Single-photon sub-pixel positioning system and method based on point spread function coding reconstruction

Abstract

The invention provides a single-photon sub-pixel positioning system and method based on point spread function coding reconstruction. The system comprises an imaging module, a point spread function coding component, a single-photon array detector, a measurement matrix calculation module and a decoding reconstruction positioning module. The point spread function coding component performs coding modulation on phase information of a target optical signal passing through the imaging module, forms a light spot on an image surface of the imaging module, and transmits a phase coding mode to the measurement matrix calculation module; the single photon array detector measures the light spot image and transmits the photon number to the decoding reconstruction positioning module; the measurement matrix calculation module constructs a measurement matrix and transmits the measurement matrix to the decoding reconstruction positioning module; and the decoding reconstruction positioning module reconstructs the high-resolution image, and obtains the sub-pixel positioning coordinates of the point target to be detected by extracting the pixel coordinates greater than the detection threshold in the high-resolution image. The method has the advantage that the problem that the positioning precision is restricted due to insufficient pixel scale is solved.

Description

Technical Field

[0001] The present application belongs to the field of optics, and specifically relates to a single-photon sub-pixel positioning system and method based on point spread function coding reconstruction. Background Art

[0002] Point target positioning at the photon level is of great significance in fields such as deep space exploration and super-resolution microscopy. However, due to the limitation of the low pixel size of single-photon detectors, traditional photon counting imaging often has the problem of insufficient positioning accuracy. In order to improve the accuracy of target positioning, a series of positioning algorithms such as centroid positioning method, Gaussian distribution fitting method, and spatial moment edge positioning method have been developed to improve the positioning accuracy to the sub-pixel level. However, existing sub-pixel positioning methods are generally aimed at high signal-to-noise ratio detection or are based only on light intensity measurement. In photon counting measurements at low photon count levels, the measurement results are usually more susceptible to noise interference, and the above positioning algorithms cannot be directly applied. On the other hand, in real scenes such as low, small and slow detection and bioluminescence microscopy, there may be multiple targets to be positioned, and traditional sub-pixel positioning algorithms are often only discussed for single point targets, which is difficult to meet the positioning requirements of some scenes in actual applications. To this end, researchers have proposed a variety of positioning methods, including STROM, to achieve multi-target positioning. These methods use the Gaussian point spread function of the optical system to perform compressed sensing reconstruction on low-resolution measurement results to obtain a high-resolution image and thus the sub-pixel coordinates of the target. However, these methods do not consider the impact of the properties of the measurement matrix on the reconstruction quality. Instead, they construct a measurement matrix based on the point spread function of the conventional optical imaging system for image inversion. In fact, because the Gaussian function is continuous and smooth, the matrix constructed from this function is highly correlated and has poor properties as a measurement matrix. It does not fully meet the RIP criterion in compressed sensing theory, thus limiting the reconstruction quality and further affecting the actual positioning accuracy.

[0003] In summary, how to construct a multi-target sub-pixel positioning model at low photon levels, improve the properties of the measurement matrix in the sub-pixel positioning algorithm based on decoding and reconstruction, and ultimately achieve high-precision sub-pixel positioning of multiple targets at low photon levels is still an urgent problem to be solved. Summary of the Invention

[0004] The purpose of this application is to overcome the above-mentioned defects and propose a single-photon sub-pixel positioning system based on point spread function coding and reconstruction, which includes an imaging module, a point spread function coding component, a single-photon array detector, a measurement matrix calculation module and a decoding and reconstruction positioning module; wherein,

[0005] The imaging module is used to image one or more point targets;

[0006] The single-photon array detector is located on the imaging surface of the imaging module and is used to perform two-dimensional measurement of the light spot and transmit the number of photons measured at each pixel position to the decoding and reconstruction positioning module;

[0007] The point spread function encoding component is located between the imaging module and the single photon array detector, and is used to encode and modulate the phase information of the target light signal so that it forms a light spot image with a certain spatial distribution on the single photon array detector; and also transmits the corresponding phase encoding method to the measurement matrix calculation module;

[0008] The measurement matrix calculation module is used to construct a measurement matrix according to phase encoding and transmit the measurement matrix to the decoding and reconstruction positioning module;

[0009] The decoding and reconstruction positioning module obtains the sub-pixel positioning coordinates of the target point to be measured through a compressed sensing reconstruction algorithm based on the measurement matrix constructed by the measurement matrix calculation module and the measurement results of the single-photon array detector.

