Digital holographic imaging technique with twin-image elimination

Abstract

A digital holographic imaging technique with the following iterative steps: a) determining (S03a) an object field involving spatial distributions of absorption and phase shift of the imaged object by back-propagating a hologram field comprising an amplitude spatial distribution and a phase spatial distribution corresponding to the intensity spatial distribution of the hologram to the object coordinates, b) thresholding (S03b) the spatial distributions of absorption and phase shift by reducing their values below respective threshold values, the threshold values being reduced at each iteration, c) determining (S03c) a modified hologram field comprising a modified amplitude spatial distribution and a modified phase spatial distribution by re-propagating the object field to the hologram coordinates, d) replacing (S03d) the phase spatial distribution of the hologram field with the modified phase spatial distribution, the spatial distributions of phase shift and absorption of the imaged object being those of the object field of the last iteration.

Description

Technical Field

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

[0002] Digital holography is a method of recording holograms using sensors to represent the phase and amplitude of waves diffracted by an object. The hologram records the spatial distribution of the intensity of the interference pattern generated by the illumination beam and the light diffracted by the imaging object. Holograms make it possible to reconstruct an image of the object computationally using digital reconstruction algorithms. More precisely, the phase and absorption characteristics of the imaging object are obtained through backpropagation of the hologram, which is calculated using, for example, a propagation algorithm based on Rayleigh-Sommerfeld diffraction theory.

[0003] Digital holography is particularly useful for biological imaging because it has the ability to image transparent objects, such as biological cells or organisms, and is especially useful in digital holographic microscopy. Specifically, unlike other imaging methods, digital holography does not require the injection of dyes to make transparent objects visible, nor does it require the use of high-energy radiation (such as X-rays) that could damage the biological object being imaged.

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

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

[0006] However, online holography has a major drawback: the presence of twin images, or orthogonal images. This is due to the loss of phase information in the hologram, which only records intensity. Twin images are artifacts appearing in the hologram and are caused by additional imaging objects arranged symmetrically with respect to the plane of the hologram and the imaged object. Because twin images are out of focus, they cause shape distortion of the imaged object during the reconstruction of the phase and absorption images, which may hinder the use of these images. Summary of the Invention

[0007] The present invention aims to allow the removal of artifacts caused by the presence of twin images during online holography.

[0008] Therefore, the present invention provides a digital holographic imaging method, comprising the following steps:

[0009] 1) A hologram is obtained by holography, wherein the hologram represents the spatial intensity distribution of interference caused by the interaction between the illumination beam and the object placed at the object coordinates on the imaging axis in the hologram plane at the hologram coordinates of the imaged object.

[0010] 2) Implement multiple iterations, each iteration including the following steps:

[0011] 2.a) By backpropagating the holographic field, which includes the spatial distribution of amplitude and phase corresponding to the spatial distribution of intensity in the hologram, to the object coordinates, determine the object field containing the spatial distribution of absorption and the spatial distribution of phase shift of the imaged object.

[0012] 2.b) Thresholding is performed on the values ​​of the absorption spatial distribution and phase shift spatial distribution of the imaged object by reducing the values ​​of the absorption spatial distribution below the absorption threshold and the phase shift spatial distribution below the phase shift threshold, with the absorption threshold and phase shift threshold decreasing with each iteration.

[0013] 2.c) By repropagating the object field to the holographic coordinates, the modified holographic field, including the modified amplitude spatial distribution and the modified phase spatial distribution, is determined.

[0014] 2.d) Replace the phase space distribution of the hologram field with the modified phase space distribution, while preserving the amplitude space distribution of the hologram field.

[0015] 3) The phase shift spatial distribution and absorption spatial distribution of the imaged object are determined as the phase shift spatial distribution and absorption spatial distribution of the object field in the last iteration.

