation of the
interferogram I(r,t), there is obtained a sequence of N averaged interferograms I.sub.i (r) corresponding to N values .phi..sub.i of the phase difference averaged during the integration time of the detector. In FIG. 3B, N is equal to four and
.phi..sub.1, .phi..sub.2, .phi..sub.3 and .phi..sub.4 are respectively references of the four values of the averaged phase difference.
The device according to the invention also makes it possible to study vibrating objects, for example by using acousto-optical modulators, an exemplary implementation of which shall be described in detail here below. The object, having at least
one vibration frequency f.sub.v, is for example illuminated in reflection. The offset frequency F.sub.0 between the reference wave WREF and the illumination wave WS.sub.1 is then adjusted to be substantially equal to the sum of the vibration frequency
f.sub.v and the ratio .delta.f of the acquisition rate f.sub.im to the number N of interferograms (typically N=4) or to the sum of one of the harmonics f'.sub.v of the vibration frequency f.sub.v, equal to the product M.f.sub.v of said vibration
frequency with a relative integer M=0, 1, -1, 2, -2, etc., and the ratio .delta.f of the acquisition rate f.sub.im to the number N of interferograms (typically N=4). In other words, this offset frequency is:
Advantageously, since the frequency offsets of the acousto-optical modulators correspond to synthesized frequencies, programmable by means of a digital synthesizer, it is possible through the device of the invention to make measurements
throughout the vibration spectrum of the object by making the offset frequency F.sub.0 vary so that it corresponds to the fundamental frequency of the vibration f.sub.v explored and to the harmonic rank M chosen.
The device according to the invention thus makes it possible to obtain a digital demodulation of the interferogram I.sub.i (r,t) at a demodulation frequency whose magnitude is that of the rate of acquisition of the detector. For example, the
demodulation frequency is substantially equal to the ratio f.sub.im /N.
In certain cases, for example in the case of a shifting object, the interferogram may show temporal modulations at frequencies other than the difference in frequency induced by the phase modulation .phi..sub.i (t). In this case, an appropriate
demodulation frequency will be chosen.
Let us now take a more precise look at the way in which the device according to the invention, and as described in the example of FIG. 2, can be used to determine, in the plane of the detector, the complex amplitude A.sub.s (r,z.sub.0) of the
wave coming from the object, on the basis of the N interferograms. We shall consider for example the case in which the reference wave, with respect to the illumination wave, has a frequency shift F.sub.0 that is substantially equal to the ratio
.delta.f. The fields E.sub.s (r,t) and E.sub.0 (r,t) of the signal wave WS.sub.2 and reference wave WREF can be written as a function of the time t and the position vector r:
where f.sub.s is the frequency of the signal wave and f.sub.0 is the frequency of the reference wave, with f.sub.0 =f.sub.s +.delta.f. A.sub.s (r,z.sub.0) and A.sub.0 (r,z.sub.0) are the complex amplitudes respectively of the signal wave
WS.sub.2 and the reference wave WREF in the plane of the detector.
After interference between the signal wave and the reference wave, the interferogram I(r,t) obtained by the detection means DET is written as follows:
where .eta. is the quantum efficiency of the detector.
Thus, if the signal wave WS.sub.2 incident on the detector is split up into a superimposition of elementary plane waves and, for a plane reference wave WREF with a constant phase .phi..sub.0, the component of the interferogram corresponding to an
elementary plane wave of the signal wave is written as follows:
where k.sub.s and k.sub.0 are the wave vectors respectively of the elementary signal wave and the reference wave. It must be noted that this type of detection enables the measurement of the complex amplitude of the signal wave in the mode of the
reference wave. Thus, if the reference wave is linearly polarized, the signal field will be measured according to his polarization.
