DIGITAL HOLOGRAPHIC IMAGE TECHNOLOGY WITH DOUBLE IMAGE IMINATION

Description

Domaine technique

[0001] The present invention relates to the field of digital holography, and more specifically deals with a method of removing a twin image in digital holographic imaging. Arrière-plan technologique

[0002] Digital holography is a process by which a sensor records a hologram representing the phase and amplitude of the wave diffracted by an object. The hologram records the spatial intensity distribution of the interference patterns generated by the illumination beam and the light diffracted by the imaged object. The hologram allows the image of the object to be reconstructed computationally, using a digital reconstruction algorithm. More precisely, the phase and absorption characteristics of the imaged object are obtained by backpropagation calculations from the hologram, using a propagation algorithm, for example, based on Rayleigh-Sommerfeld diffraction theory.

[0003] Digital holography is particularly useful in biological imaging due to its ability to image transparent objects, such as organisms or biological cells, and especially in digital holographic microscopy. Indeed, unlike other imaging techniques, digital holography does not require the injection of dyes to make transparent objects visible, nor does it use high-energy radiation (e.g., X-rays) that can damage the biological objects being imaged.

[0004] Holographic imaging aims to determine the spatial distribution of phase shift and absorption of the imaged object. These characteristics of the imaged object allow for its precise characterization, and thus enable its identification, for example.

[0005] Among the various holography methods, line holography exhibits high phase sensitivity, and is therefore the most suitable method for imaging low-phase biological objects.

[0006] However, in-line holography has a major drawback: the presence of a twin or orthoscopic image, resulting from the loss of phase information in the hologram, which only records intensity. The twin image is an artifact that appears in the hologram as if it were an additional imaged object positioned symmetrically to the imaged object with respect to the hologram plane. Because the twin image is out of focus, it distorts the shape of the imaged object during the reconstruction of the phase and absorption images, potentially preventing the use of these images. "Digital in-line particle holography: twin-image suppression using sparse blind source separation" (Hattay et al., Signal, Image and Video Processing, Nov-2015) proposes an alternative technique for twin-image suppression. Présentation de l'invention

[0007] The invention aims to eliminate artifacts due to the presence of a twin image during online holography.

[0008] To this end, the invention proposes a digital holographic imaging method, comprising the following steps: 1) obtaining a hologram by holography, said hologram being representative of a spatial intensity distribution, on a hologram plane at a hologram coordinate of an imaged object, of the interferences caused by interactions between an illumination beam and said imaged object placed at an object coordinate on an imaging axis, 2) implementation of a plurality of iterations each comprising the following steps: 2.a) by backpropagation towards the object coordinate of a hologram field comprising a spatial amplitude distribution corresponding to the spatial intensity distribution of the hologram and a spatial phase distribution, determination of an object field involving a spatial absorption distribution and a spatial phase distribution of the imaged object, 2.b) thresholding of the values ​​of the spatial absorption distribution and the spatial phase shift distribution of the imaged object by decreasing the values ​​of the spatial absorption distribution below an absorption threshold and by decreasing the values ​​of the spatial phase shift distribution below a phase shift threshold, the absorption threshold and the phase shift threshold decreasing at each iteration, 2.c) by re-propagation of the object field to the hologram coordinate, determination of a modified hologram field comprising a modified spatial amplitude distribution and a modified spatial phase distribution, 2.d) replacement of the spatial phase distribution of the hologram field by the modified spatial phase distribution, the spatial amplitude distribution of the hologram field being conserved, 3) determination of the spatial phase shift distribution and the spatial absorption distribution of the imaged object as being those of the object field of the last iteration.

[0009] The invention is advantageously complemented by the following various features, taken individually or in their various possible combinations: During thresholding, the values ​​of the spatial absorption distribution below the absorption threshold and the values ​​of the spatial phase shift distribution below the phase shift threshold are set to zero; the absorption threshold depends on maximum values ​​of the spatial absorption distribution, and the phase shift threshold depends on maximum values ​​of the spatial phase shift distribution involved in the object field; in the first iteration, the absorption threshold and / or the phase shift threshold corresponds to between 40% and 15% of a maximum value of the spatial absorption distribution or the spatial phase shift distribution, respectively; in each iteration, the absorption threshold and / or the phase shift threshold is decreased by 1% to 6% of a maximum value of the spatial absorption distribution or the spatial phase shift distribution; in the last iteration, the absorption threshold and the phase shift threshold are zero;During thresholding, the values ​​of the spatial absorption and phase shift distributions are kept positive or zero during the iterations. Before the iterations, the hologram field is normalized by dividing the values ​​of the spatial intensity distribution by a background image value corresponding to an intensity of the illumination beam at the hologram coordinate. Thresholding includes smoothing the modified spatial absorption distribution and the modified spatial phase shift distribution. The hologram field and / or the object field exhibit a spatial resolution that increases with the iterations. Présentation des figures