[0016] The invention is advantageously complemented by a variety of features, which can be implemented individually or in various possible combinations thereof:

[0017] - During thresholding, the values ​​of the absorption spatial distribution below the absorption threshold and the phase shift spatial distribution below the phase shift threshold are set to zero;

[0018] - The absorption threshold depends on the maximum value of the absorption spatial distribution, and the phase shift threshold depends on the maximum value of the phase shift spatial distribution contained in the object field;

[0019] - In the first iteration, the absorption threshold and / or phase shift threshold correspond to between 40% and 15% of the maximum values ​​of the absorption spatial distribution and the phase shift spatial distribution, respectively;

[0020] - In each iteration, the absorption threshold and / or phase shift threshold are reduced by 1% to 6% of the maximum value of the absorption spatial distribution or the phase shift spatial distribution;

[0021] - In the last iteration, the absorption threshold and phase shift threshold are set to zero;

[0022] -During thresholding, the values ​​of the absorption spatial distribution and the phase shift spatial distribution are kept positive or zero during iteration;

[0023] - Before iteration, the hologram field is normalized by dividing the value of the intensity spatial distribution by the background image value corresponding to the intensity of the illumination beam at the hologram coordinates;

[0024] - Thresholding includes smoothing the modified absorption spatial distribution and the modified phase shift spatial distribution;

[0025] - The holographic field and / or object field have increasing spatial resolution with iteration. Attached Figure Description

[0026] Other features, objects, and advantages of the invention will become apparent from the following description, which is purely illustrative and non-limiting, and must be read with reference to the accompanying drawings, in which:

[0027] - Figure 1 This is a flowchart illustrating the main steps of a method according to a possible embodiment of the present invention.

[0028] - Figure 2 An example of a holographic imaging system for acquiring holograms according to a possible embodiment of the present invention is illustrated schematically.

[0029] - Figure 3 A hologram of a bacterial cluster illustrating a first example of an implementation of a method according to a possible embodiment of the present invention is shown.

[0030] - Figure 4a This illustrates a first example of an implementation of a method according to a possible embodiment of the present invention, from... Figure 3 The initial phase shift spatial distribution determined by the hologram,

[0031] - Figure 4b This illustrates a first example of an implementation of a method according to a possible embodiment of the present invention, from... Figure 3 The initial absorption spatial distribution determined by the hologram,

[0032] - Figure 4c It shows Figure 4a Distribution of phase shift values ​​in bacteria.

[0033] - Figure 4d It shows Figure 4b Distribution of bacterial uptake values ​​in the medium.

[0034] - Figure 5aThe diagram illustrates the spatial distribution of phase shifts after the first iteration in a first example of an implementation of the method according to a possible embodiment of the invention.

[0035] - Figure 5b The illustration shows the spatial distribution of absorption after the first iteration in a first example of an implementation of the method according to a possible embodiment of the present invention.

[0036] - Figure 5c It shows Figure 5a Distribution of phase shift values ​​in bacteria.

[0037] - Figure 5d It shows Figure 5b Distribution of bacterial uptake values ​​in the medium.

[0038] - Figure 6a The diagram illustrates the spatial distribution of the phase shift after the fifth iteration in a first example of an implementation of the method according to a possible embodiment of the invention.

[0039] - Figure 6b The illustration shows the absorption spatial distribution after the fifth iteration in a first example of an implementation of the method according to a possible embodiment of the present invention.

[0040] - Figure 6c It shows Figure 6a Distribution of phase shift values ​​in bacteria.

[0041] - Figure 6d It shows Figure 6b Distribution of bacterial uptake values ​​in the medium.

[0042] - Figure 7a The diagram illustrates the spatial distribution of the phase shift after the twentieth iteration in a first example of an implementation of the method according to a possible embodiment of the invention.

[0043] - Figure 7b The illustration shows the absorption spatial distribution after the twentieth iteration in a first example of an implementation of the method according to a possible embodiment of the present invention.

[0044] - Figure 7c It shows Figure 7a Distribution of phase shift values ​​in bacteria.

[0045] - Figure 7d It shows Figure 7b Distribution of bacterial uptake values ​​in the medium.

[0046] - Figure 8a The illustration shows a second example of an implementation of the method according to a possible embodiment of the present invention, featuring a hologram of polystyrene beads acquired by an imaging system.

[0047] - Figure 8b A photograph of polystyrene beads illustrating a second example of an implementation of the method is shown.

[0048] - Figure 9a This illustrates a second example of an implementation of the method according to a possible embodiment of the invention, where, prior to the first iteration, from Figure 8a The initial phase shift spatial distribution determined by the hologram,

[0049] - Figure 9b This illustrates a second example of an implementation of the method according to a possible embodiment of the invention, where, prior to the first iteration, from Figure 8b The initial absorption spatial distribution determined by the hologram,

[0050] - Figure 10a The diagram illustrates the spatial distribution of the phase shift after the twentieth iteration in a second example of an implementation of the method according to a possible embodiment of the invention.