According to the expression (3), it is seen that the interferogram I(r,t) is modulated both spatially and temporally. To obtain information that can be exploited, it is necessary that the density of the fringes corresponding to the spatial
modulation of the interference signal should not exceed the resolution of the matrix detector constituted by elementary detectors (this is called the anti-aliasing condition). With the signal wave WS.sub.2 incident on the detector being decomposed into
a sum of elementary plane waves of wave vectors k.sub.s, the region S.sub.k0 of the space of the wave vectors that fulfills the anti-aliasing condition for a plane reference wave, with a wave vector k.sub.0, is defined by:
where e.sub.A is a factor of excitation quantifying the loss of contrast of the fringes related to the spatial integration of the detector, (k.sub.x,k.sub.y) and (k.sub.x0,k.sub.y0) are respectively the components of the wave vectors k.sub.s and
k.sub.0 along the orthogonal axes x and y of the plane of the detector that define the directions of the sides of the elementary detectors which are assumed to be substantially rectangular and have dimensions respectively d.sub.x and d.sub.y.
The condition (4) then makes it possible to define a set of vectors k.sub.s that fulfill the anti-aliasing condition for a given resolution defined by the dimensions of the elementary detectors of the detector. Thus, depending on the precision
sought, the measurement has to be limited to an elementary angular field of the signal wave WS.sub.2 incident on the detector, corresponding to a cone with aperture angles .alpha..sub.x, .alpha..sub.y around the detection of the wave vector k.sub.0 of
the reference wave incident on the detector. The dimensions .alpha..sub.x and .alpha..sub.y of this elementary angular field must be substantially lower than or equal to .lambda./2.multidot.d.sub.x and .lambda./2.multidot.d.sub.y respectively to meet
the condition (4).
Thus, when for example the object DUT is a light-scattering object and the signal wave coming from the object is split up into a superimposition of elementary plane waves of wave vectors k.sub.s, only one part of the wave vectors complies with
the anti-aliasing condition. Thus, the digital holography device according to the invention may comprise filtering means used to limit the direction of the wave vectors k.sub.s of the wave incident on the detector around that of the vector k.sub.0 in
order to strictly meet the anti-aliasing condition. Such means shall be described hereinafter.
When the anti-aliasing condition given by the equation (4) is met, the computation means of the device according to the invention can be used to determine the restriction of the hologram of the object DUT at the cone with aperture angles
.alpha..sub.x, .alpha..sub.y. The restriction is determined from the demodulation of the interferograms I.sub.i (r,t) at the frequency .delta.f for each elementary detector. For example, for N=4, the part in phase with the reference wave of the complex
amplitude A.sub.s (r,z.sub.0) may be determined from the difference I.sub.3 (r)-I.sub.1 (r) where I.sub.1 (r) and I.sub.3 (r) are the averaged interferograms obtained by the replacement, in the expression (3), of the expression 2.delta.ft respectively by
0 and .pi.. The in-quadrature part of the complex amplitude A.sub.s (r,z.sub.0) can be determined from the difference I.sub.4 (r)-I.sub.2 (r) where I.sub.2 (r) and I.sub.4 (r) are obtained by the replacement, in the equation (3), of the expression
2.delta.ft respectively by .pi./2 and 3.pi./2. These interferograms are obtained for example by adjusting the offset frequency .delta.f in such a way that this frequency must be substantially be equal to a quarter of the acquisition frequency f.sub.im
of the detector.
This computation shows how, by using the device according to the invention, it is possible to obtain a sampled measurement of the complex amplitude of the signal wave coming from the object throughout the surface of the detector. This
measurement is obtained according to a particular implementation of the device by taking the difference between the images made by the same detector at different points in time. This minimizes the possible measurement bias.
We shall now provide a more precise description, according to an exemplary embodiment, of the means of implementation of the device according to the invention in the example of FIG. 2.
The source LAS is for example a continuous helium-neon laser of some milliwatts. The detector is a CCD camera with an acquisition frequency f.sub.im of 25 Hz, comprising 752.times.582 elementary detectors with dimensions d.sub.x =10.6 .mu.m and
d.sub.y =8.6 .mu.m. The laser emits an emission wave that will enable the generation of the object illumination wave WS.sub.1 and the reference wave WREF. Advantageously, these waves are formed by means of two acousto-optical modulators AOM.sub.1 and
AOM.sub.2 working at opposite orders of diffraction, respectively .DELTA.f+F.sub.0 and .DELTA.f with typically .DELTA.f=80 MHz and in the case, | | |