[0010] Other features, purposes and advantages of the invention will become apparent from the following description, which is purely illustrative and not limiting, and which should be read in conjunction with the accompanying drawings on which: there figure 1 is a flowchart illustrating the main steps of the process according to one possible embodiment of the invention; the figure 2 schematically shows an example of a holographic imaging system used to acquire a hologram according to one possible embodiment of the invention; the figure 3 shows a hologram of a cluster of bacteria from a first example of implementing the process according to a possible embodiment of the invention, the figure 4a shows a spatial distribution of initial phase shift determined from the hologram of the figure 3 , in the first example of implementing the process according to a possible embodiment of the invention, the figure 4b shows an initial spatial absorption distribution determined from the hologram of the figure 3 , in the first example of implementing the process according to a possible embodiment of the invention, the figure 4c shows a phase shift value profile of a bacterium in the figure 4a , there figure 4d shows a profile of absorption values ​​of a bacterium in the figure 4b , there figure 5a shows a spatial phase shift distribution after the first iteration, in the first example of implementing the process according to a possible embodiment of the invention, the figure 5b shows a spatial absorption distribution after the first iteration, in the first example of implementation of the process according to a possible embodiment of the invention, the figure 5c shows a phase shift value profile of a bacterium in the figure 5a , there figure 5d shows a profile of absorption values ​​of a bacterium in the figure 5b , there figure 6a shows a spatial phase shift distribution after the fifth iteration, in the first example of implementing the process according to a possible embodiment of the invention, the figure 6b shows a spatial absorption distribution after the fifth iteration, in the first example of implementation of the process according to a possible embodiment of the invention, the figure 6c shows a phase shift value profile of a bacterium in the figure 6a , there figure 6d shows a profile of absorption values ​​of a bacterium in the figure 6b , there figure 7a shows a spatial distribution of phase shift after the twentieth iteration, in the first example of implementation of the process according to a possible embodiment of the invention, the figure 7b shows a spatial absorption distribution after the twentieth iteration, in the first example of implementation of the process according to a possible embodiment of the invention, the figure 7c shows a phase shift value profile of a bacterium in the figure 7a , there figure 7d shows a profile of absorption values ​​of a bacterium in the figure 7b , there figure 8a shows a hologram of polystyrene beads acquired by an imaging system in a second example of implementing the process according to a possible embodiment of the invention, the figure 8b shows a photograph of the polystyrene beads from the second example of implementing the process, the figure 9a shows an initial spatial phase shift distribution before the first iteration, determined from the hologram of the figure 8a , in the second example of implementing the process according to a possible embodiment of the invention, the figure 9b shows an initial spatial absorption distribution before the first iteration, determined from the hologram of the figure 8b , in the second example of implementing the process according to a possible embodiment of the invention, the figure 10a shows a spatial distribution of phase shift after the twentieth iteration, in the second example of implementation of the process according to a possible embodiment of the invention, the figure 10b shows a spatial absorption distribution after the twentieth iteration, in the second example of implementation of the process according to a possible embodiment of the invention. Description détaillée

[0011] With reference to the figure 1 ,The digital holographic imaging process first involves obtaining a hologram of a holographically imaged object (step S01), typically by online holography. While online holography is not required to implement the invention, the problem of the twin image arises most acutely in the context of online holography. The hologram can be obtained in various ways, but the method of acquisition does not affect the process. In particular, the hologram acquisition method can be arbitrary, provided that the hologram is representative of a spatial distribution of interference intensity in the imaged object.

