Self-reference holographic imaging system

Abstract

A system for recording a digital hologram of an object comprises: a coherent source intended to illuminate the object and thus produce a wave diffracted by the object; and a digital sensor intended to record the digital hologram of the object. It furthermore comprises a spatial phase modulating assembly able to produce in the plane of the sensor a plurality of duplicates of the wave diffracted by the object, the duplicates being offset from each other but overlapping partially, these duplicates forming on the sensor a digital hologram of the object, this hologram being what is referred to as a self-reference hologram.

Claims

1. A system for recording a digital hologram of an object, comprising: a partially coherent or coherent source intended to illuminate the object and thus produce a wave diffracted by the object; and a digital sensor intended to record the digital hologram of the object, characterized in that it furthermore comprises a spatial phase modulating assembly consisting of: a spatial phase modulator located between the object and the sensor, associated with: a first image-forming device able to form an image A of the object at a non-zero distance z1 from the spatial phase modulator; and a second image-forming device able to form: an image of the plane of the spatial phase modulator in a plane located at a non-zero distance z2 from a plane of the sensor; and an image A of the image A of the object, in a plane located at a distance z from the plane of the sensor, the modulating assembly being able to produce in the plane of the sensor a plurality of identical duplicates of the wave diffracted by the object, said identical duplicates being offset from each other but overlapping partially, the identical duplicates forming on the sensor a digital hologram of the object, the hologram being a self-reference hologram.

2. The system for recording a digital hologram as claimed in claim 1, wherein the spatial phase modulator is a periodic grating.

3. The system for recording a digital hologram as claimed in claim 1, wherein the modulating assembly is able to produce 4 duplicates in the plane of the sensor.

4. The system for recording a digital hologram as claimed in claim 1, wherein the source is spatially and/or temporally partially coherent.

5. The system for recording a digital hologram as claimed in claim 1, wherein the partially coherent or coherent source is a multi-wavelength source.

6. The system for recording a digital hologram as claimed in claim 5, wherein the object being intended to be illuminated in a preset direction, it comprises a multi-wavelength source with an illumination direction that is different for each wavelength.

7. The system for recording a digital hologram as claimed in claim 1, wherein the object is intended to be illuminated in transmission or in reflection.

8. The system for recording a digital hologram as claimed in claim 1, further comprising means for modifying the direction of illumination of the object and thus is able to record, for various illumination directions, one hologram per illumination direction.

9. The system for recording a digital hologram as claimed in claim 1, further comprising means for engendering a rotation of the object about a given axis, thus making it possible to record, for various angles of rotation, one hologram per angle of rotation.

10. The system for recording a digital hologram as claimed in claim 1, wherein the sensor is a CCD or CMOS camera.

11. The system for recording a digital hologram as claimed in claim 1, wherein the first image-forming device comprises a cube beam splitter.

12. The system for recording a digital hologram as claimed in claim 11, wherein the first image-forming device furthermore comprises a lens and/or a microscope objective.

13. The system for recording a digital hologram as claimed in claim 11 wherein the second image-forming device comprises the same cube beam splitter.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other features and advantages of the invention will become apparent on reading the following detailed description, given by way of nonlimiting example and with reference to the appended drawings in which:

(2) FIG. 1, described above, schematically shows an example prior-art holographic microscope;

(3) FIGS. 2a and 2b schematically show an example self-reference holographic recording system according to the invention for the case of an in-transmission configuration (FIG. 2a) and an in-reflection configuration (FIG. 2b), respectively;

(4) FIGS. 3a, 3b and 3c illustrate an example programmed SLM diffraction grating taking the form of a bi-periodic phase grating (FIG. 3a), its spatial frequency spectrum (FIG. 3b), and the orders diffracted by this grating (FIG. 3c), respectively;

(5) FIGS. 4a and 4b respectively illustrate two three-color planar (FIG. 4a) or spherical (FIG. 4b) modes for illuminating an object;

(6) FIGS. 5a, 5b and 5c illustrate an example self-reference hologram recorded by a recording system according to the invention (FIG. 5a), its spatial frequency spectrum (FIG. 5b), and the axes of the coordinate systems in which the derivatives of the optical phase are calculated (FIG. 5c), respectively;

(7) FIGS. 6a and 6b schematically show an example system for recording self-reference holograms in transmission (FIG. 6a) or in reflection (FIG. 6b), respectively, said system being equipped with scanning means in order to obtain a tomographic recording system according to the invention; and

(8) FIGS. 7a and 7b are examples of reconstructed images that are blurred (FIG. 7a) or numerically focused (FIG. 7b), respectively.

(9) From one figure to another, elements that are the same have been referenced with the same references.