[0051] - Figure 10b The absorption space distribution after the twentieth iteration is shown in a second example of an implementation of the method according to a possible embodiment of the present invention. Detailed Implementation

[0052] refer to Figure 1 The digital holographic imaging method first includes obtaining a hologram of the object imaged by holography (step S01), typically via online holography. For the purposes of this invention, the holography need not be online, but in the case of online holography, the twin image problem is most acute. The hologram can be obtained in various ways, but the method of acquisition does not affect the method. In particular, the form in which the hologram is obtained is not important, as the hologram represents the spatial distribution of the intensity of the interference generated by the imaged object.

[0053] As a non-restrictive example, Figure 2 An in-line holographic imaging system for imaging an object 1 using a digital image sensor 2 placed in the image plane of the holographic imaging system is schematically illustrated. 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 can consist of a set of continuous straight lines defining the path of light. The object 1 is placed on the imaging axis 6 at object coordinate z. o At this location, image sensor 2 is placed at the holographic coordinate z. h The object is located at and perpendicular to the imaging axis 6. Therefore, the hologram represents the coordinates z of the object placed on the imaging axis 6. oThe spatial distribution of the intensity H(x,y) of the interference caused by the interaction between the imaging object 1 and the illumination beam at point (x,y) in the holographic plane (x,y).

[0054] Light source 4 is configured to illuminate object 1 in the field of view of the holographic imaging system with an illumination beam of sufficiently coherent light. Light source 4 can generate the illumination light, or simply be the end of an optical fiber transmitting the illumination light. The illumination beam has the conventional characteristics required for holographic imaging without any particular additional constraints. Therefore, the illumination beam can be monochromatic (e.g., with a wavelength of approximately 500 nm), or may consist of, for example, multiple wavelengths used one after another. The holographic imaging system is here equipped with a microscope objective 8 (schematically shown here by an incident lens 8a and an exit lens 8b), which is positioned between sample 1 and digital image sensor 2. However, the microscope objective 8 is optional, and the invention is not limited to a holographic microscope employing lenses. The arrangement described herein is, of course, a non-limiting example. Any holographic imaging system can be used, whether or not it employs a microscope objective, etc. Therefore, any given holographic imaging system capable of acquiring an image in which an interference pattern generated by object 1 appears is suitable for implementing this method. Conversely, it is necessary to know the object coordinates z for acquiring the obtained hologram. o and holographic coordinates z h .

[0055] During hologram acquisition, light source 4 emits a reference illumination beam, which can be considered as a reference plane wave propagating along the imaging axis 6 in the Z direction, and can be described as:

[0056] R(z)=Aexp(j2πz / λ)

[0057] Where A is the amplitude of the reference wave emitted by light source 4, and λ is the wavelength of the reference wave. Object 1 is placed on the imaging axis 6 at coordinate z. o At this location, and due to its diffraction properties, it will scatter the incident reference light. This results in a wave scattered by object 1, which is represented as O(x,y,z). The scattered wave O(x,y,z) and the reference wave R(z) interfere at image sensor 2 to form a hologram, at the hologram coordinate z. h The holographic plane is defined (in x, y), and the holographic coordinates are z. h This refers to the coordinates of image sensor 2 on imaging axis 6. Since digital image sensor 2 is only sensitive to the intensity of electromagnetic fields, the hologram corresponds to hologram coordinates z. h Spatial distribution of the total field intensity H(x,y,z) at location h It is designated as the holographic field:

[0058] H(x, y, z) h )=|R(z h)+O(x, y, z) h )| 2

[0059] In the absence of object 1, only the intensity of the reference wave will be detected, and the holographic field will be:

[0060] H(x, y, z) h )=|R(z h )| 2 =|A| 2 =B(z) h )

[0061] B(z h ) is referred to as the z-coordinate in the hologram h The background image at that location.

[0062] The scattered wave O(x,y,z) is related to the incident wave R(z) through the complex transfer function t(x,y) such that O(x,y,z) = t(x,y)R(z0), and the total field U(x,y,z) generated by the addition of the scattered wave O(x,y,z) and the reference wave R(z) can be written as:

[0063] U(x, y, z) o )=R(z o (1+t(x,y))

[0064] This relationship can be rewritten to reflect the fact that the reference wave is absorbed by object 1 and causes a phase shift:

[0065]

[0066] Where a(x,y) is the absorption, and This is due to the phase shift caused by object 1. These can be directly derived from the properties of object 1 (structure, composition, etc.). Therefore, absorption a and phase shift... It can also be considered a property related to object 1, although it is also related to certain parameters, such as the wavelength of the reference wave of the illumination beam.