[0012] By way of non-limiting example, the figure 2 This schematically represents an online holographic imaging system for imaging an object 1 using a digital image sensor 2, placed in an image plane of the holographic imaging system. The imaging system defines an imaging axis 6, simplified here by a straight line corresponding to the optical axis, but which may consist of a series of successive straight lines defining the light path, depending on the configuration of the optical components of the imaging system. Object 1 is placed at an object coordinate zo on the imaging axis 6, while the image sensor 2 is disposed at a hologram coordinate zh, and extends perpendicularly to the imaging axis 6. It results that the hologram is representative of a spatial intensity distribution H(x,y), on a hologram plane (x,y), of the interferences caused by interactions between the imaged object 1 placed at the object coordinate z 0 on an imaging axis 6 and the illumination beam.

[0013] A light source 4 is configured to illuminate the object 1 within the field-of-view of the holographic imaging system by means of a sufficiently coherent illumination beam. The light source 4 can produce the illumination light itself, or simply be the termination of an optical fiber carrying this illumination light. The illumination beam exhibits the conventional characteristics for holographic imaging, without any additional special constraints. The illumination beam can thus be monochromatic (for example, with a wavelength around 500 nm) or possibly be composed of several wavelengths, for example, used sequentially. The holographic imaging system is equipped here with a microscope objective 8, schematically represented here by an entrance lens 8a and an exit lens 8b, positioned between the sample 1 and the digital image sensor 2.The microscope objective 8 is optional, however, as the invention is not limited to holographic microscopy with a lens. The arrangement described here is, of course, a non-limiting example. Any holographic imaging system can be used, with or without a microscope objective, etc. Thus, as long as a holographic imaging system can acquire an image in which the interference patterns generated by object 1 appear, this holographic imaging system is suitable for implementing the method. However, it is necessary that the object coordinates z0 and the hologram coordinates zh that were used to acquire the resulting hologram be known.

[0014] During the acquisition of a hologram, the light source 4 emits a reference illumination beam, which can be translated into a reference plane wave propagating in the Z direction along the imaging axis 6, and which can be described by: R z = Aexp j 2 π z / λ with A the amplitude and λ the wavelength of the reference wave emitted by the light source 4. Object 1 is placed at the coordinate zo on the imaging axis 6, and by its diffraction properties, will scatter the incident reference light. This results in a wave scattered by object 1, denoted O(x, y, z). The scattered wave O(x, y, z) and the reference wave R(z) interfere on the image sensor 2 to form the hologram, defining a holographic plane (in x, y) at the hologram coordinate zh, which is that of the image sensor 2 on the imaging axis 6. Since a digital image sensor 2 is only sensitive to the intensity of the electromagnetic field, the hologram corresponds to the spatial intensity distribution H(x, y, zh) of the total field at the hologram coordinate zh, designated as the hologram field: H x y z h = R z h + O x y z h 2 In the absence of object 1, only the intensity of the reference wave would be detected as a holographic field: H x y z h = R z h 2 = A 2 = B z h B(zh ) is called the background image at the hologram coordinate zh .

[0015] The scattered wave O(x, y, z) is related to the incident wave R(z) by a complex transmission function t(x,y) such that O(x, y, z)=t(x, y)R(z₀), and the total field U(x, y, z) resulting from the addition of the scattered wave O(x, y, z) and the reference wave R(z) can be written according to the relation: U x y z o = R z o 1 + t x y .

[0016] This relationship can be rewritten to reflect the fact that the reference wave is modified by absorption and phase shift by object 1: U x y z o = R z o 1 − a x y exp − jφ x y with a(x,y) representing absorption and φ(x,y) representing the phase shift introduced by object 1, which are directly derived from the characteristics of object 1 (structure, composition, etc.). The absorption a and the phase shift φ can therefore also be considered as characteristics related to object 1, although also related to certain parameters such as the wavelength of the reference wave of the illumination beam.

[0017] Before proceeding, it is possible to normalize (step S02) the spatial intensity distribution H(x,y) represented by the hologram, using the background image B(zh) at the hologram coordinate zh. Dividing the values ​​of the spatial intensity distribution H(x,y) by the background image B(zh), which has a uniform intensity value B, is equivalent to setting the amplitude A of the reference wave of the illumination beam to 1, and thus simplifies the calculations. Subsequently, the amplitude A will no longer be considered different from 1.

