Phase retrieval based irregular particle shape reconstruction method

Abstract

The application discloses a kind of irregular particle shape reconstruction methods based on phase recovery, builds interference particle imaging system;In defocus image plane obtains the defocus speckle image I of irregular particle to be measured M ; The defocus speckle image I M It is sheared, and the speckle region image I located in the center position and the size of N×N after shearing is retained;Speckle region image I is input into phase recovery algorithm model and iterative calculation is carried out, and preliminary reconstruction result is obtained;Proportion factor factor SF is set, and the preliminary reconstruction result of the above iteration, i.e. new particle estimate p k+1 (x0,y0) is scaled with proportion factor SF, and final reconstruction particle shape is obtained.Compared with prior art, the application can directly obtain accurate shape information of irregular particle through particle interference defocus image, without additional optical path setting, and the device is simple, which provides basis for the measurement of complex particle field.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of optical measurement, and particularly relates to a measurement method suitable for irregular particle shape detection in an optical system. BACKGROUND

[0002] Irregularly shaped particles exist widely in natural environment, daily life and engineering practice. Determining the size, shape, velocity, concentration, three-dimensional position and other parameters of the particles in a particle distribution field has important scientific significance for studying environmental climate change and evaluating engineering production safety. Based on Mie scattering theory, interference particle imaging technology obtains information related to particle parameters by analyzing and processing irregular particle interference images in the frequency domain. In meteorology, combustion, nuclear industry, cosmetic detection and other fields, a large number of irregular particles exist in production activities. The shape parameters of these particles have an impact on the scattering light distribution, so the study on the shape of irregular particles has important and far-reaching significance in the measurement process.

[0003] Chinese invention patent CN106092859A discloses a particle shape discrimination system and method based on laser interference imaging and coaxial holography. The off-focus fringe pattern and the coaxial hologram of the interfering particles are obtained by the laser interference imaging and the coaxial holography imaging system, and then the shape of the particles is discriminated. Chinese invention patent CN108593528A discloses a method for measuring the shape and size of non-spherical rough particles based on laser interference. The off-focus image and the focused image are collected simultaneously, and the focused image is enhanced to obtain the shape information of the particles.

[0004] The above-mentioned Chinese patents measure the shape of irregular particles based on the laser interference imaging system, but both need the assistance of reference beams or focused images. At present, there is no method for directly obtaining the shape of irregular particles from the off-focus speckle pattern. SUMMARY

[0005] The purpose of the present application is to provide a phase recovery-based irregular particle shape reconstruction method, which realizes the application of phase recovery algorithm to reconstruct the shape of irregular particles from off-focus speckles.

[0006] The present application realizes the following technical solutions:

[0007] A phase recovery-based irregular particle shape reconstruction method, characterized in that the specific steps are as follows:

[0008] Step 1, building an interference particle imaging system;

[0009] Step 2, obtaining the off-focus speckle image I of the irregular particle to be measured on the off-focus image plane M ;

[0010] Step 3, performing shearing on the defocus speckle image I M Step 3, performing shearing on the defocus speckle image I

[0011] Step 4, inputting the speckle region image I into a phase recovery algorithm model to obtain a preliminary reconstruction result;

[0012] The specific steps of the phase recovery algorithm model are as follows:

[0013] Step 1: initializing a particle to be reconstructed, and setting the number of iterations k;

[0014] Set the initial emitted light field distribution p0(x0, y0) as follows:

[0015]

[0016] Wherein, |A(x, y)| is a random amplitude distribution, taking a value of 0-255, is a random phase distribution, taking a value of 0-2π, (x0, y0) is the initial position coordinate of the particle to be reconstructed, and i is an imaginary unit;

[0017] Step 2: in the forward propagation process of the emitted light, the kth iteration measurement plane light field distribution q' k (x, y) of the particle to be reconstructed is calculated by fast Fourier transform, as follows:

[0018] q' k (x, y) = F[p k (x0, y0)] (2)

[0019] Wherein, F represents fast Fourier transform, p k (x0, y0) is the emitted light field distribution of the particle to be reconstructed in the kth iteration, (x, y) is the position coordinate of the defocus image plane, and k is the iteration number;

[0020] Step 3: performing measurement domain amplitude replacement, replacing the measurement plane light field distribution q' k (x, y) obtained in Step 2 with the square root of the speckle region image I to obtain the corrected measurement plane light field distribution q k (x, y), as follows:

[0021]

[0022] Step 4: in the reverse propagation process of the emitted light, the (k+1)th iteration preliminary estimated emitted light field distribution p' k+1 (x0, y0) of the particle to be reconstructed is calculated by inverse Fourier transform, as follows:

[0023] p' k+1 (x0,y0)=F -1 [q k (x,y)] (4)