DETAILED DESCRIPTION

(10) Conventionally, a system for holographic imaging of an object comprises a system for recording a hologram of the object and a system for reconstructing the object from the recorded hologram. Each of these systems is described separately below.

(11) FIG. 2a illustrates an example in-transmission configuration of a self-reference holographic microscopy recording system according to the invention. A coherent or partially coherent beam emitted by a laser source 1 or even a light-emitting diode, passes through a collimator 3 and illuminates the object A 10. A first optical imaging device, in this case a microscope objective 9 associated with a lens 18 and a polarizing cube beam splitter 16, forms on or in proximity to a spatial light modulator 15 (or SLM) the image A of the object A. The distance between the image A and the spatial light modulator 15 is denoted z1. If z10, propagation of the field A to the distance z1 in which the SLM 15 is located produces a blurred image, or more precisely the diffraction pattern of the image A in the plane of the SLM, which cannot therefore be in the Fourier plane of the image of the object, as may be seen in FIGS. 2a and 2b.

(12) A second optical imaging device, in this case the same polarizing cube beam splitter 16 associated with an afocal optical system 17, forms of the image plane A an image A on or in proximity to (upstream or downstream from) the plane of the sensor 12, at a distance z. As will be seen below, the same second optical imaging device forms of the plane B of the SLM 15 an image B, at the distance z2 from the sensor 12.

(13) If z0, the propagation of the field A to the distance z at which the sensor 12 is located produces a blurred image or more precisely the diffraction pattern of the image A on the sensor plane, the blur possibly being compensated for by numerical reconstruction in a focusing step as will be seen below.

(14) The SLM 15 may be used in reflection, as in the example in the figure, or in transmission.

(15) A preferably multi-periodic programmed SLM phase grating 15 allows A (or the diffraction pattern of A in the plane of the SLM if z10) to be reflected in a plurality of directions. This phase grating may also be obtained using a diffractive optical element (DOE), such as a diffractive holographic element coded into a photosensitive silver gelatin illuminated in order to generate a periodic grating allowing identical duplicates of the field diffracted by the object illuminated by the light source to be produced in a plurality of directions.

(16) The directions are oriented symmetrically when the grating is multi-periodic. Below, by way of example, a multi-periodic pure phase grating is used, an example bi-directional pattern of which is shown in FIG. 3a, this grating therefore being able to form duplicates of A (or its diffraction pattern) in four different directions, as shown in FIG. 3c. The positions of the spatial frequencies of this grating 15, four in our example, are illustrated by the spatial frequency spectrum 15 thereof shown in FIG. 3b. The spatial frequency spectrum 12 of the self-reference hologram recorded with this grating 15 is shown in FIG. 5b.

(17) A non-periodic grating could also be used, which would then orientate the optical field reflected by the modulator in asymmetric directions.

(18) The sensor 12 is positioned so that the image B of the plane B is formed by the second optical device 16-17, upstream (as shown in the figure) or downstream of the plane of the sensor, at the distance z2 so that, on the sensor, the duplicates are offset from each other by a non-zero amount while partially overlapping in order thus to form a self-reference hologram. The distance z2 thus allows a self-reference hologram to be formed with duplicates the characteristics of which are related to the offset generated by the distance z2, and to the variations in the wave engendered by the object 10. Adjustment of this distance z2 allows the parameters of the reconstructing method to be adjusted to obtain a better estimation of the phase and amplitude of the object 10.

(19) The plane corresponding to a distance z2 of zero corresponds to the zero-sensitivity plane for which there is no offset between the duplicates and for which, therefore, no information is obtained on the wave variations engendered by the object 10.

(20) When the SLM is not rigorously planar (when it is etched for example), the distances z, z1 and z2 are measured by considering, as the plane of the SLM, an average plane; this has no impact on the result provided that on the sensor the duplicates are offset while partially overlapping.

(21) In our example, a self-reference hologram 12 is obtained with 4 duplicates one example of which is shown in FIG. 5a, and a distance z2 is chosen allowing an adjustable overlap to be obtained between these duplicates.

(22) The polarizing cube beam splitter 16 is used to optimize, via a half-wave plate (/2) placed downstream of the light source, the amount of light incident on the modulator. A quarter-wave plate (/4) 19 advantageously adjusts the polarization of the light reflected (or transmitted) by the SLM in order to obtain an optimal transmission to the CCD sensor.

(23) The sensor 12 and the SLM 15 are preferably controlled together by a computer 20 so as to synchronize the modulation of the SLM with the recording of the holograms 12 by the sensor.

(24) An example self-reference holographic microscope configured in an in-reflection configuration is shown in FIG. 2b. Its operation is similar to the microscope in FIG. 2a. The only difference lies in the way in which the object is illuminated, in reflection in this case.

