Method for simultaneous amplitude and quantitative phase contrast imaging by numerical reconstruction of digital holograms

Claims

What is claimed as new and desired to be secured by letters patent of the United States is:

1. A method for simultaneous amplitude and quantitative phase contrast imaging of a specimen by numerical reconstruction of a digital hologram of the specimen comprising the following steps:

a) providing a hologram of the specimen using an illumination source, wherein the hologram of the specimen results from interference between two waves issued from the illumination source, one of the two waves, named an object wave, having interacted with the specimen, and another of the two waves, called a reference wave, having not interacted with the specimen;

b) acquiring an image of the hologram by an image acquisition system;

c) digitizing the image of the hologram by an image digitizer in order to produce the digital hologram;

d) transmitting the digital hologram to a computer or to a processor;

e) determining and defining an analytical expression of the reference wave and determining and defining a first group of reconstruction parameters as reference wave parameters;

f) computing a first array of complex numbers as a digital reference wave, wherein said computing the first array of complex numbers step is performed on a basis of the analytical expression of the reference wave and on a basis of the reference wave parameters;

g) computing a multiplication of the digital hologram and the digital reference wave in order to create a digital transmitted wavefront in a hologram plane;

h) determining and defining a second group of reconstruction parameters as a reconstruction distance;

i) computing a propagation of the digital transmitted wavefront from the hologram plane to an observation plane in order to calculate a digital reconstructed wavefront in the observation plane wherein said computing the propagation of the digital transmitted wavefront step is performed by a numerical calculation of an integral describing a diffraction of waves in a scalar approximation and wherein a distance between the hologram plane and the observation plane is defined by the reconstruction distance;

j) determining and defining an analytical expression of a phase aberration and determining and defining a third group of reconstruction parameters as aberration correction parameters;

k) computing a second array of complex numbers as a digital phase mask which represents a complex conjugate of a phase aberration function in the observation plane, said computing the second array of complex numbers step being performed on a basis of the analytical expression of the phase aberration and on a basis of the aberration correction parameters;

l) digitally correcting the phase aberration by computation of multiplication between the digital reconstructed wavefront in the observation plane and the digital phase mask in order to obtain a digital corrected reconstructed wavefront in the observation plane;

m) computing square of a modulus of the digital corrected reconstructed wavefront in the observation plane in order to obtain an amplitude contrast image of the specimen;

n) computing an argument of the digital corrected reconstructed wavefront in the observation plane in order to obtain a quantitative phase contrast image of the specimen; and

o) adjusting the reconstruction parameters comprising adjusting of:

the reconstruction distance, the reference wave parameters, and the aberration correction parameters.

2. A method for simultaneous amplitude and quantitative phase contrast imaging of a specimen by numerical reconstruction of a digital hologram of the specimen comprising the following steps:

a) providing a hologram of the specimen using an illumination source, wherein the hologram of the specimen results from interference between two waves issued from the illumination source, one of the two waves, named an object wave, having interacted with the specimen, and another of the two waves, called a reference wave, having not interacted with the specimen;

b) acquiring an image of the hologram by an image acquisition system;

c) digitizing the image of the hologram by an image digitizer in order to produce the digital hologram;

d) transmitting the digital hologram to a computer or to a processor;

e) determining and defining a first group of reconstruction parameters as a reconstruction distance;

f) computing a digital reconstructed wavefront in an observation plane by computation of a diffraction pattern of the digital hologram, wherein said computing the digital reconstructed wavefront step is performed by a numerical calculation of an integral describing a diffraction of waves in a scalar approximation and wherein a distance between a hologram plane and the observation plane is given by the reconstruction distance;

g) determining and defining an analytical expression of the reference wave and determining and defining a second group of reconstruction parameters as reference wave parameters;

h) computing a first array of complex numbers as a digital reference wave, wherein said computing the first array of complex numbers step is performed on a basis of the analytical expression of the reference wave and on a basis of the reference wave parameters;

i) computing a multiplication of the digital reconstructed wavefront in the observation plane and the digital reference wave in order to correct a phase distortion induced by the reference wave in the observation plane to provide a digital corrected reconstructed wavefront in the observation plane;

j) determining and defining an analytical expression of a phase aberration and determining and defining a third group of reconstruction parameters as aberration correction parameters;

k) computing a second array of complex numbers as a digital phase mask which represents a complex conjugate of a phase aberration function in the observation plane, said computing the second array of complex numbers step being performed on a basis of the analytical expression of the phase aberration and on a basis of the aberration correction parameters;

l) digitally correcting the phase aberration by computation of multiplication between the digital reconstructed wavefront in the observation plane and the digital phase mask in order to obtain the digital corrected reconstructed wavefront in the observation plane;

m) computing a square of a modulus of the digital corrected reconstructed wavefront in the observation plane in order to obtain an amplitude contrast image of the specimen;

n) computing an argument of the digital corrected reconstructed wavefront in the observation plane in order to obtain a quantitative phase contrast image of the specimen; and

o) adjusting the reconstruction parameters comprising adjusting of:

the reconstruction distance, the reference wave parameters, and the aberration correction parameters.