[0067] Before proceeding with this method, the holographic coordinates z can be used. h Background image B(z) at that location h This is performed to normalize the intensity spatial distribution H(x,y) represented by the hologram (step S02). The value of the intensity spatial distribution H(x,y) is divided by the background image B(z) with a uniform intensity value B. h This is equivalent to setting the amplitude A of the reference wave of the illumination beam to 1, and thus allows for simplified calculations. Therefore, in the following text, the amplitude A will be considered equal to 1.

[0068] The method then includes implementing an iterative step (step S03) aimed at determining the phase of the imaging object 1 via multiple cycles of backpropagation and repropagation of the light field. And absorption α properties in order to find the phase of the total field not retained in the hologram. During these cycles, the phase is... The absorption process employs increasingly stringent thresholding to retain only the region of highest amplitude, while other regions gradually disappear. The number of iterations depends particularly on the reduction of the applied threshold. Typically, the number of iterations is at least 8, and preferably at least 12.

[0069] Corresponding to the object field U(x,y,z) o ) to holographic coordinates z h The propagating holographic field is a complex field, which includes the spatial distribution of amplitude and the spatial distribution of phase, represented by the spatial distribution of intensity H(x,y) of the hologram. h Therefore, the holographic field is written as:

[0070]

[0071] Since image sensor 2 is only sensitive to the intensity of electromagnetic fields, the holographic coordinates z h The phase spatial distribution Ω at point z is initially unknown and must be set to an initial value. It is advantageously chosen as the reference wave R(z). h In the hologram coordinates z h Phase Ω(z) at the point h It is estimated through direct propagation:

[0072] exp(j2πz h / λ)=exp(jΩ(z h ))

[0073] Therefore, an initial holographic field is obtained from the hologram, which includes an amplitude spatial distribution corresponding to the intensity spatial distribution of the hologram and an initial phase spatial distribution set to initial values.

[0074] In the first iteration step S03a, the object coordinates z are backpropagated to the holographic field. oTo determine the field of a complex object, backpropagation utilizes optical diffraction models, such as the Rayleigh-Sommerfeld model or the Kirchhoff diffraction model. These models allow for the determination of the expression for the optical field at a second point based on knowledge of the field expression at the first point. In this respect, it is advantageous to operate in the frequency domain, and particularly using plane-wave angular spectral methods utilizing Fourier transforms, as described in Joseph W. Goodman's "Introduction to Fourier Optics," McGraw-Hill, 3rd edition, 2005.

[0075] In the second iteration step S03b, the absorption spatial distribution a(x, y) and phase shift spatial distribution of the imaged object 1 are extracted. The value of . As mentioned above, the object field U(x,y,z) o The image contains the absorption spatial distribution a(x,y) and phase shift spatial distribution of the imaged object 1. (The following text is in normalized form):

[0076]

[0077] By multiplying by the conjugate of the reference wave incident on object 1, i.e., multiplying by exp(-jΩ(z) o Extract the absorption 'a' and displacement that form the complex transfer function. Absorption a and displacement These values ​​are derived from the holographic field to the object's z-coordinate. o It is generated by back propagation and can be extracted due to the presence of a reference wave.

[0078] Certain constraints are imposed on the possible values ​​of absorption *a* and phase shift of the imaged object 1. First, due to energy conservation, this means that absorption by object 1 cannot lead to an increase in light amplitude due to diffraction; therefore, the absorption value must be non-negative, i.e., *a(x,y) ≥ 0. If negative absorption values ​​appear, they are the result of interference between the twin image and the reference wave, and they are replaced by zero values. Furthermore, a positive phase shift is also necessary. In most cases, the imaged object 1 does indeed have a refractive index greater than or equal to the refractive index of the light propagation medium. This is especially true when the imaged object 1 is a microorganism such as bacteria in an aqueous solution. This is true for almost all objects in the air. Therefore, the value of the absorption spatial distribution a(x,y) and the phase shift spatial distribution... The value is kept either positive or zero during the iteration.