(25) A plurality of laser beams 1a, 1b, 1c, three for example, are advantageously used. Specifically, the use of three colors, namely red, green and blue, allows an RGB (red, green, blue) color image to be reconstructed without using white light. It is often paramount to observe a color image in microscopy as it also enables optical phase, and therefore relief, to be seen. Moreover, pairwise combination of the measurements of optical phase of the wave of the object (for example R-G, R-B or G-B) allows ambiguities related to phase jumps at 2 to be removed and thus the dynamic range of object profile measurements to be increased, in particular because the optical phase difference obtained by two different wavelengths engenders a synthetic wavelength of greater value, as explained in the publication by KUHN J., COLOMB T., MONTFORT F., CHARRIERE F., EMERY Y., CUCHE E., MARQUET P., DEPEURSINGE C., Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition, Optics Express, Vol. 15, p. 7231-7242, 2007. In case of phase ambiguity, it is therefore possible to record one self-reference hologram per color, or a plurality of self-reference holograms, each from two colors, engendering a synthetic color.

(26) The ability to use 3 wavelengths also makes it possible to enrich the phase information. Thus, simultaneous planar or spherical illumination in a plurality of directions, as illustrated in FIGS. 4a and 4b, respectively (in the case of spherical illumination the direction is considered to be that of the central ray) allows, possibly in a single hologram, spatial/spectral information enabling a broader coverage of the spatial frequency spectrum of the object to be obtained simultaneously. Thus, it is possible to increase the transverse and axial resolutions by a factor of 2 relative to a conventional holographic microscope using a single wavelength, as described in the publication by CHOI W., FANG-YEN C., BADIZADEGAN K., OH S., LUE N., DASARI R., FELD M., Tomographic phase microscopy, Nature Methods, Vol. 4, p. 717, 2007.

(27) These laser beams 1a, 1 b, 1c are combined with dichroic plates 14a, 14b, 14c matched to the laser sources. Each laser source is then associated with a half-wave plate 13a or 13b or 13c, and a dichroic plate located downstream of the half-wave plate. The quarter-wave plate 19 is chosen to be achromatic.

(28) The illumination provided by the light sources may also be chosen to be partially temporally coherent or partially spatially coherent, or both at the same time.

(29) Reconstruction of the image of the object is broached below.

(30) From the hologram 12 recorded by a digital sensor 12 as indicated above, its spatial frequency spectrum 12 is calculated. A discrete Fourier transform is for example used for this calculation. An example spatial frequency spectrum 12 of a self-reference hologram recorded by a CCD sensor is illustrated in FIG. 5b.

(31) On the basis of the frequency spectrum 12, filtering of the 0th order spectral spatial component and of 1st, 2nd, 3rd and 4th order spectral spatial components (four in this example because a bi-periodic grating is used) is carried out.

(32) The 0th order component allows the modulus of the complex amplitude of the field diffracted by the object to be calculated. It is extracted by filtering in the spectral plane, then by calculation of the inverse discrete Fourier transform, and calculation of the modulus of the result obtained.

(33) The calculation of the modulus of the complex amplitude of the wave front of the object in the plane of the sensor, denoted A=a.Math.exp(i), may be expressed by equation (3):
a=|TFD.sup.1{f.sub.0[TFD{H}]}|(3)
where H is the recorded hologram, a and the modulus and phase of the complex amplitude, respectively, and f.sub.0[ . . . ] represents the process of digital filtering of the 0th order component of the spatial frequency spectrum of the hologram.

(34) The other spectral components (1st, 2nd, 3rd and 4th orders) allow the derivatives of the optical phase of the complex field diffracted by the object in the plane of the sensor to be calculated. In our example, the four derivatives are calculated in two Cartesian coordinate systems represented by the systems of axes (x,y) and (x,y) shown in FIG. 5c. By calculating the inverse DFT of each filtered lobe, an image of the spatial derivative of the optical phase of the wave diffracted by the object in a given direction x, y, x or y is obtained.