[0024] Step5:Perform support domain correction, using a Gaussian blur kernel to convolve the light field amplitude |p' k+1 | of the exit light field distribution of the preliminary estimate of the k+1th iteration of the particle to be reconstructed;

[0025] The intermediate value S'(x0,y0) of the support domain update calculation is as follows:

[0026]

[0027]

[0028] wherein, is the convolution symbol, σ k is the variance of the Gaussian blur kernel of the kth iteration, p is the sampling interval of the detector, N max is the maximum number of iterations;

[0029] Then, binarize A(x0,y0) to obtain the corrected support domain S(x0,y0), as follows:

[0030]

[0031] wherein, t is the binarization threshold;

[0032] Step6: Perform particle shape reconstruction (or shape) estimate update to obtain a new particle estimate p k+1 (x0,y0), as follows:

[0033]

[0034] wherein, β is the feedback coefficient, β is set to 0.9, p' k (x0,y0) is the exit light field distribution of the preliminary estimate of the k+1th iteration of the particle to be reconstructed, p k (x0,y0) is the exit light field distribution of the particle to be reconstructed in the kth iteration;

[0035] Repeat Step2 to Step6 until the iteration number k satisfies the specified iteration number N max ;

[0036] Step7: Set the scaling factor SF, and scale the reconstruction result of the above iteration, i.e. the new particle estimate p k+1 (x0,y0), by the scaling factor SF to obtain the final reconstructed particle shape.

[0037] Compared with the prior art, the present application can directly obtain accurate shape information of irregular particles through particle interference out-of-focus images, without additional optical path setting, and provides a basis for measurement of complex particle field. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 is a phase retrieval-based irregular particle shape reconstruction method flowchart of the present application;

[0039] Figure 2 is a phase retrieval algorithm flowchart of the present application;

[0040] Figure 3 is an interference particle imaging system of the present application, wherein: 1, laser, 2, microscope objective, 3, pinhole, 4, collimating lens, 5, first cylindrical lens, 6, second cylindrical lens, 7, glass slide, 8, imaging lens, 9, CCD camera;

[0041] Figure 4 is an irregular particle microscope photo, out-of-focus speckle pattern and shape reconstruction result in the present application, wherein: (a) (d) (g) (j) are four different sand grain microscope photos; (b) (e) (h) (k) are out-of-focus speckles obtained in the interference particle imaging system; (c) (f) (i) (l) are reconstruction results obtained by inputting the out-of-focus images into the phase reconstruction algorithm and scaling by the scaling factor. DETAILED DESCRIPTION

[0042] The present application will be further described below in conjunction with the drawings. It should be understood that the specific implementation described herein is only used to explain the present application, and is not used to limit the present application.

[0043] As shown in Figure 1 , it is an irregular particle shape reconstruction method based on out-of-focus speckle of the present application, and the specific steps are as follows:

[0044] Step 1, build an interference particle imaging system, which consists of two parts of collimating system and imaging system; it includes laser 1, microscope objective 2, pinhole 3, collimating lens 4, first cylindrical lens 5, second cylindrical lens 6, glass slide 7, imaging lens 8 and CCD camera 9;

[0045] Step 2, place the CCD camera at the out-of-focus image plane of the interference particle imaging system, and use the CCD camera to obtain the out-of-focus speckle image I M of the irregular particle;

[0046] Step 3, cut the above out-of-focus speckle image I M , and keep the speckle region image I located at the center position and with a size of N×N after cutting; the cutting speckle region size N is set to 512 pixels;

[0047] Step4, input the speckle region image I into a phase retrieval algorithm model to obtain a preliminary reconstruction result;

[0048] The specific steps of the phase retrieval algorithm model are as follows:

[0049] Step1: initialize a particle to be reconstructed, and set the number of iterations k;

[0050] Let the initial exit light field distribution p0(x0, y0) be as follows:

[0051]

[0052] Where |A(x, y)| is a random amplitude distribution, taking a value of 0-255, is a random phase distribution, taking a value of 0-2π, (x0, y0) is the initial position coordinate of the particle to be reconstructed, and i is an imaginary unit;

[0053] Step2: in the forward propagation process of the exit light, the kth iteration measurement plane light field distribution q' k (x, y) of the particle to be reconstructed is calculated by fast Fourier transform, as follows:

[0054] q' k (x, y) = F[p k (x0, y0)] (2)

[0055] Where F represents fast Fourier transform, p k (x0, y0) is the exit light field distribution of the particle to be reconstructed in the kth iteration, (x, y) is the position coordinate of the defocus image plane, and k is the iteration number;

[0056] Step3: perform measurement domain amplitude replacement, replace the measurement plane light field distribution q' k (x, y) obtained in Step2 with the square root of the speckle region image I to obtain the corrected measurement plane light field distribution q k (x, y), as follows:

[0057]