[0018] The process then involves implementing iterative steps (steps S03) to determine the phase characteristics φ and absorption characteristics α of the imaged object 1 through a plurality of backpropagation and repropagation cycles of light fields, in order to recover the phase of the total field, which is not preserved in the hologram. During these cycles, increasingly stringent thresholding is applied to the phase φ and absorption α, in order to preserve the most intense areas while reducing the intensity of others. The number of iterations depends in particular on the decay of the applied thresholds. Typically, the number of iterations is at least 8, and preferably at least 12.

[0019] The hologram field, which corresponds to the propagation up to the hologram coordinate zh of the object field U(x,y,zo), is a complex field that includes the spatial amplitude distribution, which is translated by the spatial intensity distribution H(x, y) of the hologram, and a spatial phase distribution Ω(x,y,zh). The hologram field can therefore be written as: U x y z h = H x y exp j Ω x y z h

[0020] Since image sensor 2 is only sensitive to the intensity of the electromagnetic field, the spatial phase distribution Ω at the hologram coordinate zh is initially unknown and must be fixed to an initial value. Advantageously, this value is chosen to be the phase Ω(zh) of the reference wave R(zh) at the hologram coordinate zh, estimated by direct propagation: exp j 2 πz h / λ = exp j Ω z h

[0021] Thus, from the hologram, we have an initial hologram field comprising a spatial amplitude distribution corresponding to the spatial intensity distribution of the hologram, and an initial phase spatial distribution at an initialization value.

[0022] In a first iterative step S03a, a complex object field is determined by backpropagation to the object coordinate zo of the hologram field. Backpropagation relies on a light diffraction model, such as the Rayleigh-Sommerfeld or Kirchhoff diffraction model. Such a light diffraction model allows us to determine the light field expression at a second point, given the field expression at a first point. In this respect, we can advantageously operate in the frequency domain, and in particular use the method of the angular spectrum of a plane wave, which employs the Fourier transform, as described in Joseph W. Goodman's "Introduction to Fourier Optics," McGraw-Hill companies, 3rd edition, 2005.

[0023] In a second iterative step S03b, we extract the values ​​of the spatial absorption distribution a(x,y) and the spatial phase shift distribution φ(x,y) of the imaged object 1. As indicated above, the object field U(x,y,zo ) implies a spatial absorption distribution a(x,y) and a spatial phase shift distribution φ(x,y) of the imaged object 1 (below and below in normalized form): U x y z o = exp jΩ z o 1 − a x y exp − jφ x y

[0024] By multiplying with the conjugate of the reference wave incident on object 1, i.e., by exp(-jΩ(zo )), we extract the absorption a and the shift φ that form the complex transmission function. These values ​​of absorption a and shift φ result from the backpropagation of the hologram field towards the object coordinate zo , and can be extracted thanks to the presence of the reference wave.

[0025] Certain constraints are imposed on the possible values ​​of the absorption α and the phase shift of the imaged object 1. First, due to the conservation of energy, which implies that absorption by object 1 must not lead to an increased light amplitude following diffraction, it is imposed that the absorption values ​​must not be negative, i.e., α(x,y) ≥ 0. If negative absorption values ​​occur, they are the result of interference between the twin image and the reference wave, and they are replaced by zero values. Furthermore, it is also imposed that the phase shift be positive, i.e., φ(x,y) ≥ 0. In the vast majority of cases, the imaged object 1 has a refractive index greater than or equal to that of the medium through which the light propagates. This is particularly true when the imaged object 1 is a microorganism such as a bacterium in an aqueous solution. This is also the case for almost all objects in the air.Thus, the values ​​of the spatial absorption distribution a(x,y) and phase shift φ(x,y) are kept positive or zero during the iterations.

[0026] Once extracted, the values ​​of the spatial absorption distribution a(x,y) and the spatial phase shift distribution φ(x,y) of the imaged object 1 are modified by thresholding: they are modified by decreasing the values ​​below a respective threshold. More precisely, the values ​​of the spatial absorption distribution a(x,y) below an absorption threshold are decreased, while the values ​​of the spatial phase shift distribution φ(x,y) below a phase shift threshold are decreased. The values ​​of the spatial absorption distribution a(x,y) above the absorption threshold are not decreased, and the values ​​of the spatial phase shift distribution φ(x,y) above the phase shift threshold are not decreased.The values ​​of the spatial absorption distribution a(x,y) below the absorption threshold and of the spatial phase shift distribution φ(x,y) below the phase shift threshold are greatly reduced, by more than 50%, preferably by more than 75%, and preferably are set to zero.

