Digital holographic imaging technology using double image cancellation

Abstract

The digital holographic imaging technique comprises the following iterative steps: 1) obtaining a hologram by holography (S01), said hologram being obtained by the holographic coordinates (z h ) in the hologram plane and the object coordinates (z o 2) performing a plurality of iterative steps (S03), each of which comprises the steps of: a) determining an object field associated with a spatial absorption distribution and a phase shift distribution of the object to be imaged through backpropagation to the object coordinates of a hologram field having a spatial amplitude distribution and a spatial phase distribution corresponding to the spatial intensity distribution of the hologram (S03a); b) thresholding the values ​​of the spatial absorption distribution and the phase shift distribution by reducing their values ​​below respective thresholds (S03b), the thresholds decreasing with each iteration; c) determining a modified hologram field including a modified spatial amplitude distribution and a modified spatial phase distribution through repropagation of the object field to the hologram coordinates (S03c); and d) replacing the spatial phase distribution of the hologram field with the modified spatial phase distribution (S03d). The spatial phase shift distribution and absorption distribution of the object to be imaged are those of the object field of the last iteration.

Description

[Technical Field]

[0001] This invention relates to the field of digital holography, and more precisely, to a method for removing double images in digital holographic imaging. [Background technology]

[0002] Digital holography is a method of recording a hologram using a sensor that represents the phase and amplitude of waves diffracted by an object. The hologram records the spatial intensity distribution of the interference pattern generated by the illumination beam and the light diffracted by the object being imaged. The hologram allows for the computational reconstruction of the object's image using a digital reconstruction algorithm. More precisely, the phase and absorption characteristics of the imaged object are obtained through backpropagation from the hologram. Backpropagation is calculated, for example, using a propagation algorithm based on Rayleigh-Sommerfeld diffraction theory.

[0003] Digital holography is used particularly in biological imaging, especially in digital holographic microscopy, due to its ability to image transparent objects such as biological cells and organisms. Specifically, in contrast to other imaging methods, digital holography does not require the injection of dyes to visualize transparent objects or the use of high-energy radiation (such as X-rays) that could damage the biological object being imaged.

[0004] Holographic imaging aims to find the spatial phase shift and absorption distribution of the object being imaged. Specifically, these properties of the imaged object allow for precise characterization of the object, and therefore, for example, identification of it.

[0005] Among various holographic techniques, inline holography exhibits high phase sensitivity, making it the most suitable method for imaging low-phase biological objects.

[0006] However, in-line holography has a major drawback. That is, there is a twin image or orthoscopic image resulting from the fact that the hologram records only intensity and the phase information in the hologram is lost. The twin image is an artifact that appears in the hologram to result from an additional imaged object symmetrically arranged with respect to the imaged object with respect to the plane of the hologram. Since the twin image is out of focus, during the reconstruction of the phase and absorption images, the shape of the imaged object is distorted, which may prevent the use of these images. SUMMARY OF THE INVENTION PROBLEM TO BE SOLVED BY THE INVENTION

[0007] An object of the present invention is to allow artifacts due to the presence of twin images to be removed during in-line holography. MEANS FOR SOLVING THE PROBLEM

[0008] For this purpose, the present invention provides a digital holographic imaging method including the following steps: 1) A step of obtaining a hologram by holography, wherein the hologram represents the spatial intensity distribution of interference caused by the interaction between an illumination beam and the imaged object placed at object coordinates on the imaging axis in the hologram plane at the hologram coordinates of the imaged object; 2) A step of performing a plurality of iterative processes, each iterative process including the following steps, namely: 2.a) Determining an object field including a spatial absorption distribution and a spatial phase shift distribution of the imaged object by inverse propagation of a hologram field having a spatial amplitude distribution and a spatial phase distribution corresponding to the spatial intensity distribution of the hologram to the object coordinates; 2.b) Thresholding the values of the spatial absorption distribution and the spatial phase shift distribution of the object to be imaged by reducing the values of the spatial absorption distribution below an absorption threshold and reducing the values of the spatial phase shift distribution below a phase shift threshold, wherein the absorption threshold and the phase shift threshold decrease in each iteration step. 2.c) Determining a corrected hologram field including a corrected spatial amplitude distribution and a corrected spatial phase distribution by re-propagating the object field to the hologram coordinates. 2.d) Replacing the spatial phase distribution of the hologram field with the corrected spatial phase distribution, wherein the spatial amplitude distribution of the hologram field is retained. 3) Determining the spatial phase shift distribution and the spatial absorption distribution of the object to be imaged as those of the object field in the last iteration step.