[0079] Once extracted, the values ​​of the absorption spatial distribution a(x,y) and phase shift spatial distribution of the imaged object 1 are obtained. The values ​​are modified through thresholding: they are modified by reducing the values ​​below their respective thresholds. More precisely, the values ​​of the absorption spatial distribution a(x,y) decrease below the absorption threshold, while the values ​​of the phase-shifted spatial distribution decrease below the phase-shift threshold. The value decreases. The value of the absorption spatial distribution a(x,y) above the absorption threshold does not decrease, and the value of the phase shift spatial distribution above the phase shift threshold also decreases. The value did not decrease. The values ​​of the absorption spatial distribution a(x,y) below the absorption threshold and the phase shift spatial distribution below the phase shift threshold... The value is greatly reduced, by more than 50%, preferably by more than 75%, and more preferably set to zero.

[0080] The threshold value decreases with each iteration. Preferably, the absorption threshold depends on the value of the absorption spatial distribution a(x,y), and the phase shift threshold depends on the phase shift spatial distribution. The value of . Preferably, the absorption threshold depends on the maximum value of the absorption spatial distribution a(x,y), and more preferably on the maximum value taken by the absorption spatial distribution a(x,y). Similarly, the phase shift threshold depends on the phase shift spatial distribution The maximum value, and preferably depends on the phase shift space distribution. The maximum value taken. Specifically, the absorption threshold can correspond to the proportion of the maximum value taken by the absorption space distribution a(x,y), which decreases with each iteration. Similarly, the phase shift threshold can correspond to the phase shift space distribution. The proportion of the maximum value taken, which decreases with each iteration. Of course, this proportion can also be defined based on multiple values ​​of the spatial distribution, for example, it is a proportion of the average or other indicators.

[0081] For example, in the first iteration, the absorption threshold and / or phase shift spatial distribution of the absorption spatial distribution a(x,y) of the imaged object. The phase shift thresholds correspond to the absorption spatial distribution a(x,y) or the phase shift spatial distribution, respectively. The maximum value is between 40% and 15%, and preferably corresponds to the absorption spatial distribution a(x,y) or the phase shift spatial distribution, respectively. The threshold is between 30% and 20% of the maximum value. Then, in each iteration, the threshold decreases the absorption spatial distribution a(x,y) or the phase shift spatial distribution. The maximum value is 2% to 6%. In the last iteration, the threshold of the absorption spatial distribution a(x,y) is set to zero, and the phase shift spatial distribution of the imaged object is... The threshold is set to zero. The initial values ​​of the thresholds, and their decreasing with each iteration, depend particularly on the properties of the imaged object 1, and can therefore be adapted accordingly. As mentioned above, the number of iterations essentially depends on the initial values ​​of the thresholds, and their decreasing with each iteration. The reduction of the thresholds can be regular or irregular.

[0082] As long as the noise caused by the twin image is always lower in amplitude than the representation of the imaged object in the hologram, the thresholding process will contribute more to removing the twin image than to the representation of the imaged object. Specifically, by definition, the imaged object is at the focal point in the object field, while the twin image is out of focus.

[0083] After applying thresholding, the modified absorption spatial distribution a'(x,y) and the modified phase shift spatial distribution were obtained. These define the modified complex object field U'(x,y,z) o ):

[0084]

[0085] Preferably, the second iterative step includes smoothing the modified absorption spatial distribution and the modified phase shift spatial distribution, typically by applying a low-pass filter, such as a Gaussian filter. Smoothing prevents the generation of high-frequency components at edges due to thresholding. Preferably, the size of the smoothing filter (i.e., the number of neighboring pixels considered simultaneously during filtering) decreases as the iteration proceeds, for example, as the threshold decreases. This allows for the localization of significant contrast within the imaged object at the end of the iteration.

[0086] In the third iteration step (step S03c), the modified object field U'(x,y,z) is... o Then propagate to the holographic coordinates z. h Determine the modified holographic field U'(x,y,z) h The repropagation takes the same form as the backpropagation described above, and therefore can utilize optical diffraction models, such as, for example, the Rayleigh-Sommerfeld model or the Kirchhoff diffraction model. The resulting modified holographic field U'(x,y,z) h This includes the modified amplitude and modified phase Ω'(x,y,z) h This reflects the modifications made to the absorption and phase shift of the imaged object 1 in the previous thresholding step. In subsequent steps, only the modified phase is used.