[0027] The threshold values ​​decrease at each iteration. Preferably, the absorption threshold depends on the values ​​of the spatial absorption distribution a(x,y), and the phase shift threshold depends on the values ​​of the spatial phase shift distribution φ(x,y). Preferably, the absorption threshold depends on the maximum values ​​of the spatial absorption distribution a(x,y), and more preferably on the maximum value taken by the spatial absorption distribution a(x,y). Similarly, the phase shift threshold depends on the maximum values ​​of the spatial phase shift distribution φ(x,y), and more preferably on the maximum value taken by the spatial phase shift distribution φ(x,y). In particular, the value of the absorption threshold can correspond to a proportion of the maximum value taken by the spatial absorption distribution a(x,y), a proportion that decreases at each iteration.Similarly, the phase shift threshold value can correspond to a proportion of the maximum value taken by the spatial phase shift distribution φ(x,y), a proportion that decreases with each iteration. It is of course also possible for the proportion to be defined from several values ​​of the spatial distributions, for example as a proportion of a mean or other indicator.

[0028] For example, in the first iteration, the absorption threshold for the spatial absorption distribution a(x,y) and / or the phase shift threshold for the spatial phase shift distribution φ(x,y) of the imaged object corresponds to between 40% and 15% of the maximum value of the spatial absorption distribution a(x,y) or the spatial phase shift distribution φ(x,y), respectively, and preferably corresponds to between 30% and 20% of the maximum value of the spatial absorption distribution a(x,y) or the spatial phase shift distribution φ(x,y), respectively. Then, in each subsequent iteration, the threshold is decreased by 2% to 6% of the maximum value of the spatial absorption distribution a(x,y) or the spatial phase shift distribution φ(x,y). During the last iteration, the threshold for the spatial distribution of absorption a(x,y) is zero and the threshold for the spatial distribution of phase shift φ(x,y) of the imaged object is zero.The initial threshold values, as well as their decrease at each iteration, depend in particular on the nature of the imaged object 1, and can therefore be adapted accordingly. As mentioned above, the number of iterations depends primarily on the initial threshold values, as well as their decrease at each iteration. The threshold decrease can be regular or irregular.

[0029] Since the noise caused by the twin image is always less intense than the representation of the imaged object in the hologram, thresholding removes more contribution from the twin image than from the representation of the imaged object. Indeed, by definition, the imaged object is in focus, while the twin image is out of focus.

[0030] After applying the thresholding, we obtain a modified spatial absorption distribution a'(x,y) and a modified spatial phase shift distribution φ'(x,y), which therefore define a modified complex object field U'(x,y,zo ): U x y z o = exp jΩ z o 1 − a ′ x y exp − jφ ′ x y

[0031] Preferably, the second iterative step includes smoothing the modified spatial absorption distribution and the modified spatial phase shift distribution, typically by applying a low-pass filter, for example, a Gaussian or equivalent filter. This smoothing avoids the generation of high-frequency components at the cutoffs caused by thresholding. Preferably, the size of the smoothing filter (i.e., the adjacent pixels considered simultaneously during filtering) is decreased with each iteration, for example, at the same time as the thresholds are decreased. This allows the significant contrasts of the imaged object to be recovered at the end of the iterations.

[0032] In a third iterative step (step S03c), a modified hologram field U'(x,y,zh) is determined by re-propagating the modified object field U'(x,y,zo) to the hologram coordinate zh. The re-propagation follows the same modalities as the backpropagation described above, and can thus employ a light diffraction model, such as the Rayleigh-Sommerfeld or Kirchhoff diffraction model. The resulting modified hologram field U'(x,y,zh) comprises a modified amplitude and a modified phase Ω'(x,y,zh), which reflects the changes made to the absorption and phase shift of the imaged object 1 during the previous thresholding step. Only the modified phase is used in the following step.

[0033] In a fourth iterative step (step S03d), the phase of the hologram field Ω(x,y,zh) is replaced by the modified phase Ω'(x,y,zh), while the amplitude of the hologram field remains unchanged. In other words, the modified hologram field U'(x,y,zh) becomes the hologram field, with the modified spatial amplitude distribution replaced by the initial spatial amplitude distribution. Recall that the hologram represents a spatial intensity distribution H(x,y) corresponding to the spatial amplitude distribution of the hologram field U(x,y,zh). It follows that the spatial amplitude distribution of the hologram field U(x,y,zh) is determined by the hologram and does not need to be modified. However, the phase of the hologram field Ω(x,y,zh) is not fixed and is updated at each iteration.