[0009] The present invention is advantageously supplemented by the following various characteristics, which can be implemented alone or in 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 0. · The absorption threshold depends on the maximum value of the spatial absorption distribution, and the phase shift threshold depends on the maximum value of the spatial phase shift distribution included in the object field. · In the first iteration step, the absorption threshold and / or the phase shift threshold respectively correspond to between 40% and 15% of the maximum value of the spatial absorption distribution or the spatial phase shift distribution. · In each iteration step, the absorption threshold and / or the phase shift threshold decrease by 1% to 6% of the maximum value of the spatial absorption distribution or the spatial phase shift distribution. · In the last iteration step, the absorption threshold and the phase shift threshold are set to 0. · During the iteration steps and during thresholding, the values of the spatial absorption and phase shift distributions are kept positive or 0. Prior to each iterative step, the hologram field is normalized by dividing the values ​​of the spatial intensity distribution by the background image values ​​corresponding to the intensity of the illumination beam in the hologram coordinates; The thresholding process includes smoothing the modified spatial absorption distribution and the modified spatial phase shift distribution; The hologram field and / or the object field have increasing spatial resolution with each iterative step. [Brief explanation of the drawing]

[0010] Other features, purposes, and advantages of the present invention will become apparent from the following description. This description is purely illustrative and non-limiting and should be read with reference to the accompanying drawings. [Figure 1] This is a summary of the main steps of a method according to one possible embodiment of the present invention. [Figure 2] A schematic example of a holographic imaging system used to obtain a hologram according to one possible embodiment of the present invention is shown. [Figure 3] A hologram of a bacterial cluster is shown as a first example of an implementation of a method according to one possible embodiment of the present invention. [Figure 4a] In a first example of implementing a method according to one possible embodiment of the present invention, the initial spatial phase shift distribution determined from the hologram in Figure 3 is shown. [Figure 4b] In a first example of implementing a method according to one possible embodiment of the present invention, the initial spatial absorption distribution determined from the hologram in Figure 3 is shown. [Figure 4c] Figure 4a shows the bacterial phase shift profile. [Figure 4d] Figure 4b shows the bacterial absorption profile. [Figure 5a] In a first example of implementing a method according to one possible embodiment of the present invention, the spatial phase shift distribution after the first iteration is shown. [Figure 5b] In a first example of implementing a method according to one possible embodiment of the present invention, the spatial absorption distribution after the first iteration is shown. [Figure 5c] Figure 5a shows the bacterial phase shift profile. [Figure 5d] Figure 5b shows the bacterial absorption profile. [Figure 6a] In a first example of an implementation of a method according to one possible embodiment of the present invention, the spatial phase shift distribution after the fifth iteration is shown. [Figure 6b] In a first example of implementing a method according to one possible embodiment of the present invention, the spatial absorption distribution after the fifth iteration is shown. [Figure 6c] Figure 6a shows the bacterial phase shift profile. [Figure 6d] Figure 6b shows the bacterial absorption profile. [Figure 7a] In a first example of implementing a method according to one possible embodiment of the present invention, the spatial phase shift distribution after the 20th iteration is shown. [Figure 7b] In a first example of implementing a method according to one possible embodiment of the present invention, the spatial absorption distribution after the 20th iteration is shown. [Figure 7c] Figure 7a shows the bacterial phase shift profile. [Figure 7d] Figure 7b shows the bacterial absorption profile. [Figure 8a] In a second example of implementing a method according to one possible embodiment of the present invention, a hologram of polystyrene beads acquired by an imaging system is shown. [Figure 8b] A photograph of polystyrene beads is shown as a second example of the implementation of the method described above. [Figure 9a] In a second example of implementing the method according to one possible embodiment of the present invention, the initial spatial phase shift distribution determined from the hologram in Figure 8a, prior to the first iteration step, is shown. [Figure 9b] In a second example of implementing the method according to one possible embodiment of the present invention, the initial spatial absorption distribution determined from the hologram in Figure 8b is shown prior to the first iteration step. [Figure 10a]In a second example of implementing a method according to one possible embodiment of the present invention, the spatial phase shift distribution after the 20th iteration is shown. [Figure 10b] In a second example of implementing a method according to one possible embodiment of the present invention, the spatial absorption distribution after the 20th iteration is shown. [Modes for carrying out the invention]

[0011] Referring to Figure 1, the digital holographic imaging method first includes obtaining a hologram of an object, typically imaged by inline holography (step S01). While the holography does not need to be inline for the present invention to be carried out, the biimage problem is most serious in the context of inline holography. Holograms can be obtained in various ways, but the method of acquisition does not affect the method. In particular, since the hologram represents the spatial intensity distribution of interference generated by the imaged object, the manner in which the hologram is obtained is not important.