3. A method according to claims 1 or 2 wherein said reconstruction parameters comprise a set of constants being supplied to a first program which executes the numerical reconstruction of the digital hologram and wherein said constants are supplied to the computer which executes the first program by one of inputting by a human operator the reconstruction parameters and initiating by the human operator execution of the first program, inputting by a measuring apparatus the reconstruction parameters and initiating by the measuring apparatus execution of the first program, and inputting by a second program the reconstruction parameters and initiating by the second program execution of the first program.

4. A method according to claims 1 or 2 wherein said hologram is provided by an off-axis hologram, wherein directions of propagation of the reference and object waves are not parallel at incidences of the reference and object waves on plane where the hologram is created, whereby an acquisition and reconstruction of the off-axis hologram allows a separation of a zero order of diffraction of a twin image and a real image which can be observed separately in the observation plane.

5. A method according to claims 1 or 2 wherein said hologram is an off-axis hologram and wherein said digital hologram is processed, before said step 3), by an image processing method comprising the steps of:

computing a two dimensional discrete Fourier transform of the digital hologram;

locating, in the two dimensional discrete Fourier transform of the digital hologram, spatial frequencies which correspond to at least one of a real image and a twin image;

computing a multiplication of the two dimensional discrete Fourier transform of the digital hologram by a 2D function which eliminates or attenuates the spatial frequencies that correspond with at least one of the real image and the twin image; and

computing a discrete inverse Fourier transform.

6. A method according to claims 1 or 2 wherein said hologram is spatially filtered by applying an optical method, including a 4-f system and a mask designed for high-pass filtering.

7. A method according to claims 1 or 2 wherein said integral describing the diffraction of waves in the scalar approximation is a Fresnel-Kirchhoff integral, a Rayleigh-Sommerfeld integral, a Fresnel integral or an approximation of the Fresnel-Kirchhoff integral, the Rayleigh-Sommerfeld integral, or the Fresnel integral.

8. A method according to claims 1 or 2 wherein said numerical calculation of the integral describing the diffraction of waves in the scalar approximation is performed by a numerical calculation of a discrete formulation of a Fresnel integral called a discrete Fresnel transform which is computed using the following equations: ##EQU16##

where F(m.DELTA..xi.,n.DELTA..eta.) denotes the discrete Fresnel transform of a discrete function f(k.DELTA.x,l.DELTA.y) and is a third array of complex numbers, f(k.DELTA.x,l.DELTA.y) is a fourth array of complex numbers or an array of real or integer numbers, .lambda. is a wavelength of the illumination source, d.sub.R is the reconstruction distance, A=exp(i2.pi./.lambda.)/(i.lambda.d.sub.R) is a complex constant and k,l,m,n are integers,

where a product N.sub.x xN.sub.y represents a number of elements of F(m.DELTA..xi.,n.DELTA..eta.) and of f(k.DELTA.x,l.DELTA.y), DFT is a discrete Fourier transform operator which is calculated using a Fast Fourier Transform (FFT) algorithm, .DELTA.x and .DELTA.y are sampling intervals in the hologram plane and, when the image acquisition system and said image digitizer produce a rectangular image, N.sub.x lines along an 0x axis and N.sub.y lines along an 0y axis are contained in the rectangular image, and ##EQU17##

where L.sub.x and L.sub.y are dimensions of the digital hologram along respectively the 0x and the 0y axis, and wherein sampling intervals in the observation plane 0.xi..eta.) are defined by .DELTA..xi. and .DELTA..eta., said sampling intervals in the observation plane being related to .DELTA.x and .DELTA.y, to N.sub.x and N.sub.y and to the reconstruction distance by the following relations: ##EQU18##

.

9. A method according to claims 1 or 2 wherein said hologram is provided by a set-up which provides a Fresnel hologram wherein the numerical calculation of the integral describing the diffraction of waves in the scalar approximation is performed by numerical calculation of a Fresnel transform.