[0058] Step4: in the reverse propagation process of the exit light, the (k+1)th iteration preliminary estimated exit light field distribution p' k+1 (x0, y0) of the particle to be reconstructed is calculated by inverse Fourier transform, as follows:

[0059] p' k+1 (x0, y0) = F -1 [q k(x, y)] (4)

[0060] Step5: Support domain correction is performed, and a light field amplitude |p k+1 is convolved with a preliminary estimate of the exit light field distribution of the particle to be reconstructed in the k+1th iteration;

[0061] An intermediate value S'(x0, y0) of the support domain update calculation is as follows:

[0062]

[0063] σ k The relationship with the iteration number k is as follows:

[0064]

[0065] wherein, is a convolution symbol, σ k is the variance of the Gaussian blur kernel in the kth iteration, which is continuously reduced during the iteration process, p is the sampling interval of the detector, and N max is the maximum iteration number;

[0066] Then, the binary S'(x0, y0) is obtained, and the corrected support domain S(x0, y0) is as follows:

[0067]

[0068] wherein, t is a binary threshold value;

[0069] Further, the initial value of σ k is set to 3p and linearly decreases to 1.5p during the iteration process, the maximum iteration number N max is set to 500 times, and the value of t is 20% of the maximum pixel value of S'(x0, y0).

[0070] Step6: Particle shape estimation update is performed to obtain a new particle estimate p k+1 (x0, y0), as follows:

[0071]

[0072] wherein, β is a feedback coefficient, β is set to 0.9, p' k (x0, y0) is a preliminary estimate of the exit light field distribution of the particle to be reconstructed in the k+1th iteration, p k (x0, y0) is the exit light field distribution of the particle to be reconstructed in the kth iteration;

[0073] Steps 2 to 6 are repeated until the iteration number k satisfies the specified iteration number N max .

[0074] Step 7: Set the scaling factor SF to represent the initial reconstruction results from the above iterations. New particle estimate p k+1 (x0, y0) The particle shape is obtained by scaling using the scaling factor SF.

[0075] The formula for calculating the scaling factor SF is as follows:

[0076]

[0077] Where B represents the system transmission matrix coefficients, as shown in the following equation:

[0078]

[0079] Where z1 is the object distance, z2 is the image distance, f is the focal length of the imaging lens, N is the size of the defocus speckle, p0 is the sampling interval of the particle emission light field, λ is the laser wavelength, and p r This represents the sampling interval of the detector.

[0080] Specific implementation examples are as follows:

[0081] Example 1: Interferometric Particle Imaging System

[0082] like Figure 3 As shown, this invention uses an interferometric particle imaging system. In this system, laser 1 is a semiconductor laser with a wavelength of 532nm. The emitted laser beam is expanded by a microscope objective 2 with a magnification of 10×, filtered by a pinhole 3 with a aperture width of 10μm, and collimated by a collimating lens 4. After passing through cylindrical lenses 5 and 6, it is compressed into a sheet-like laser beam with a length of 15mm and a width of 1mm. The imaging lens 8 that collects the scattered light from the particles is a Nikon 50mm f / 1.4D fixed-focus lens. The detector 9 is a CCD with a pixel size of 5.86μm, an effective pixel count of 1080×1920, and a frame rate of 165fps. The system scattering angle θ is 90°, the system magnification is 2.27, the object distance is 70mm, the image distance is 208mm, and the defocus distance is 33mm. The irregular particles to be measured are coarse sand grains with a maximum size range of 500μm to 1000μm. During the defocus speckle acquisition process, the sand grains are fixed on the glass slide 7 with random orientation.

[0083] Example 2: Obtaining Irregular Particle Shapes Using a Phase Retrieval Algorithm

[0084] like Figure 4Fig. 1 shows the microscope photos, defocus speckle patterns and shape reconstruction results of the ellipsoidal particles in the present application, wherein: (a), (d), (g) and (j) are four microscope photos of different sand particles; (b), (e), (h) and (k) are four defocus speckle patterns obtained by the interference particle imaging system; (c), (f), (i) and (l) are the reconstruction results obtained by inputting the defocus images into the phase reconstruction algorithm and scaling by a scaling factor. The labels in the figure represent four different sand particles. The interference defocus images of the sand particles are speckle patterns. The sampling interval p0 of the particle exit light field is 1 μm. After the speckle patterns are center-cut, they are input Figure 2 The phase reconstruction algorithm shown is iterated 500 times to obtain the preliminary reconstruction results, and the scaling factor is scaled to obtain the reconstruction results shown in (c), (f), (i) and (l).

[0085] It should be noted that although the present application has been shown and described with respect to certain exemplary embodiments thereof, it should be understood by those skilled in the art that various changes in form and detail can be made therein without departing from the scope of the application.