[0012] As a non-limiting example, Figure 2 schematically illustrates an inline holographic imaging system for imaging object 1 by a digital image sensor 2 positioned in the image plane of the holographic imaging system. The imaging system defines an imaging axis 6, which, for simplicity, is represented here by a straight line corresponding to the optical axis, but depending on the configuration of the optical components of the imaging system, it may consist of a set of straight lines defining the path of light. Object 1 is located at object coordinate z on the imaging axis 6. o The image sensor 2 is placed at the hologram coordinate z h It is positioned and perpendicular to the imaging axis 6. As a result, the hologram is positioned at the object coordinate z on the imaging axis 6. o This represents the spatial intensity distribution H(x,y) of interference caused by the interaction between the object 1 being imaged and the illumination beam, placed on the hologram plane (x,y).

[0013] The light source 4 is configured to illuminate object 1 within the field of view of the holographic imaging system with a sufficiently coherent illumination beam. The light source 4 may generate illumination light or simply be the end of an optical fiber transmitting this illumination light. The illumination beam has the conventional properties required for holographic imaging, without any additional constraints. Thus, the illumination beam may be monochromatic (e.g., with a wavelength of about 500 nm) or may consist of multiple wavelengths, which may be used, for example, in sequence. Here, the holographic imaging system includes a microscope objective lens 8 (illustrated here by an inlet lens 8a and an outlet lens 8b) placed between the sample 1 and the digital image sensor 2. However, the microscope objective lens 8 is arbitrary, and the present invention is not limited to holographic microscopy using lenses. The configuration described here is, of course, a non-limiting example. Any holographic imaging system can be used, whether or not a microscope objective lens is used. Thus, any given holographic imaging system is suitable for implementing this method as long as it can acquire an image in which the interference pattern generated by object 1 appears. In contrast, the object coordinate z was used to obtain the resulting hologram. o and hologram coordinate z h It needs to be known.

[0014] During hologram acquisition, light source 4 emits a reference illumination beam. This reference illumination beam may be considered a reference plane wave propagating in the Z direction along the imaging axis 6. R(z) = Aexp(j2πz / λ) It may also be described by: where A and λ are the amplitude and wavelength of the reference wave emitted by the light source 4. Object 1 is at coordinate z on the imaging axis 6. ois arranged to scatter the incident reference light due to its diffraction - causing characteristics. As a result, a wave scattered by the object 1 is generated, which is represented as O(x, y, z). The scattered wave O(x, y, z) and the reference wave R(z) interfere at the image sensor 2 to form a hologram, which is the hologram coordinate z at the coordinates of the image sensor 2 on the imaging axis 6 h defines the hologram plane (in x, y) at. Since the digital image sensor 2 is only sensitive to the intensity of the electromagnetic field, the hologram is the spatial intensity distribution H(x, y, z h of the total field at h ), which is designated as the hologram field: H(x, y, z h ) = |R(z h ) + O(x, y, z h )| 2

[0015] When the object 1 does not exist, only the intensity of the reference wave is detected, and the hologram field is as follows: H(x, y, z h ) = |R(z h )| 2 = |A| 2 = B(z h ) B(z h ) is called the background image at the hologram coordinate z h .

[0016] The scattered wave O(x, y, z) is related to the incident wave R(z) by a complex transfer function t(x, y) such that O(x, y, z) = t(x, y)R(z), 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 as follows: U(x, y, z o ) = R(z o )(1 + t(x, y))

[0017] This relationship can be rewritten to reflect the fact that the reference wave is absorbed and its phase is shifted by the object 1: U(x, y, z o ) = R(z o)(1-a(x,y)exp(-jφ(x,y))) Here, a(x,y) is the absorption, and φ(x,y) is the phase shift due to object 1. These may directly originate from the properties of object 1 (structure, composition, etc.). Therefore, the absorption a and phase shift φ can be considered properties related to object 1, although they are also related to certain parameters such as the wavelength of the reference wave of the illumination beam.