10. A method according to claims 1 or 2 wherein said hologram is provided by a set-up which produces Fourier holograms and wherein said numerical calculation of the integral describing the diffraction of waves in the scalar approximation is performed by a Fourier transformation.

11. A method according to claims 1 or 2 wherein said illumination source produces at least one of electromagnetic radiation and a photon density wave and one of an acoustic wave, a mechanical wave and a pressure wave.

12. A method according to claims 1 or 2 wherein said reference wave is provided by a device which allows an adjustment of a length of a path of the reference wave.

13. A method according to claims 1 or 2 wherein the object wave is produced by an assembly of optics components which produces a magnified or a demagnified image of the specimen.

14. A method according to claims 1 or 2 wherein said acquiring the image of the hologram is performed after transmission of the hologram through space, by one or more lenses or with an endoscope constituted of at least one of Hopkins relay optics and gradient index rods and optical fibers and bundles of the optical fibers and multicore fibers.

15. A method according to claims 1 or 2 wherein said image digitizer is an apparatus which transforms the image of the hologram into a form which can be transmitted to said computer or mid processor.

16. A method according to claims 1 or 2 wherein said analytical expression of the reference wave is a two-dimensional complex function.

17. A method according to claims 1 or 2 wherein said reference wave parameters are parameters which are involved in the analytical expression of the reference wave and are used for a definition of the digital reference wave.

18. A method according to claims 1 or 2 wherein, if said reference wave is a plane wave of given wavelength .lambda., the digital reference wave R.sub.D k.DELTA.x,l.DELTA.y) is computed using the following expression: ##EQU19##

where k.sub.x, k.sub.y and A.sub.R are the reference wave parameters K and k, are two real numbers which represent components of a normalized wavevector, a direction of propagation of the plane wave, A.sub.R is a third real number which represents an amplitude of the reference wave, k, l are integers and .DELTA.x and .DELTA.y are sampling intervals in the hologram plane.

19. A method according to claims 1 or 2 wherein, if said reference wave is a spherical wave of given wavelength .lambda., the digital reference wave R.sub.D k.DELTA.x,l.DELTA.y) is computed using the following expression: ##EQU20##

where (x.sub.R, y.sub.R, z.sub.R) are coordinates of a point source with respect to a center of the hologram plane 0xy and A.sub.R is an amplitude at the point source k, l are integers, and .DELTA.x and .DELTA.y are sampling intervals in the hologram plane.

20. A method according to claims 1 or 2 wherein said digital reference wave is calculated using a mirror as a combination of Zernicke polynomials.

21. A method according to claims 1 or 2 wherein a phase of said digital reference wave is measured using an interferometric method with a mirror as a reference object.

22. A method according to claims 1 or 2 wherein said reconstruction distance is adjusted in order to fit approximately distance or a length of an optical path between the specimen and a plane where the hologram is created.

23. A method according to claims 1 or 2 wherein, if said object wave is provided by magnification or demagnification optics, said reconstruction distance is adjusted in order to fit approximately a distance between the image of the specimen and a plane where the hologram is created.

24. A method according to claims 1 or 2 wherein, if said object wave is provided by magnification or demagnification optics, the phase aberration appears in the observation plane and, as a consequence, said digital reconstructed wavefront in the observation plane is corrected in order to allow a corrected reconstruction of said quantitative phase contrast image of the specimen.

25. A method according to claims 1 or 2 wherein said analytical expression of the phase aberration is a two-dimensional function of complex numbers defined in such a way that said digital phase mask closely matches the complex conjugate of the phase aberration function in the observation plane.

26. A method according to claims 1 or 2 wherein said aberration correction parameters are parameters which are involved in the analytical expression of the phase aberration with the aberration correction parameters being adjusted in such a way that multiplication of said digital reconstructed wavefront in the observation plane by said digital phase mask corrects approximately the phase aberration in the observation plane.

27. A method according to claims 1 or 2 wherein, if said object wave is provided by a single spherical lens as magnification or demagnification optics, said phase aberration C(m.DELTA..xi.,n.DELTA..eta.) can be computed using the following expression: ##EQU21##

where .lambda. is a wavelength of the illumination source, .DELTA..xi. and .DELTA..eta. are sampling intervals in the observation plane m,n are integers, D is an aberration correction parameter which depends on a specimen-lens distance d.sub.o and on a lens-image distance d.sub.i ##EQU22##

28. A method according to claims 1 or 2 wherein said phase aberration is calculated using a combination of Zernicke polynomials.

29. A method according to claims 1 or 2 wherein said phase aberration is measured using an interferometric method with a mirror as a reference object.