(35) The calculation of the derivatives of the optical phase of the complex field, denoted A=a.Math.exp(i), diffracted by the object in the plane of the sensor may be expressed by equations (4-7):

(36) $\begin{array}{cc}\frac{4}{p_{\mathrm{slm}}}{z}_2\frac{}{x}=\arg \left({\mathrm{TFD}}^{-1}\left\{f_1\left[\mathrm{TFD}\left\{H\right\}\right]\right\}\right)& \left(4\right)\\ \frac{4}{p_{\mathrm{slm}}}{z}_2\frac{}{x}=\arg \left({\mathrm{TFD}}^{-1}\left\{f_2\left[\mathrm{TFD}\left\{H\right\}\right]\right\}\right)& \left(5\right)\\ \frac{4\sqrt{2}}{p_{\mathrm{slm}}}{z}_2\frac{}{x^{}}=\arg \left({\mathrm{TFD}}^{-1}\left\{f_3\left[\mathrm{TFD}\left\{H\right\}\right]\right\}\right)& \left(6\right)\\ \frac{4\sqrt{2}}{p_{\mathrm{slm}}}{z}_2\frac{}{y^{}}=\arg \left({\mathrm{TFD}}^{-1}\left\{f_4\left[\mathrm{TFD}\left\{H\right\}\right]\right\}\right)& \left(7\right)\end{array}$
where f.sub.n[ . . . ], n=1, 2, 3, 4, represents the process of digital filtering of the nth order component of the spectrum of the hologram (FIG. 5b) and p.sub.slm is the period (taking the form of a length along the axis in question) of the grating of the optical phase modulator.

(37) These equations do not contain correcting terms that could optionally be applied to the calculation.

(38) These spatial derivatives are integrated in order to obtain the optical phase of the wave diffracted by the object in the plane of the sensor. For this numerical integration calculation, one of the various methods proposed in the literature, and notably in the publication by FRANKOT R. T., CHELLAPPA R., A method for enforcing integrability in shape from shading algorithms, in Shape from Shading (eds.), B. K. P. Horn and M. J. Brooks, M.I.T. Press, p. 89-122, 1989, may be used.

(39) The modulus of the complex amplitude and the optical phase of the field diffracted by the object are then combined to obtain the complex wave diffracted by the object in the plane of the sensor.

(40) This reconstructing method may be applied to each wavelength used to record a self-reference hologram, or to any one of these wavelengths.

(41) This reconstructing method may be carried out with a digital system for reconstructing the image of an object, from a hologram obtained by a recording system such as described, which comprises means for implementing the reconstructing method described above.

(42) This reconstructing method may notably be carried out with a computer program product, this computer program comprising: code instructions allowing the steps of the reconstructing method to be performed. It is recorded on a computer-readable medium, such as for example the computer 20 used for synchronizing the recording and modulation. The medium may be electronic, magnetic, optical, electromagnetic or be a storage medium read using infrared light. Such media are for example semiconductor memories (random access memory RAM or read-only memory ROM), tapes, floppy or magnetic disks or optical discs (read only memory compact discs (CD-ROMs), read/write compact disks (CD-R/W) and DVDs).

(43) The holographic system may be enhanced to obtain a tomographic self-reference holography system. The tomographic aspect is for example obtained by scanning during the recording (FIGS. 6a and 6b). To do this, a rotary mirror 30, controlled by a computer 20 and synchronized with the sensor 12, is added to the architecture of the system in FIG. 2a, as shown in FIG. 6a, or added to the architecture of the system in FIG. 2b, as shown in FIG. 6b. It allows holograms to be recorded at various projection angles.

(44) According to one alternative, the tomographic aspect is obtained using means for engendering a rotation of the object about a given axis, thus making it possible to record, for various angles of rotation, one hologram per angle of rotation.

(45) An image is reconstructed for each recorded hologram, i.e. for each direction of illumination of the object. The images reconstructed for these various directions are then combined to calculate the 3D shape of the objects. The calculating method used is similar to that employed in diffractive tomography techniques.

(46) The tomography system may also be obtained using a system exerting a rotation on the object about a given axis.

(47) The fields of application are typically the following: Biological imaging: study of biological specimens such as bacteria and microorganisms (3D tomography). Material science: characterization of materials and structured surfaces. Microtechnology: quality control of microsystems such as microaccelerometers, microphones on silicon, arrays of micromirrors, etc.

(48) A self-reference holographic imaging system according to the invention was used to observe uncalibrated objects, such as 100 m-diameter glass fibers the cladding of which had been peeled off (the left-hand portion of FIG. 7b). The holographic recording device was used without the microscope objective and the lens of the first image-forming device. The hologram was recorded with non-zero values of z1 and z; the image reconstructed from the amplitude and phase measurements using the described reconstructing method was therefore blurred (see FIG. 7a). This image was focused (see FIG. 7b) numerically using the Fresnel integral calculated with the form of convolution described in the publication by LI J. C., TANKAM P., PENG Z., PICART P., Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification, Optics Letters, Vol. 34, p. 572-574, 2009.

(49) The self-reference holographic imaging system was also used to observe a square-shaped pattern etched into a glass plate. In this example, the distance z is zero. In this case, and for this object, numerical focusing of the image of the object was not necessary. The image of the object was given by the calculated amplitude and phase.