[0018] Before continuing with this method, hologram coordinate z h Background image B(z h Using ), it is possible to implement the normalization (step S02) of the spatial intensity distribution H(x,y) represented by the hologram. The values ​​of the spatial intensity distribution H(x,y) are normalized to a background image B(z) with uniform intensity values ​​B. h Dividing by ) is equivalent to setting the amplitude A of the reference wave of the illumination beam to 1, thus simplifying the calculation. Therefore, we will assume that the amplitude A is equal to 1 below.

[0019] Next, the method includes the implementation of a sequential iterative step (step S03) aimed at determining the characteristics of the phase φ and absorption a of the imaged object 1 through multiple cycles of backpropagation and repropagation of the optical field in order to find the total field phase that is not retained in the hologram. During these cycles, increasingly strict thresholding is applied to the phase φ and absorption a, so that only the region of the highest amplitude is retained and the others are faded out. In particular, the number of iterations depends on the decreasing threshold applied. Typically, the number of iterations is at least 8, preferably at least 12.

[0020] Object field U(x,y,z o ) Hologram coordinates z h The hologram field corresponding to propagation is represented by the spatial amplitude distribution H(x,y) of the hologram's spatial intensity distribution and the spatial phase distribution Ω(x,y,z h It is a complex field that includes ). Therefore, the hologram field can be written as follows: U(x,y,z h)=(√H(x,y))exp[jΩ(x,y,z h )]

[0021] Image sensor 2 is only sensitive to the strength of the electromagnetic field, therefore the hologram coordinate z h The spatial phase distribution Ω is initially unknown and needs to be set to an initialization value. The initialization value is the hologram coordinate z h Reference wave R(z h ) Phase Ω(z h Choosing such a configuration is advantageous, and this can be estimated by direct propagation: exp(j2πz h / λ)=exp(jΩ(z h ))

[0022] In this way, an initial hologram field is obtained from the hologram, which includes a spatial amplitude distribution corresponding to the spatial intensity distribution of the hologram and an initial spatial phase distribution set as the initialization value.

[0023] In the first sequential iteration stage S03a, the object coordinate z of the hologram field o The complex object field is determined by backpropagation. Backpropagation utilizes optical diffraction models, such as the Rayleigh-Sommerfeld model or the Kirchhoff diffraction model. Such optical diffraction models allow us to determine the representation of the optical field at a second point based on knowledge of the representation of the field at a first point. In this regard, it is advantageous to use the plane waveangle spectral method, which operates in the frequency domain and in particular utilizes the Fourier transform, as described in Non-Patent Literature 1. [Non-Patent Document 1] Joseph W. Goodman, "Introduction to Fourier Optics", McGraw-Hill companies, 3rd edition, 2005

[0024] In the second sequential iteration stage S03b, the values ​​of the spatial absorption distribution a(x,y) and the spatial phase shift distribution φ(x,y) of the object 1 being imaged are extracted. As shown above, the object field U(x,y,z o) includes the spatial absorption distribution a(x,y) and spatial phase shift distribution φ(x,y) of the object 1 being imaged (see the following equation and its normalized form below): U(x,y,z o )=exp(jΩ(z o ))(1-a(x,y)exp(-jφ(x,y)))

[0025] The conjugate of the reference wave incident on object 1, i.e., exp(-jΩ(z o Multiplying by )) extracts the absorption a and shift φ that form the complex transfer function. These values ​​of absorption a and shift φ are the object coordinates z of the hologram field. o This can be extracted as a consequence of backpropagation and thanks to the existence of a reference wave.

[0026] Certain constraints are imposed on the possible values ​​of the absorption a and shift of the object 1 being imaged. Firstly, for the sake of energy conservation, meaning that absorption by object 1 must not lead to an increase in light amplitude as a result of diffraction, the absorption value must not be negative, i.e., a(x,y)≧0. If a negative absorption value occurs, it is the result of interference between the biimage and the reference wave, and it is replaced with a value of 0. Also, the phase shift must be positive, i.e., φ(x,y)≧0. In most cases, the object 1 being imaged actually has a refractive index greater than or equal to the refractive index of the light propagation medium. This is especially true when the object 1 being imaged is a microorganism such as bacteria in an aqueous solution. This is also true for almost all objects in the air. Thus, during the iterative process, the values ​​of the spatial absorption distribution a(x,y) and the phase shift distribution φ(x,y) are kept positive or 0.