30. A method according to claims 1 or 2 wherein said steps j), k) and l) are suppressed if appear in the observation plane.

31. A method according to claims 1 or 2 wherein said adjusting the reconstruction parameters is performed in such a way to reconstruct a real image of the specimen.

32. A method according to claims 1 or 2 wherein said adjusting the reconstruction parameters is performed in such a way to reconstruct a twin image of the specimen.

33. A method according to claims 1 or 2 wherein said adjusting the reconstruction parameters is performed by measuring associated physical quantities on a setup used for creating the hologram with said measuring associated physical quantities being performed by an apparatus which communicates with the computer.

34. A method according to claims 1 or 2 wherein said adjusting the reconstruction parameters is performed interactively by executing several times the numerical reconstruction of the digital hologram in a loop and modifying the reconstruction parameters in order to improve at least one of image quality and plausibility, wherein said loop is repeated until the reconstruction parameters have reached optimal values.

35. A method according to claims 1 or 2 wherein said adjusting the reconstruction parameters is performed by at least one of translating ad rotating at least one of the specimen and components of a set-up used for creation of the hologram.

36. A method according to claims 1 or 2 wherein said adjusting the reconstruction parameters is performed by analyzing the digital hologram with a numerical method.

37. A method according to claims 1 or 2 wherein a phase of said digital reference wave and phase of said digital phase mask are measured experimentally using the specimen of a known phase distribution and subtracting the known phase distribution of the specimen from a reconstructed phase distribution without correction of the phase aberration and without multiplication by the digital reference wave.

38. A method according to claims 1 or 2 wherein said amplitude contrast image and said quantitative phase contrast image are reconstructed simultaneously and are two different representations of the specimen at a same instant.

39. A method according to claims 1 or 2 wherein the quantitative phase contrast image of the specimen is used for quantitative measurements of at least one of optical properties and structural information including, refractive index measurements or thickness measurements.

40. A method according to claims 1 or 2 wherein said quantitative phase contrast image is used for measurement of a topography of the specimen.

41. A method according to claims 1 or 2 wherein said quantitative phase contrast image is used for surface profilometry.

42. A method according to claim 1 wherein said steps e), f), g), j), k), l) and o) are suppressed if the quantitative phase contrast image of the specimen is not desired.

43. A method according to claim 2 wherein said steps g), h), i), j), k), l) and o) are suppressed if the quantitative phase contrast image of the specimen is not desired.

44. A method according to claim 1 or 2 wherein said image acquisition system provides real-time image acquisition and wherein the numerical reconstruction of the digital hologram is performed instantaneously after the real-time image acquisition in order to allow real-time amplitude and quantitative phase contrast imaging.

45. A method according to claim 1 or 2 wherein said illumination source is a low-coherence or a pulsed illumination source and wherein the hologram is created with a light that is reflected by a selected slice inside semi-transparent said specimen where a depth of the selected slice is modified and wherein said reference wave is provided by means which allow an adjustment of a length of a path of the reference wave.

46. A method according to claim 1 or 2 wherein said object wave and said reference wave have a same wavelength in order to perform a homodyne detection of the hologram.

47. A method according to claims 1 or 2 wherein at least one of said reference wave and said object wave are provided by means which modify at least one of a wavelength and an amplitude and a frequency and a polarization and a phase and an optical path length of said reference and said object waves.

48. A method according to claims 1 or 2 wherein at least one of said reference wave and said object wave are provided by means which produce different wavelengths or frequencies for the object wave and for the reference wave, in order to achieve heterodyne detection of the hologram.

49. A method according to claims 1 or 2 wherein said hologram is provided by a set-up designed to create an in-line or Gabor hologram.

50. A method for simultaneous amplitude and quantitative phase contrast imaging of a specimen by numerical reconstruction of a set of digital holograms of the specimen comprising the following steps:

a) providing a set of holograms of the specimen using an illumination source;

b) acquiring a set of images of the set of holograms by an image acquisition system;

c) digitizing the set of images of the set of holograms by an image digitizer in order to produce the set of digital holograms;

d) processing each digital hologram of the set of digital holograms following steps d) to o) of claims 1 or 2, in order to product a set of amplitude contrast images of the specimen and a set of quantitative phase contrast images of the specimen.

51. A method according to claim 50 wherein said set of holograms of the specimen recorded in a reflection geometry for different orientations of the specimen and wherein information content of reconstructed said amplitude contrast images and reconstructed said quantitative phase contrast images, corresponding to the different orientations of the specimen, is used in order to build a computed three dimensional replica of the specimen.