[0087] In the fourth iteration step (step S03d), the holographic field Ω(x,y,z) h The phase of Ω'(x,y,z) is modified. hThe holographic field is replaced by a variable, while the amplitude of the holographic field is preserved. In other words, the modified holographic field U'(x,y,z) is... h The hologram is transformed into a holographic field, and the modified amplitude spatial distribution is replaced by the initial amplitude spatial distribution. Specifically, as will be recalled, the hologram represents the holographic field U(x,y,z). h The amplitude spatial distribution and intensity spatial distribution H(x,y) of the holographic field U(x,y,z) are shown. h The spatial distribution of the amplitude of the hologram is determined by the hologram and does not need to be modified. Conversely, the hologram field Ω(x,y,z) is determined by the hologram. h The phase of ) is not set and is updated in each iteration.

[0088] Following this fourth iteration (step S03d), the holographic field will have thus updated its phase space distribution Ω(x,y,z). h A new iteration can begin from the first iteration step (step S03a), however, the absorption threshold and shift threshold are lower than in the previous iteration. The iteration loop ends when a criterion is met, such as the absorption threshold and / or shift threshold being zero or at least below the threshold. Alternatively, an iteration number can be set, and the criterion is the number of iterations that have been reached.

[0089] After iteration, the values ​​of the phase shift spatial distribution and the absorption spatial distribution of the imaged object are determined (step S04) to be the values ​​obtained in the last iteration. More precisely, the values ​​of the phase shift spatial distribution and the absorption spatial distribution of the imaged object are the values ​​of the last object field obtained by backpropagating to the object coordinates of the last hologram field.

[0090] In each iteration, absorption and phase shift values ​​are obtained. However, these values ​​are contaminated with noise, primarily due to the twin images. Thresholding allows the most important contributions to be preserved while gradually eliminating less important contributions contaminated with noise. Thus, noise is reduced in each iteration. Compared to existing methods, the method according to the invention has the advantage of fast convergence and completely eliminates noise caused by the twin images.

[0091] As a result of the gradually decreasing threshold, this method can be interpreted as first removing noise caused by twin images in most scattering regions, ignoring all details. Then, as the threshold decreases, information is recovered from elements with less scattering. Therefore, by initially using a low-resolution holographic field and / or object field, and then increasing this resolution as iterations proceed, for example, while the threshold decreases, this gradual recovery of detail can be leveraged to accelerate the method. Specifically, at the beginning of the iteration, the image is approximated only by the most scattering regions, while increasingly finer details are recovered as the threshold gradually decreases, demonstrating the increase in resolution. At the end of the iteration, the field can recover the same resolution as the initial hologram. Applying iterations to a lower-resolution field makes it possible to significantly speed up the method.

[0092] This method is particularly suitable for bioimaging, where the object being imaged is a biological sample acquired through holographic microscopy. Specifically, biologically derived objects typically exhibit well-defined positive absorption and phase shifts. Therefore, bioimaging is a preferred application of this method. However, this method can also be used for object types that are not biological.

[0093] To illustrate the effect of iteration, Figures 2 to 5d The first example shown is of implementing these iterations on a hologram of a set of objects representing microcolonies of rod-shaped bacteria, generated by computer. Figure 3 The original computer-generated hologram is shown, generated from the intensity spatial distribution H(x,y) recorded by image sensor 2. As can be seen, the twin image induced by this population strongly distorts the shape of the individual bacteria that compose it. These rod-shaped bacteria contain an arrangement of four internal scattering structures. The bacteria have an absorbance of 0.02, and The phase shift is 0.08, the maximum absorption rate of the internal scattering structure is 0.05, and the maximum phase shift is 0.1.

[0094] Figure 4a This shows that after the holographic field is backpropagated to the object coordinates, corresponding to... Figure 3 The initial spatial distribution of the phase shift of the object field, and Figure 4b This shows that after the holographic field propagates backward to the object coordinates, corresponding to... Figure 3 The absorption spatial distribution of the initial object field. Figure 4c A distribution of phase shift values ​​along the longitudinal axis of the rod-shaped bacterium between the two arrows is shown. It can be seen that the phase shift profile is quite flat due to the significant noise generated by the twin images, peaking at approximately 0.05, or half the maximum phase shift. Therefore, the noise hinders the identification and characterization of the four internal scattering structures within the bacterium. Figure 4dA distribution of absorbance values ​​along the longitudinal axis of the rod-shaped bacteria between the two arrows is shown. It can be seen that, due to the significant noise generated by the twinning image, the absorbance profile peaks at approximately 0.04, or half of the maximum absorbance. Therefore, noise hinders the characterization of the four internal scattering structures within the bacteria.