[0027] Once extracted, the spatial absorption distribution a(x,y) and spatial phase shift distribution φ(x,y) of the imaged object 1 are modified by thresholding. That is, their values ​​are modified by reducing them below their respective thresholds. More precisely, spatial absorption distribution a(x,y) values ​​below the absorption threshold are reduced, and spatial phase shift distribution φ(x,y) values ​​below the phase shift threshold are reduced. Spatial absorption distribution a(x,y) values ​​above the absorption threshold are not reduced, and spatial phase shift distribution φ(x,y) values ​​above the phase shift threshold are not reduced. Spatial absorption distribution a(x,y) values ​​below the absorption threshold and spatial phase shift distribution φ(x,y) values ​​below the phase shift threshold are reduced significantly, by more than 50%, preferably more than 75%, and more preferably set to 0.

[0028] The threshold value decreases in each iteration. Preferably, the absorption threshold depends on the value of the spatial absorption distribution a(x,y), and the phase shift threshold depends on the value of the spatial phase shift distribution φ(x,y). Preferably, the absorption threshold depends on the maximum value of the spatial absorption distribution a(x,y), and preferably on the maximum value that the spatial absorption distribution a(x,y) takes. Similarly, the phase shift threshold depends on the maximum value of the spatial phase shift distribution φ(x,y), and preferably on the maximum value that the spatial phase shift distribution φ(x,y) takes. In particular, the value of the absorption threshold may correspond to a certain proportion of the maximum values ​​that the spatial absorption distribution a(x,y) takes, and this proportion decreases in each iteration. Similarly, the value of the phase shift threshold may correspond to a certain proportion of the maximum values ​​that the spatial phase shift distribution φ(x,y) takes, and this proportion decreases in each iteration. Of course, this proportion can also be defined based on the number of values ​​of those spatial distributions, for example, a certain proportion of the mean or other indicators.

[0029] 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 object being imaged correspond 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, preferably 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 iteration, the threshold decreases 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). In the final iteration, the threshold for the spatial absorption distribution a(x,y) is set to 0, and the threshold for the spatial phase shift distribution φ(x,y) of the object being imaged is set to 0. The initial values ​​of these thresholds, and their decrease with each iteration, depend in particular on the properties of the object being imaged 1, and may therefore be adapted accordingly. As mentioned above, the number of iterations essentially depends on the initial values ​​of those thresholds and their decrease with each iteration. The decrease in thresholds can be regular or irregular.

[0030] Thresholding removes the contribution of the biimage from the representation of the imaged object, as long as the noise caused by the biimage is always smaller in amplitude than the representation of the imaged object in the hologram. Specifically, by definition, the imaged object is at the focal point in the object field, while the biimage is out of focus.

[0031] After applying thresholding, the corrected spatial absorption distribution a'(x,y) and the corrected spatial phase shift distribution φ'(x,y) are obtained, which are the corrected complex body field U'(x,y,z o ) define: U(x,y,z o )=exp(jΩ(z o ))(1-a'(x,y)exp(-jφ'(x,y)))

[0032] Preferably, the second sequential iteration step includes smoothing the modified spatial absorption distribution and the modified spatial phase shift distribution, typically by applying a low-pass filter, such as Gaussian filtering. Smoothing allows for the avoidance of high-frequency components at edges caused by thresholding. Preferably, the size of the smoothing filter (i.e., the number of adjacent pixels considered simultaneously during filtering) is decreased as the sequential iteration progresses, for example, as the threshold is decreased. This makes it possible to find significant contrast in the imaged object at the end of the sequential iteration.

[0033] In the third sequential iteration stage (stage S03c), the modified hologram field U'(x,y,z h ) is the modified object field U'(x,y,z o ) Hologram coordinates z h This is determined by repropagation. Repropagation uses the same modality as the backpropagation described above, and therefore, optical diffraction models such as the Rayleigh-Sommerfeld model or the Kirchhoff diffraction model can be used. The resulting modified hologram field U'(x,y,z) h ) is the corrected amplitude and corrected phase Ω'(x,y,z h This includes the corrections made to the absorption and phase shift of object 1 imaged in the previous thresholding stage. In the next stage, only the corrected phase is used.