52. A method according to claim 51 wherein said specimen include several distinct objects located at different locations in a three dimensional volume.

53. A method according to claim 50 wherein said set of holograms of the specimen recorded in a transmission geometry for different orientations of the specimen and wherein information content of reconstructed said amplitude contrast images and reconstructed said quantitative phase contrast images corresponding to the different orientations of the specimen is used in order to build a three dimensional computed tomography of the specimen.

54. A method according to claim 50 wherein said set of holograms of the specimen are recorded for different wavelengths of the illumination source or with different illumination sources of different wavelengths and wherein information content of reconstructed said amplitude contrast images and reconstructed said quantitative phase contrast images corresponding to the different wavelengths are used for spectroscopic investigations of three-dimensional said specimen.

55. A method according to claim 50 wherein said set of holograms of the specimen are recorded for different wavelengths of the illumination source or with different illumination sources of different wavelengths and wherein data corresponding to different holograms are combined to yield a three-dimensional conformation of the specimen by computing a 3D Fourier transform or a combined 1D Fourier 2-D Fresnel transform of the set of holograms.

56. A method according to claim 50 wherein said specimen is semi-transparent and wherein said set of holograms of the specimen are recorded in a transmission geometry for different wavelengths of the illumination source or with different illumination sources of different wavelengths and wherein a model describing a behavior of a refractive index as a function of a wavelength is used in order to measure at least one of a three-dimensional distribution of the refractive index and a thickness of the specimen, on a basis of data corresponding to different holograms corresponding to different wavelengths.

57. A method according to claim 50 wherein said set of holograms of the specimen are recorded with different off-axis geometries to include different orientations of a mirror which reflects a reference wave whereby reconstructed images will appear in different locations of an observation plane and represent the specimen at different instants.

58. A method according to claim 50 wherein said set of holograms of the specimen are recorded with different polarization states of a reference wave, and wherein reconstructed images corresponding to the different polarization states of the reference wave are used to investigate birefringence or dichroism or scattering behavior of the specimen.

59. A method according to claim 50 wherein said set of holograms of the specimen are recorded at different instants and wherein reconstructed images corresponding to the different instants are used in order to do at least one of the following to build a computed video animation and monitor a deformation of the specimen and monitor a movement of the specimen and monitor a modification of optical properties of the specimen.

60. A method according to claim 59 wherein said set of holograms are recorded at the different instants with a same or with a different said specimen and wherein the reconstructed images corresponding to the different instants are used in order to build the computed video animation.

61. A method according to claim 59 wherein said specimen include several distinct objects located at different locations in a three dimensional volume.

62. A method according to claim 50 wherein said set of holograms of the specimen are recorded using several image acquisition systems and an appropriate set-up wherein corresponding reconstructed images represent the specimen with different direction of observation at different instants.

63. A method according to anyone of claims 1 or 2 wherein said specimen includes several distinct objects located at different locations in a three dimensional volume.

64. A method according to claims 1 or 2 wherein said hologram is created using a plurality of reference waves.

65. A method according to claims 1 or 2 wherein said hologram is created using one reference wave and a plurality of object waves.

66. A method according to claims 1 or 2 wherein said hologram is created using a plurality of reference waves and a plurality of object waves.

67. A method according to claims 1 or 2 wherein said hologram is created using two reference waves of crossed polarization and different directions of propagation and one object wave.

68. A method according to claims 1 or 2 wherein said hologram is created using one reference wave and two object waves of crossed polarization and different directions of propagation.

69. A method according to claims 1 or 2 wherein said hologram is created using two reference waves of crossed polarization and different directions of propagation and two object waves of crossed polarization and different directions of propagation.

70. A method according to claims 1 or 2 wherein a synchronized series of object waves interferes with a series of reference waves to form a single hologram, reconstructed amplitude and phase contrast images yielding an evolution in time of an object at different locations of the observation plane to allow for study of object changes under modification of an external parameter in a rapid time sequence.

71. A method according to claims 1 or 2 comprising an application of digital image processing methods before numerical reconstruction of the digital hologram wherein said digital image processing methods are applied, before said step e), to the digital hologram.

72. A method according to claims 1 or 2 comprising an application of digital image processing methods after numerical reconstruction of the digital hologram wherein said digital image processing methods are applied, after said step m), to the amplitude contrast image of the specimen.

73. A method according to claims 1 or 2 comprising an application of digital image processing which methods after numerical reconstruction of digital hologram wherein said digital image processing methods are applied, after said step n) to said quantitative phase contrast image of the specimen.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method for simultaneous amplitude and quantitative phase contrast imaging by numerical reconstruction of digitally encoded holograms.