[0095] Figure 5a The spatial phase shift distribution after the first iteration is shown, and Figure 5b The spatial distribution of absorption is shown. In this example, the initial threshold is set to 25% of the maximum value. Figure 5c A plot showing the distribution of phase shift values ​​along the longitudinal axis of the rod-shaped bacteria between the two arrows is presented. Figure 4c Compared to the previous cross-sectional view, the maximum value of the phase shift cross-sectional view has increased significantly, now to approximately 0.07. Figure 5d A graph showing the distribution of absorbance values ​​along the longitudinal axis of the rod-shaped bacteria between the two arrows is presented. Figure 4d Compared to the previous profile, the maximum value of the absorption profile has increased to approximately 0.05.

[0096] Figure 6a The spatial distribution of the phase shift is shown after the fifth iteration, and Figure 6b The spatial distribution of absorption is shown. The absorption threshold and phase shift threshold gradually decrease with each iteration. Figure 6c A plot showing the distribution of phase shift values ​​along the longitudinal axis of the rod-shaped bacteria between the two arrows is presented. Figure 5c Compared to the previous cross-sectional plot, the maximum value of the phase-shifted cross-sectional plot has increased significantly further, now reaching approximately 0.09. However, the value difference between the internal scattering structures and bacteria remains small. Figure 6d A graph showing the distribution of absorbance values ​​along the longitudinal axis of the rod-shaped bacteria between the two arrows is presented. Figure 5d Compared to previous cross-sectional images, the value differences between the internal scattering structure and bacteria have intensified.

[0097] Figure 7a The phase shift spatial distribution after the twentieth and final iteration is shown, and Figure 7b The spatial distribution of absorption is shown. The absorption and phase shift thresholds gradually decrease in each iteration, reaching zero in the last iteration. Figure 7c A plot showing the distribution of phase shift values ​​along the longitudinal axis of the rod-shaped bacteria between the two arrows is presented. Figure 6c Compared to the previous profile, the maximum value of the phase-shifted profile has increased, now reaching approximately 0.10. Furthermore, the value difference between the internal scattering structures and bacteria has widened, with the bacterial absorbance now approaching 0.08. Therefore, the true value of the spatial distribution of absorption of the imaged object has indeed been found. Figure 7d A graph showing the distribution of absorbance values ​​along the longitudinal axis of the rod-shaped bacteria between the two arrows is presented. Figure 6dCompared to previous cross-sectional images, the differences in values ​​between the internal scattering structure and bacteria are further amplified. Now, the maximum value corresponding to the internal scattering structure reaches 0.05, while the minimum value corresponding to bacteria reaches 0.02. Therefore, the true values ​​of the spatial distribution of absorption of the imaged object have indeed been found.

[0098] Therefore, in this example, the method requires only 20 iterations to completely eliminate noise and find precise values ​​for the phase shift and uptake of the bacteria, including their internal scattering structure. Convergence is faster as long as the contribution of the thresholding process to eliminating the twin image is greater than the contribution of the imaged object, due to the large spatial region set to zero at the end of the iteration. Convergence is therefore even faster when the region of interest in the image is small. Figure 3 The cluster contains more bacteria, meaning that if there are more objects of interest to be imaged, the number of iterations must be increased to find accurate phase shift and absorption values, for example, by lowering the threshold more slowly.

[0099] Figures 8a to 10b An example of implementing this method with experimental data is shown. Polystyrene beads with a diameter of 1.1 μm were randomly placed on a glass slide by drying the colloidal suspension, then immersed in oil, and obtained… Figure 8a The polystyrene beads exhibit a large phase shift but very low absorption. As a non-limiting example, the holographic imaging system used to acquire this example hologram is an in-line holographic microscope system employing a monochromatic LED emitting at 405 nm as the light source 4, with a full width at half maximum (FWHM) of 12 nm. The light source 4 is positioned 100 nm from the slide. The holographic imaging system includes a microscope objective 8 with a numerical aperture of 100 x 1.3 and a magnification of 80. A CMOS sensor is used as the image sensor 2. The refractive index of the beads is approximately 1.63, and the refractive index of the oil-impregnated beads is approximately 1.53. Figure 8a The hologram, normalized to the background image, is shown. By comparison, Figure 8b A non-holographic image of beads with the same configuration is shown.