[0034] In the fourth sequential iteration stage (stage S03d), the hologram field Ω(x,y,z h The phase of ) is corrected to phase Ω'(x,y,z h It is replaced by ), but the amplitude of the hologram field is preserved. In other words, the modified hologram field U'(x,y,z h ) becomes the hologram field, and the modified spatial amplitude distribution is replaced by the initial spatial amplitude distribution. Specifically, the hologram is the hologram field U(x,y,z hIt can be inferred that this represents the spatial intensity distribution H(x,y) corresponding to the spatial amplitude distribution of the hologram field U(x,y,z h The spatial amplitude distribution of the hologram field Ω(x,y,z) is determined by the hologram and does not need to be corrected. In contrast, the spatial amplitude distribution of the hologram field Ω(x,y,z) is determined by the hologram and does not need to be corrected. h The phase of ) is not set and is updated in each iteration.

[0035] Following this fourth sequential iteration stage (stage S03d), the hologram field has a spatial phase distribution Ω(x,y,z h The values ​​may be updated, and a new iteration process may begin from the first sequential iteration stage (stage S03a), provided that the absorption threshold and shift threshold are reduced compared to the previous iteration process. The cycle of the iteration process ends when a criterion is met, for example, that the absorption threshold and / or shift threshold are 0 or at least less than the threshold. The number of iterations can be set, in which case the criterion is that the set number of iterations has been reached.

[0036] Following these iterative steps, the values ​​of the spatial phase shift and absorption distribution of the imaged object are determined to be the values ​​resulting from the final iterative step (step S04). More precisely, the values ​​of the spatial phase shift and absorption distribution of the imaged object are the values ​​corresponding to the final object field obtained by backpropagating the final hologram field to the object coordinates.

[0037] In each iteration, absorption and phase shift values ​​are obtained. However, these values ​​are contaminated with noise, essentially due to the biimage. Thresholding allows the most important contributions to be retained, while less important contributions contaminated with noise are gradually eliminated. Thus, the noise decreases with each iteration. Compared to existing methods, the method according to the present invention has the advantages of rapid convergence and complete elimination of noise caused by the biimage.

[0038] This method may be interpreted as first removing the noise caused by the biimage in the most scattering regions as a result of gradually decreasing the threshold, thus ignoring all details. Subsequently, as the threshold decreases, information is recovered from less scattering elements. Therefore, the speed of the method can be accelerated by first working with low-resolution hologram and / or object fields and then, as the sequential iterations progress, by increasing this resolution, for example, simultaneously with decreasing the threshold. Specifically, at the start of the sequential iterations, the image is approximated by only the most scattering regions, while as the threshold gradually decreases, finer details are recovered, justifying the increase in resolution. At the end of the sequential iterations, those fields may recover the same resolution as the initial hologram. Applying the sequential iterations to lower-resolution fields can significantly accelerate the speed of the method.

[0039] This method is particularly suitable for biological imaging, where the object being imaged is a biological sample acquired by holographic microscopy. Specifically, objects of biological origin generally have positive absorption and phase shift with clear contours. Therefore, biological imaging is a preferred application of this method. However, this method may also be used for types of objects other than biological objects.

[0040] To illustrate the effect of sequential iteration, Figures 2 through 5d show a first example of the implementation of these sequential iterations with respect to computer-generated holograms of groups of objects representing bacilli microcolonies. Figure 3 shows the original computer-generated hologram, i.e., the hologram generated from the spatial intensity distribution H(x,y) recorded by image sensor 2. As can be seen, the biimage induced by the group strongly distorts the shapes of the individual bacteria that make it up. These bacilli contain an alignment of four internal scattering structures. The bacteria have an absorption of 0.02 and a φ phase shift of 0.08, while the internal scattering structures have a maximum absorption of 0.05 and a maximum phase shift of 0.1.

[0041] Figure 4a shows the spatial phase shift distribution corresponding to the initial object field in Figure 3 after backpropagation of the hologram field to object coordinates, and Figure 4b shows the spatial absorption distribution corresponding to the initial object field in Figure 3 after backpropagation of the hologram field to object coordinates. Figure 4c shows the distribution profile of phase shift values ​​along the longitudinal axis of the bacillus between the two arrows. As a result of a considerable amount of noise generated by the biimage, the phase shift profile can be seen to be very flat, peaking at approximately 0.05 or half of the maximum phase shift. Thus, the noise prevents the identification and characterization of the four internal scattering structures within the bacillus. Figure 4d shows the distribution profile of absorption values ​​along the longitudinal axis of the bacillus between the two arrows. As a result of a large amount of noise generated by the biimage, the absorption profile can be seen to peak at 0.04 or half of the maximum absorption. Thus, the noise prevents the characterization of the four internal scattering structures within the bacillus.