2. Discussion of the Background

The idea of recording a hologram of the specimen and reconstructing the hologram with a numerical method has been reported for the first time in 1967 by J. W. Goodman and R. W. Laurence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967). who used a vidicon detector for the hologram recording, and in 1971 by M. A. Kronrod et al., "Reconstruction of a hologram with a computer," Soviet Phys.--Technical Phys. 17, 333-334 (1972) who used a digitized image of a hologram recorded on a photographic plate. In these two references, the holograms were recorded in the holographic Fourier configuration for which amplitude contrast images of the specimen can be numerically reconstructed by simply calculating the modulus of the two-dimensional Fourier transform of the hologram. A recent development using a Charged Coupled Device (CCD) camera as recording device, also in the Fourier configuration, has been patented (U.S. Pat. No. 4,955,974 and U.S. Pat. No. 5,214,581) and reported by W. S. Haddad et al., "Fourier-transform holographic microscope," Applied Optics 31, 4973-4978 (1992)., and by K. Boyer et al., "Biomedical three-dimensional holographic microimaging at visible, ultraviolet and X-ray wavelength," Nature Medicine 2, 939-941 (1996)., for X-ray amplitude contrast imaging of biological specimens.

In 1994, on the basis of precedent works about digital holography, L. P. Yaroslavskii and N. S. Merzlyakov, Methods of Digital Holography, (Consultants Bureau. New York, 1980)., Schnars et al., "Direct recording of holograms by a CCD target and numerical reconstruction," Applied Optics 33, 179-181 (1994). have reported the first numerically reconstructed amplitude contrast image from an off-axis hologram recorded in the Fresnel holographic configuration with a CCD camera. With the same reconstruction algorithm but with a low-coherence light source, E. Cuche et al., "Optical Tomography at the Microscopic scale by means of a Numerical Low Coherence Holographic Technique," Proceedings SPIE on Optical and Imaging techniques for Bioimaging, Vienna, Vol. 2927, 61-66 (1996) have reported an application of numerical holography for tomographic imaging. An application in micro-endoscopy, using also a Fresnel calculation for the hologram reconstruction, has been reported by O. Coquoz et al., "Performances of endoscopic holography with a multicore optical fiber," Applied Optics 34, 7186-7193 (1995).

All the above mentioned works concern amplitude contrast imaging for which only the modulus of the numerically reconstructed optical field is considered. The first use of a numerically reconstructed phase distribution, from a Fresnel hologram, has been reported by Schnars et al., "Direct phase determination in hologram interferometry with use of digitally recorded holograms," J.Opt.Soc.Am.A 11, 2011-2015 (1994). for an application in holographic interferometry. As presented in Ref. Schnars et al., the used reconstruction algorithm is the same as for amplitude contrast imaging and do not really allows phase contrast imaging, because, in this case, the reconstructed optical field is the product of the object wave by the complex conjugate of the reference wave (or the product of the complex conjugate of the object wave by the reference wave). However, this reconstruction algorithm can be used in holographic interferometry, because the subtraction between two reconstructed phase distributions obtained with the same reference wave provides an image which represents only the phase difference between the deformed and undeformed states of the object.

The first example of a numerically reconstructed phase contrast image has been reported in 1997 by E. Cuche et al., "Tomographic optique par une technique d'holographie numerique en faible coherence," J. Opt. 28, 260-264 (1997). who have used a modified reconstruction algorithm including a multiplication of the digital hologram by a digital replica of the reference wave (digital reference wave). In Ref. Cuche et al., the phase contrast image has been obtained with a plane wave as reference and in direct observation, meaning that no magnification or demagnification optics is introduced along the optical path of the object wave.

SUMMARY OF THE INVENTION

In comparison with existing methods for phase contrast microscopy, such as the Zernicke or the Nomarski methods, the present invention provides a straightforward link between phase contrast imaging and optical metrology.

"Quantitative phase contrast" means that the phase contrast image is free of artifacts or aberrations and can be directly used for quantitative measurements of optical properties (e.g. refractive index) or structural information (e.g. topography, thickness). More precisely, "quantitative phase contrast" means here that the value of each pixel of the phase contrast image is equal, modulo 2.pi., to the value of the phase of the object wave at the corresponding area of specimen.