Claims

1. A method for reconstructing the shape of irregular particles based on phase retrieval, characterized in that, The specific steps are as follows: Step 1: Construct an interferometric particle imaging system; Step 2: Acquire the defocus speckle image I of the irregular particle to be tested on the defocused image plane. M ; Step 3: Process the above defocused speckle image I M Perform cropping to retain the N×N speckle region image I located at the center after cropping; the size N of the cropped speckle region is set to 512 pixels. Step 4: Input the speckle region image I into the phase retrieval algorithm model to obtain preliminary reconstruction results; The specific steps of the phase retrieval algorithm model are as follows: Step 1: Initialize the particles to be reconstructed and set the number of iterations k; Assume the initial output light field distribution As shown in the following formula: （1）； in, The amplitude is randomly distributed, with values ​​ranging from 0 to 255. The phase distribution is random, with values ​​ranging from 0 to 2π. Let i be the initial position coordinates of the particle to be reconstructed, where i is the imaginary unit; Step 2: During the forward propagation of the outgoing light, the light field distribution of the measurement surface of the particle to be reconstructed in the kth iteration is calculated by fast Fourier transform. As shown in the following formula: （2）； Where F represents the Fast Fourier Transform, Let represent the outgoing light field distribution of the particle to be reconstructed in the k-th iteration. represents the position coordinates of the defocused image plane, and k is the number of iterations; Step 3: Perform measurement domain amplitude replacement, replacing the measurement surface light field distribution obtained in Step 2 with the square root of the speckle region image I. Obtain the corrected light field distribution on the measurement surface. As shown in the following formula: （3）； Step 4: During the backward propagation of the outgoing light, the preliminary estimated outgoing light field distribution of the particle to be reconstructed in the (k+1)th iteration is obtained by calculating using the inverse Fourier transform. As shown in the following formula: （4）； Step 5: Perform support domain correction, using the Gaussian blur kernel and the light field amplitude of the output light field distribution estimated in the (k+1)th iteration of the particle to be reconstructed. Perform convolution; Intermediate value of support domain update calculation As shown in the following formula: （5）； in, σ is the convolution symbol. k Let N be the variance of the Gaussian blur kernel in the k-th iteration, p be the sampling interval of the detector, and N be the variance of the Gaussian blur kernel in the k-th iteration. max This represents the maximum number of iterations. Then, binarization The corrected support domain is obtained. As shown in the following formula: （6）； Where t is the binarization threshold; Step 6: Perform particle shape reconstruction estimation update to obtain new particle estimates. As shown in the following formula: （7）； Where β is the feedback coefficient, and β is set to 0.

9. This is a preliminary estimate of the emitted light field distribution for the (k+1)th iteration of the particle to be reconstructed. The output light field distribution of the particle to be reconstructed in the k-th iteration; Repeat Steps 2 through 6 until the number of iterations k satisfies the requirement of reaching the specified number of iterations N. max ; Step 7: Set the scaling factor SF to apply the reconstruction results from the above iterations, i.e., the new particle estimate. The particle shape is obtained by scaling using the scaling factor SF.

2. The method for reconstructing irregular particle shapes based on phase retrieval as described in claim 1, characterized in that, The formula for calculating the scaling factor SF is as follows: （8）； in, The system transmission matrix coefficients are shown in the following equation: （9）； Where z1 is the object distance, z2 is the image distance, f is the focal length of the imaging lens, N is the size of the defocus speckle, p0 is the sampling interval of the particle emission light field, and λ is the laser wavelength. This represents the sampling interval of the detector.

3. The method for reconstructing irregular particle shapes based on phase retrieval as described in claim 1, characterized in that, The interferometric particle imaging system consists of two parts: a collimation system and an imaging system. Specifically, it includes a laser, a microscope objective, a pinhole, a collimating lens, a first cylindrical mirror, a second cylindrical mirror, a glass slide, an imaging lens, and a CCD camera. The laser is a semiconductor laser with a wavelength of 532nm. The emitted laser beam is expanded by a microscope objective with a magnification of 10x, filtered by a pinhole with a width of 10μm, and collimated by the collimating lens. Then, it is compressed into a sheet-like laser beam with a length of 15mm and a width of 1mm by the first and second cylindrical mirrors. The imaging lens collects the scattered light from the particles, and the CCD camera acts as a detector.

4. The method for reconstructing irregular particle shapes based on phase retrieval as described in claim 3, characterized in that, The scattering angle θ of the interferometric particle imaging system is 90°, the system magnification is 2.27, the object distance is 70mm, the image distance is 208mm, and the defocus distance is 33mm.

5. The method for reconstructing irregular particle shapes based on phase retrieval as described in claim 1, characterized in that, The irregular particles to be tested are coarse sand grains with a maximum size ranging from 500 μm to 1000 μm. During the defocused speckle sampling process, the sand grains are fixed on the glass slide with random orientation.

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