[0042] After the first iteration, Figure 5a shows the spatial phase shift distribution, and Figure 5b shows the spatial absorption distribution. In this example, the initial threshold is set to 25% of the maximum value. Figure 5c shows the distribution profile of phase shift values ​​along the longitudinal axis of the bacilli between the two arrows. Compared to the previous profile in Figure 4c, the maximum value of the phase shift profile has clearly increased and is now approximately 0.07. Figure 5d shows the distribution profile of absorption values ​​along the longitudinal axis of the bacilli between the two arrows. Compared to the previous profile in Figure 4d, the maximum value of the absorption profile has increased to approximately 0.05.

[0043] After the fifth iteration, Figure 6a shows the spatial phase shift distribution, and Figure 6b shows the spatial absorption distribution. The absorption and phase shift thresholds were gradually decreased with each iteration. Figure 6c shows the distribution profile of phase shift values ​​along the longitudinal axis of the bacilli between the two arrows. Compared to the previous profile in Figure 5c, the maximum value of the phase shift profile has clearly increased further and is now approximately 0.09. However, the difference in values ​​between the internal scattering structure and the bacteria is still small. Figure 6d shows the distribution profile of absorption values ​​along the longitudinal axis of the bacilli between the two arrows. Compared to the previous profile in Figure 5d, the difference in values ​​between the internal scattering structure and the bacteria is highlighted.

[0044] After the 20th and final iteration, Figure 7a shows the spatial phase shift distribution, and Figure 7b shows the spatial absorption distribution. The absorption and phase shift thresholds were gradually decreased in each iteration, reaching 0 in this final iteration. Figure 7c shows the distribution profile of phase shift values ​​along the longitudinal axis of the bacilli between the two arrows. Compared to the previous profile in Figure 6c, the maximum value of the phase shift profile has increased and is now approximately 0.10. Furthermore, the difference in values ​​between the internal scattering structure and the bacteria is highlighted, and the absorption value for bacteria is now approaching 0.08. Thus, the actual value of the spatial absorption distribution of the imaged object is actually found. Figure 7d shows the distribution profile of absorption values ​​along the longitudinal axis of the bacilli between the two arrows. Compared to the previous profile in Figure 6d, the difference in values ​​between the internal scattering structure and the bacteria is further highlighted. Now, the maximum value corresponding to the internal scattering structure has reached 0.05, and the minimum value corresponding to the bacteria has reached 0.02. Thus, the actual value of the spatial absorption distribution of the imaged object is actually found.

[0045] Therefore, this method, in this example, allows for the complete elimination of noise and the discovery of precise values ​​for the phase shift and absorption of bacteria, including internal scattering structures, in just 20 sequential iterations. The speed of convergence improves as the size of the spatial region, which is set to 0 at the end of the sequential iterations, increases, as long as the thresholding eliminates the contribution of the biimages more than the contribution of the object being imaged. Thus, convergence is faster when the region of interest in the image is small. If the cluster in Figure 3 had contained more bacteria, that is, if there had been more objects of interest to be imaged, a larger number of iterations would have been necessary to find the precise values ​​for the phase shift and absorption. This could be done, for example, by decreasing the threshold more slowly.

[0046] Figures 8a to 10b show an example of the implementation of this method for experimental data. Polystyrene beads with a diameter of 1.1 μm were randomly placed on a slide by drying a colloidal suspension and then immersing it in oil to obtain the hologram in Figure 8a. The polystyrene beads produced a large phase shift but had very low absorption. As a non-limiting example, the holographic imaging system used to obtain the hologram in this example was an in-line holographic microscopy system, using a monochromatic LED emitting at 405 nm with a full width at half maximum of 12 nm as the light source 4. Light source 4 was positioned 100 nm from the slide. The holographic imaging system had a microscope objective lens 8 with a numerical aperture of 100 × 1.3 at a magnification of 80. A CMOS sensor was used as the image sensor 2. The refractive index of the beads was approximately 1.63, and the refractive index of the immersion oil was approximately 1.53. Figure 8a shows the hologram after normalization with a background image. For comparison, Figure 8b shows a non-holographic image of the beads with the same configuration.