[0034] Following this fourth iterative step (step S03d), the hologram field has had its spatial phase distribution Ω(x,y,zh) updated, and a new iteration can begin with the first iterative step (step S03a), but with a lower absorption threshold and shift threshold compared to the previous iteration. The iteration cycles end when a criterion is met, such as when the absorption threshold and / or shift threshold are zero, or at least below a threshold value. It is also possible to set a fixed number of iterations, the criterion then being that the fixed number of iterations has been reached.

[0035] Following the iterations, the values ​​of the spatial distribution of phase shift and absorption of the imaged object are determined (step S04) as those resulting from a final iteration. More precisely, the values ​​of the spatial distribution of phase shift and absorption of the imaged object are those corresponding to the last object field obtained by backpropagation towards the object coordinate of the last hologram field.

[0036] During each iteration, absorption and phase shift values ​​are obtained. However, these values ​​are affected by noise, primarily from the twin image. Thresholding allows the most significant contributions to be retained, while the less significant contributions, polluted by noise, are progressively eliminated. The noise is thus reduced at each iteration. Compared to existing methods, the method according to the invention has the advantage of rapid convergence and complete elimination of noise due to the twin image.

[0037] The process, through the progressive decrease of thresholds, can be interpreted as first removing the noise caused by the twin image in the most diffuse areas, ignoring all details. Then, as the thresholds decrease, information is recovered from less diffuse elements. It is therefore possible to leverage this progressive recovery of details to accelerate the process speed by initially working with a low-resolution hologram and / or object field, and then increasing this resolution with each iteration, for example, simultaneously with the decrease of the thresholds. Indeed, at the beginning of the iterations, the image is approximated by only the most diffuse areas, while with the progressive decrease of the thresholds, increasingly finer details are recovered, justifying the increase in resolution. At the end of the iterations, the fields can regain the same resolution as the initial hologram.Applying iterations to lower resolution fields greatly accelerates the speed of the process.

[0038] The process is particularly well-suited to biological imaging, where the imaged object is a biological sample acquired by holographic microscopy. Indeed, objects of biological origin generally exhibit positive absorption and phase shifts with well-defined contours. Biological imaging is therefore the preferred application of the process. However, the process can also be used with other types of objects besides biological ones.

[0039] To illustrate the effects of iterations, the figures 2 à 5d They show a first example of implementing these iterations on a computer-generated hologram of a group of objects representing a micro-colony of rod-shaped bacteria. figure 3 The original computer-generated hologram, based on the spatial intensity distribution H(x,y) recorded by image sensor 2, is shown. As can be seen, the twin image induced by the group strongly distorts the shapes of the individual bacteria composing it. These bacteria appear as rods containing an alignment of four internal diffusing structures. The bacteria exhibit an absorption of 0.02 and a phase shift φ of 0.08, with the internal diffusing structures exhibiting a maximum absorption of 0.05 and a maximum phase shift of 0.1.

[0040] There figure 4a shows the spatial phase shift distribution corresponding to the initial object field of the figure 3 , after backpropagation of the hologram field towards the object coordinate, while the figure 4b shows the spatial absorption distribution corresponding to the initial object field of the figure 3 , after backpropagation of the hologram field towards the object coordinate. The figure 4c This shows the distribution profile of phase shift values ​​along the longitudinal axis of a rod-shaped bacterium, between the two arrows. It can be seen that, due to significant noise from the twin image, the phase shift profile is quite flat and peaks at approximately 0.05, or half the maximum phase shift. This noise therefore prevents the four internal diffusing structures within the bacterium from being distinguished and characterized. figure 4d This shows the absorption distribution profile along the longitudinal axis of a rod-shaped bacterium, between the two arrows. It can be seen that, due to significant noise from the twin image, the absorption profile peaks at approximately 0.04, or half the maximum absorption. This noise therefore prevents the characterization of the four internal diffusing structures within the bacterium.