[0100] Similar to Figure 2 a and Figure 2 b, Figure 9a This shows that after the holographic field is backpropagated to the object coordinates, corresponding to... Figure 8a The phase shift spatial distribution of the initial hologram, and Figure 9b This shows that after the holographic field propagates backward to the object coordinates, it corresponds to... Figure 8a The absorption spatial distribution of the original image is shown. It can be seen here that the phase shift spatial distribution and absorption spatial distribution are again greatly affected by the noise generated by the twin image. In particular, the absorption spatial distribution contains large fluctuations, even though the beads are considered to have low absorption.

[0101] As mentioned above, multiple iterative loops were implemented. Figure 10a The phase shift spatial distribution after the fiftieth and final iteration is shown, and Figure 10b The absorption spatial distribution is shown. The absorption threshold and phase shift threshold gradually decrease in each iteration, reaching zero in the final iteration. It can be seen that, on the one hand, the phase shift spatial distribution now clearly corresponds to the distribution of the beads, such as... Figure 8b As shown. On the other hand, the low values ​​of the absorption spatial distribution correctly reflect the low absorption of the polystyrene beads. Therefore, noise caused by twin images is effectively eliminated, and the values ​​of the phase shift spatial distribution and the absorption spatial distribution are correctly determined.

[0102] This invention is not limited to the embodiments described and shown in the accompanying drawings. Modifications are still possible without departing from the scope of protection of this invention, particularly from the perspective of the nature of various technical features or substitutions for technical equivalents.

Claims

1. A digital holographic imaging method, comprising the following steps: A hologram (S01) is obtained by holography, the hologram representing the holographic coordinates (z) of the imaged object (1). h In the holographic plane at position (z0), the spatial distribution of the intensity of the interference caused by the interaction between the illumination beam and the object placed on the imaging axis (6) at coordinate (z0) is shown. Implement (S03) multiple iterations, each iteration including the following steps: By backpropagating the holographic field, which includes the amplitude spatial distribution and phase spatial distribution corresponding to the intensity spatial distribution of the hologram, to the object coordinates, an object field containing the absorption spatial distribution and phase shift spatial distribution of the imaged object is determined (S03a). Thresholding is performed on the values ​​of the absorption spatial distribution and the phase shift spatial distribution of the imaged object by reducing the values ​​below the absorption threshold and by reducing the values ​​below the phase shift threshold, respectively (S03b). The absorption threshold and the phase shift threshold decrease with each iteration. By repropagating the object field to the hologram coordinates, a modified hologram field (S03c) including the modified amplitude spatial distribution and the modified phase spatial distribution is determined. The phase space distribution of the hologram field is replaced by the modified phase space distribution, while the amplitude space distribution of the hologram field is preserved. The phase shift spatial distribution and absorption spatial distribution of the imaged object are determined as the phase shift spatial distribution and absorption spatial distribution of the object field in the last iteration.

2. The method according to claim 1, wherein, During threshold processing, the values ​​of the absorption spatial distribution below the absorption threshold and the values ​​of the phase shift spatial distribution below the phase shift threshold are set to zero.

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

4. The method according to claim 1, wherein, In the first iteration, the absorption threshold and / or the phase shift threshold correspond to between 40% and 15% of the maximum value of the absorption spatial distribution and the phase shift spatial distribution, respectively.

5. The method according to claim 1, wherein, In each iteration, the absorption threshold and / or the phase shift threshold are reduced by 1% to 6% of the maximum value of the absorption spatial distribution or the phase shift spatial distribution.

6. The method according to claim 1, wherein, In the last iteration, the absorption threshold and the phase shift threshold were set to zero.

7. The method according to claim 1, wherein, During thresholding, the values ​​of the absorption spatial distribution and the phase shift spatial distribution are kept positive or zero during iteration.

8. The method according to claim 1, wherein, Before the iteration, the holographic field is normalized by dividing the value of the intensity spatial distribution by the background image value corresponding to the intensity of the illumination beam at the holographic coordinates.

9. The method according to claim 1, wherein, The threshold processing includes smoothing the modified absorption spatial distribution and the modified phase shift spatial distribution.

10. The method according to claim 1, wherein, The holographic field and / or the object field have a spatial resolution that increases with iteration.

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