"Simultaneous amplitude and quantitative phase contrast" means that two images of the specimen can be reconstructed from the same hologram. One of these images with an amplitude contrast and the other one with a quantitative phase contrast. These images can be analyzed separately or compared the one with the other. Their information content (or the information content of several pairs of images reconstructed for different orientations of the specimen) can be associated in order to build a computed three-dimensional description of the specimen, for example a three-dimensional tomography of semi-transparent specimens. Spectroscopic measurements are also possible with the present invention by recording two or more holograms of the same specimen at different wavelengths. Such multi-wavelength procedure can also be useful for the precise determination of objects dimensions or refractive index in metrology.

In comparison with standard interference microscopy techniques which also provides simultaneously amplitude and quantitative phase contrasts, the advantage of the present invention is that the recording of only one hologram is necessary while the recording of four or more interferograms is required with interference microscopy. Moreover, no displacement or moving of optical elements is needed with the present invention. As a consequence, the acquisition time is reduced providing a lower sensitivity to thermal and mechanical drifts. Robustness is a great assess of the present invention.

An other important advantage of the present invention in comparison with interference microscopy is that the phase aberrations are corrected digitally. Indeed, a microscope objective which is introduced in an interferometer produces a curvature of the wavefronts which affects the phase of the object wave. Therefore, for phase contrast imaging with the present invention or more generally in any interferometric system, this phase aberration must be corrected. In interference microscopy, this problem is solved experimentally by inserting the same microscope objective in the reference arm, at equal distance from the exit of the interferometer. This arrangement called Linnick interferometer requires that if any change has to be made in the object arm, then the same change must be precisely reproduced in the reference arm in such a way that the interference occurs between similarly deformed wavefronts. As a consequence the experimental configuration requires a very high degree of precision. An other possibility (Mirrau interferometry) consists in magnifying the interference pattern. However, it is difficult to achieve high resolution imaging with this technique because a miniaturized interferometer must be inserted between the sample and the microscope objective. The present invention proposes a purely digital method which allows us to perform the correction by multiplying the reconstructed wavefront with the computed complex conjugate of the phase aberration.

Depending on the configuration used for the recording of the hologram, the physical interpretation of amplitude and quantitative phase contrasts vary. If the hologram is recorded with the wave that is reflected by the specimen (reflection geometry), the amplitude contrast depends on variations of the reflectance at the specimen surface and the phase contrast depends on the topography of the specimen and/or on changes of the phase shift at the reflection. If the hologram is recorded with the wave that is transmitted by a transparent or semi-transparent specimen (transmission geometry), the amplitude contrast is related to changes in absorption and the phase contrast depends on variations of the thickness and/or of the refractive index (or more generally on variations of the optical path).

In most cases, quantitative measurements of optical properties or structural information, on the basis of phase measurements is ambiguous because phase contrast generally has more than one origin. For example, the measurement of the refractive index of a transparent specimen requires the knowledge of the thickness and inversely the measurement of the thickness requires the knowledge of the refractive index. For topographic measurements with specimens composed of different materials, the analysis of the results must take into account the variation of the phase change on the reflection interface, if the complex index of refraction of the different materials is not the same. If a pure topographic or a pure refractive index or a pure thickness measurement is desired, known methods such as ellipsometry or multi-wavelength measurements could be used in combination with the present invention. In particular, refractive index measurement on a transparent specimen of unknown thickness can be performed by recording two or more holograms at different wavelengths. Assuming that the thickness of the specimen is constant for each hologram, variations of the reconstructed phase distributions are due to variations of the refractive index as a function of the wavelength. Using a model describing the variation of the refractive index as a function of the wavelength, the refractive index of the specimen or its thickness can be deduced from the quantitative phase contrast images. With a semi-transparent specimen (e.g. biological cells or tissues) or more generally with a 3D-scene composed of several reflective elements located at different depth, if a gating technique is used, such as time or coherent gating, the hologram can be recorded, in the reflection geometry, with the light that is reflected by a selected slice inside the specimen. In this case, both contrasts (amplitude and phase) depend on the optical properties of the selected slice and on the optical properties of other volumes inside the specimen where the light has traveled before and after the reflection.

The present invention provides a more general method for the numerical reconstruction of both amplitude and quantitative phase contrast images from a digital hologram. The numerical method for the hologram reconstruction comprises the calculation of a digital replica of the reference wave called digital reference wave. An array of complex numbers called digital phase mask is also calculated in order to correct the phase aberrations of the imaging system.

The present invention provides unique results. The technique provides a quantitative phase contrast meaning that the reconstructed phase distribution can be directly used for applications in metrology, in particular for surface profilometry, refractive index measurements or more generally for quantitative material testing (shape and position measurements, surface roughness measurement, optical properties measurement). Moreover, an amplitude contrast image of the specimen can be reconstructed from the same hologram. It is an important feature of the present invention that a three dimensional description of the specimen can be obtained digitally with only one image acquisition.