[0041] There figure 5a shows the spatial distribution of phase shift and the figure 5b shows the spatial distribution of absorption after the first iteration. In this example, the initial thresholds were chosen at 25% of the maximum values. figure 5c shows the distribution profile of phase shift values ​​along the longitudinal axis of a rod-shaped bacterium, between the two arrows. Compared to the previous profile of the figure 4c The maximum values ​​of the phase shift profile have increased significantly, now standing at approximately 0.07. figure 5d shows the profile of the distribution of absorption values ​​along the longitudinal axis of a rod-shaped bacterium, between the two arrows. Compared to the previous profile of the figure 4d , the maximum values ​​of the absorption profile increased, rising to approximately 0.05.

[0042] There figure 6a shows the spatial distribution of phase shift and the figure 6b shows the spatial distribution of absorption after the fifth iteration. The absorption and phase shift thresholds were progressively reduced at each iteration. figure 6c shows the distribution profile of phase shift values ​​along the longitudinal axis of a rod-shaped bacterium, between the two arrows. Compared to the previous profile of the figure 5c The maximum values ​​of the phase shift profile have increased significantly again, now reaching approximately 0.09. However, the differences in values ​​between the diffusing internal structures and the bacterium are still small. figure 6d shows the profile of the distribution of absorption values ​​along the longitudinal axis of a rod-shaped bacterium, between the two arrows. Compared to the previous profile of the figure 5d The differences in values ​​between the internal diffusing structures and the bacterium were accentuated.

[0043] There figure 7a shows the spatial distribution of phase shift and the figure 7b This shows the spatial distribution of absorption after the twentieth and final iteration. The absorption and phase shift thresholds were progressively reduced at each iteration until reaching zero in this last iteration. figure 7c shows the distribution profile of phase shift values ​​along the longitudinal axis of a rod-shaped bacterium, between the two arrows. Compared to the previous profile of the figure 6c The maximum values ​​of the phase shift profile have increased, now reaching approximately 0.10. Furthermore, the differences in values ​​between the diffusing internal structures and the bacterium have been accentuated, with the bacterium's absorption values ​​now approaching 0.08. Thus, the actual spatial distribution of absorption values ​​of the imaged object is accurately reproduced. figure 7d shows the profile of the distribution of absorption values ​​along the longitudinal axis of a rod-shaped bacterium, between the two arrows. Compared to the previous profile of the figure 6d The differences in values ​​between the diffusing internal structures and the bacterium have been further accentuated. The maximum values ​​corresponding to the diffusing internal structures now reach 0.05, while the minimum values ​​corresponding to the bacterium reach 0.02. This accurately reflects the actual spatial distribution of absorption of the imaged object.

[0044] The process thus allows, with only 20 iterations in this example, the complete removal of noise and the recovery of the exact phase shift and absorption values ​​of the bacteria, including their diffusing internal structures. Since thresholding eliminates more contributions from the twin image than from the imaged object, convergence will be faster the larger the spatial area zeroed at the end of the iterations. Convergence is therefore faster when the region of interest in the image is small. If the aggregate of the figure 3 had contained more bacteria, i.e. more object of interest to image, the number of iterations should have been chosen to be greater in order to find the exact values ​​of phase shift and absorption, for example with a less rapid decrease of the thresholds.

[0045] THE figures 8a à 10b show an example of implementing the process on experimental data. Polystyrene beads 1.1 µm in diameter were randomly arranged on a slide by drying a colloidal suspension, then immersing them in oil, and the hologram of the figure 8a was acquired. The polystyrene beads exhibit significant phase shift but very low absorption. By way of non-limiting example, the holographic imaging system used to acquire the hologram in this example is an inline holographic microscopy system, with a 405 nm monochromatic LED as the light source 4, with a full width at half maximum (FWHM) of 12 nm. The light source 4 was positioned 100 nm from the slide. The holographic imaging system included a microscope objective 8, with a numerical aperture of 100x1.3 for a magnification of 80. A CMOS sensor was used as the image sensor 2. The beads had a refractive index of approximately 1.63, and the immersion oil a refractive index of approximately 1.53. The figure 8a shows the hologram after normalization by the background image. For comparison, the figure 8b shows a non-holographic image of the marbles in the same configuration.

[0046] Similar to figures 2a and 2b, the figure 9a shows the spatial distribution of phase shift corresponding to the initial hologram of the figure 8a , after backpropagation of the hologram field towards the object coordinate, while the figure 9b shows the spatial absorption distribution corresponding to the original image of the figure 8a , after backpropagation of the hologram field towards the object coordinate. Here again, we observe that the spatial distributions of phase shift and absorption are very noisy due to the twin image. In particular, the spatial distribution of absorption shows strong fluctuations, even though the beads are supposed to exhibit low absorption.