[0047] Similar to Figures 2a and 2b, Figure 9a shows the spatial phase shift distribution corresponding to the initial hologram in Figure 8a after backpropagating the hologram field to object coordinates, and Figure 9b shows the spatial absorption distribution corresponding to the original image in Figure 8a after backpropagating the hologram field to object coordinates. Here, it can be seen that the spatial phase shift and absorption distributions are again greatly affected by the noise generated by the biimage. In particular, the spatial absorption distribution contains large fluctuations, even though the beads are thought to have low absorption.

[0048] As described above, multiple iterative cycles are performed. After the 50th and final iteration, Figure 10a shows the spatial phase shift distribution, and Figure 10b shows the spatial absorption distribution. The absorption and phase shift thresholds are gradually reduced in each iteration, becoming zero in this final iteration. On the one hand, the spatial phase shift distribution can be seen to clearly correspond to the bead distribution shown in Figure 8b. On the other hand, the low value of the spatial absorption distribution correctly reflects the low absorbency of the polystyrene beads. Thus, the noise caused by biimages is effectively eliminated, and the values ​​of the spatial phase shift and absorption distributions are correctly determined.

[0049] The present invention is not limited to the embodiments described and shown in the accompanying drawings. Modifications are still possible, particularly in terms of the nature of various technical features or in terms of substituting technical equivalents, without departing from the scope of protection of the present invention.

Claims

1. A digital holographic imaging method: 1) A step (S01) to obtain a hologram by holography, wherein the hologram is the holographic coordinate (z) of the object (1) being imaged. h In the hologram plane in ), the illumination beam and the object coordinates (z) on the imaging axis (6) o The spatial intensity distribution of interference caused by the interaction between the object being imaged and the object placed in the image is represented by steps and; 2) A stage in which multiple iterative processes are carried out (S03), each iterative process being the following steps: 2.a) A step (S03a) Determining an object field including the spatial absorption distribution and spatial phase shift distribution of the imaged object by backpropagating the hologram field, which has a spatial amplitude distribution and a spatial phase distribution corresponding to the spatial intensity distribution of the hologram, to the object coordinates. 2.b) A step in which the values ​​of the spatial absorption distribution and the spatial phase shift distribution of the object to be imaged are thresholded by reducing the value of the spatial absorption distribution below an absorption threshold and reducing the value of the spatial phase shift distribution below a phase shift threshold, wherein the absorption threshold and the phase shift threshold are reduced in each iteration step (S03b), 2.c) A step of determining a modified hologram field including a modified spatial amplitude distribution and a modified spatial phase distribution by repropagating the object field to the hologram coordinates (S03c), 2.d) A step (S03d) in which the spatial phase distribution of the hologram field is replaced with the modified spatial phase distribution, wherein the spatial amplitude distribution of the hologram field is preserved; 3) A step of determining the spatial phase shift distribution and the spatial absorption distribution of the imaged object as those of the object field in the final iteration step, method.

2. The method according to 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 0.

3. The method according to claim 1 or 2, wherein the absorption threshold depends on the maximum value of the spatial absorption distribution, and the phase shift threshold depends on the maximum value of the spatial phase shift distribution included in the object field.

4. The method according to any one of claims 1 to 3, wherein in the first iteration step, the absorption threshold and / or the phase shift threshold correspond to between 40% and 15% of the maximum value of the spatial absorption distribution or the spatial phase shift distribution, respectively.

5. The method according to any one of claims 1 to 4, wherein in each iteration, the absorption threshold and / or the phase shift threshold is reduced by 1% to 6% of the maximum value of the spatial absorption distribution or the spatial phase shift distribution.

6. The method according to any one of claims 1 to 5, wherein in the final iteration step, the absorption threshold and the phase shift threshold are set to 0.

7. The method according to any one of claims 1 to 6, wherein during sequential iterations and thresholding, the values ​​of the spatial absorption and phase shift distribution are kept positive or zero.

8. The method according to any one of claims 1 to 7, wherein, prior to sequential iteration, the hologram field is normalized by dividing the value of the spatial intensity distribution by the background image value corresponding to the intensity of the illumination beam in the hologram coordinates.

9. The method according to any one of claims 1 to 8, wherein the thresholding process includes smoothing the modified spatial absorption distribution and the modified spatial phase shift distribution.

10. The method according to any one of claims 1 to 9, wherein the hologram field and / or the object field have increasing spatial resolution with each iterative step.

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