The possibility of instantaneous acquisition of the amplitude and of the quantitative phase with a pulsed source or a time gated camera is a great advantage of the present invention.

Basically, the numerical reconstruction method performs a calculation which describes the propagation of the wavefront that would be diffracted by the hologram during a standard holographic reconstruction. The calculation consists in a numerical evaluation of the diffraction pattern which is produced in an observation plane when the hologram is illuminated by a replica of the reference wave. The scalar description of the diffraction is considered and the reconstruction method consists in the numerical calculation of the Fresnel-Kirchhoff integral or of the Rayleigh-Sommerfeld integral. Depending on the configuration used for the hologram creation, the diffraction calculation can be performed using an approximation of these integrals such as the Fraunhofer or the Fresnel integrals. In some cases such as Fourier holography, a simple Fourier transform calculation can be used.

In a preferred manner, the configuration used for the hologram creation, in particular the distance between the hologram and the specimen, is adjusted in such a way to produce a Fresnel hologram for which the diffraction calculation can be performed in the Fresnel approximation. The advantage of the Fresnel approximation is that the computations are simple and can be performed very fast using a discrete formulation of the Fresnel integral expressed in terms of a Fourier transform. In addition, a wide range of experimental configurations are covered by the Fresnel approximation.

An important feature of the present invention is that image reconstruction, in both amplitude and phase contrast, requires the adjustment of several constants which are involved by the numerical reconstruction method. These constants are called reconstruction parameters and their values are defined by the experimental configuration. The reconstruction parameters can be divided into three categories: the reconstruction distance which is related to image focusing; the reference wave parameters which are related to the definition of the digital reference wave; and the aberration correction parameters which are related to the definition of the digital phase mask. It is an object of the present invention to describe how these reconstruction parameters are defined and how their values must be adjusted. It is clear that the values of the reconstruction parameters are fixed for a given experimental configuration and that the same values of the reconstruction parameters can be used to reconstruct several holograms without new adjustment procedures if the experimental configuration is the same for these holograms.

Other parameters such as the wavelength, the detector size and the number of pixels are requested by the numerical reconstruction method but these parameters have, in general, constant values and do not require a special adjustment.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects and features of the present invention will become apparent from the following detailed description considered in conjunction with the accompanying drawings. It is to be understood, however, that the drawings are designed solely for purposes of illustration and not as a definition of the limits of the invention, for which reference should be made to the appended claims.

FIG. 1 is a view showing diagrammatically the different steps of the imaging procedure.

FIG. 2A is a view showing diagrammatically one of the possible configuration for the recording of an off-axis hologram. FIGS. 2B, 2C and 2D are views showing diagrammatically three of the possible realizations of the set-up. FIG. 2B in a Michelson configuration. FIG. 2C in a Mach-Zender configuration for transmission imaging. FIG. 2D in a Mach-Zender configuration for reflection imaging.

FIG. 3 is a view showing diagrammatically the standard optical reconstruction of an off-axis hologram which has been recorded as presented in FIG. 2A.

FIG. 4 is a view showing diagrammatically the different steps of computations of the numerical method for the reconstruction of a digital hologram.

FIG. 5 is a view showing diagramatically an other possibility for the computation of the numerical method for the reconstruction of a digital hologram.

FIGS. 6A to 6C are a views showing diagrammatically three of the possible configurations when a magnification optics is introduced along the optical path of the object wave, for the creation of a hologram of a magnified image of the specimen.

FIGS. 7A to 7C show three examples of numerically reconstructed amplitude contrast images of a USAF test target obtained with different reconstruction distances.

FIGS. 8A to 8C show examples of numerically reconstructed phase contrast images of a biological cell. For theses images, a plane wave has been used as reference for the hologram creation and a microscope objective has been used as magnification optics. FIG. 8A shows the phase contrast image obtained when all the reconstruction parameters are adequately adjusted, FIG. 8B shows the result obtained with an inadequate adjustment of the aberration correction parameters. FIG. 8C shows the result obtained with an inadequate adjustment of the reference wave parameters.

FIG. 9 is a view showing diagrammatically the different possibilities for the adjustment of the values of the reconstruction parameters.

FIGS. 10A to 10F show examples of simultaneously reconstructed amplitude and quantitative phase contrast images. FIGS. 10A and 10B show respectively the amplitude contrast image and the quantitative phase contrast image of a USAF test target. FIGS. 10C a