[0047] As explained above, a plurality of iteration cycles are implemented. The figure 10a shows the spatial distribution of phase shift and the figure 10b shows the spatial distribution of absorption after the fiftieth and final iteration. The absorption and phase shift thresholds were progressively reduced at each iteration until reaching zero in this last iteration. We observe, on the one hand, that the spatial distribution of phase shift now corresponds clearly to the distribution of the beads as illustrated in the figure 8b On the other hand, the low values ​​of the spatial absorption distribution accurately reflect the low absorption nature of the polystyrene beads. The noise caused by the twin image was therefore effectively eliminated, and the spatial distributions of phase shift and absorption were correctly determined.

[0048] The invention is not limited to the embodiment described and shown in the accompanying figures. Modifications remain possible, particularly with regard to the constitution of the various technical features or by substitution of technical equivalents, without departing from the scope of protection of the invention as claimed in the accompanying claims.

Claims

1. A digital holographic imaging method, comprising the following steps: 1) obtaining (S01) a hologram by holography, said hologram being representative of a spatial intensity distribution, in a hologram plane at a hologram coordinate (zh) of an imaged object (1), of the interference caused by interactions between an illumination beam and said imaged object placed at an object coordinate (z0) on an imaging axis (6), 2) implementing (S03) a plurality of iterations, each comprising the following steps: 2.a) by back-propagation to the object coordinate of a hologram field comprising a spatial amplitude distribution corresponding to the spatial intensity distribution of the hologram and a spatial phase distribution, determining (S03a) an object field containing a spatial absorption distribution and a spatial phase-shift distribution of the imaged object, 2.b) thresholding (S03b) the values of the spatial absorption distribution and of the spatial phase-shift distribution of the imaged object by decreasing the values of the spatial absorption distribution below an absorption threshold and by decreasing the values of the spatial phase-shift distribution below a phase-shift threshold, the absorption threshold and the phase-shift threshold decreasing with each iteration, 2.c) by re-propagation of the object field to the hologram coordinate, determining (S03c) a modified hologram field comprising a modified spatial amplitude distribution and a modified spatial phase distribution, 2.d) replacing (S03d) the spatial phase distribution of the hologram field with the modified spatial phase distribution, the spatial amplitude distribution of the hologram field being retained, 3) determining the spatial phase-shift distribution and the spatial absorption distribution of the imaged object as being those of the object field of the last iteration.

2. The method as claimed in claim 1, wherein, during thresholding, the values of the spatial absorption distribution below the absorption threshold and the values of the spatial phase-shift distribution below the phase-shift threshold are set to zero.

3. The method as claimed in any one of the preceding claims, wherein the absorption threshold depends on maximum values of the spatial absorption distribution, and the phase-shift threshold depends on maximum values of the spatial phase-shift distribution contained in the object field.

4. The method as claimed in any one of the preceding claims, wherein, in the first iteration, the absorption threshold and / or the phase-shift threshold corresponds to between 40% and 15% of a maximum value of the spatial absorption distribution or spatial phase-shift distribution, respectively.

5. The method as claimed in any one of the preceding claims, wherein, in each iteration, the absorption threshold and / or the phase-shift threshold is decreased by 1% to 6% of a maximum value of the spatial absorption distribution or spatial phase-shift distribution.

6. The method as claimed in any one of the preceding claims, wherein, in the last iteration, the absorption threshold and the phase-shift threshold are set to zero.

7. The method as claimed in any one of the preceding claims, wherein, during thresholding, the values of the spatial absorption and phase-shift distribution are kept positive or zero during the iterations.

8. The method as claimed in any one of the preceding claims, wherein, before the iterations, the hologram field is normalized by dividing the values of the spatial intensity distribution by a background image value corresponding to an intensity of the illumination beam at the hologram coordinate.

9. The method as claimed in any one of the preceding claims, wherein the thresholding comprises smoothing the modified spatial absorption distribution and the modified spatial phase-shift distribution.

10. The method as claimed in any one of the preceding claims, wherein the hologram field and / or the object field have a spatial resolution that increases with the iterations.