[0010] As an improvement to the above system, the imaging module is a telephoto lens, a microscopic lens, a single lens or a lens group.

[0011] As an improvement to the above system, the point spread function encoding component is implemented by a device having spatial light phase modulation capability including a phase plate, a mask plate and a liquid crystal spatial light modulator.

[0012] As an improvement to the above system, the phase encoding method of the point spread function encoding component adopts a random matrix, a structured matrix or an optimized design matrix.

[0013] As an improvement to the above system, the single-photon array detector is a single-photon detection device with spatial resolution capability, including a single-photon avalanche diode array or a silicon photomultiplier tube.

[0014] As an improvement of the above system, the decoding and reconstruction positioning module adopts any one of the following algorithms to implement compressed sensing reconstruction: CVX convex optimization reconstruction algorithm, matching pursuit algorithm MP, orthogonal matching pursuit algorithm OMP, basis pursuit algorithm BP, greedy reconstruction algorithm, LASSO, LARS, GPSR, Bayesian estimation algorithm, magic, IST, TV, StOMP, CoSaMP, LBI, SP, l1_ls, smp algorithm, SpaRSA algorithm, TwIST algorithm, l0 reconstruction algorithm, l1 reconstruction algorithm, l2 reconstruction algorithm, least squares method, maximum likelihood method, logistic regression algorithm, ridge regression algorithm, Lasso algorithm or gradient descent algorithm, as well as deep learning solution algorithms including CNN network, UNet network or ISTA-Net network.

[0015] The present application also provides a single-photon sub-pixel positioning method based on point spread function encoding reconstruction, based on the above-mentioned system implementation, the method includes:

[0016] The imaging module images one or more point target signals;

[0017] The point spread function encoding component performs encoding modulation on the phase of the target signal according to a preset encoding method, and transmits the corresponding encoding method to the measurement matrix calculation module;

[0018] The single-photon array detector forms a light spot image with a certain spatial distribution on the single-photon array detector after the point target to be measured passes through the imaging module and the point spread function encoding component; the single-photon array detector performs two-dimensional measurement of the light spot and transmits the number of photons measured at each pixel position to the decoding and reconstruction positioning module;

[0019] The measurement matrix calculation module divides the detection area of ​​the single photon array detector into a grid of m×n pixels, where m≥M, n≥N, and M×N is the pixel size of the single photon array detector. The pixel coordinates of the theoretical point target on the detector plane are calculated according to the encoding method of the point spread function encoding component. i ,y j ) produces a spot image I with a pixel size of M×N k , where i≤m, j≤n; by traversing the target pixel coordinates (x i ,y j ) for all possible cases, and obtain the spot images I1, I2, ..., I that should be generated theoretically when located at different pixel coordinates. k ,...,I m×n ; Stretching the m×n spot images into m×n (M×N)×1 column vectors respectively, and splicing the above column vectors into a matrix A with a pixel size of (M×N)×(m×n) as a measurement matrix to be transmitted to the decoding and reconstruction positioning module;

[0020] The decoding and reconstruction positioning module subtracts the dark count noise at the corresponding pixel position of the single-photon array detector from the number of photons at each pixel position in the measurement result of the single-photon array detector, and then stretches the subtraction result into a column as a measurement value y. According to the measurement matrix A constructed by the measurement matrix calculation module, the equation y=Aθ is solved by the compressed sensing reconstruction algorithm, where θ is a column vector of size (m×n)×1 formed by stretching the high-resolution image. A high-resolution image is obtained by reshaping θ into a matrix of m×n pixels, and the coordinates (x i ,y j ) as the sub-pixel coordinates of the target point to be measured.

[0021] Compared with the prior art, the advantages of this application are:

[0022] 1. This invention achieves high-accuracy sub-pixel positioning at low photon levels. By encoding and decoding the phase information of the target to be measured, the target positioning precision and accuracy are improved. The optical method solves the problem of limited positioning accuracy of existing single-photon array detectors due to insufficient pixel size.

[0023] 2. The present invention obtains the sub-pixel coordinates of all point targets within the field of view by reconstructing the modulated light field information, overcoming the disadvantage of traditional sub-pixel positioning methods that cannot obtain sub-pixel coordinates of multiple targets;

[0024] 3. The present invention introduces a point spread function encoding component to perform high-resolution modulation on point targets, thereby solving the problem of poor measurement matrix properties in traditional sub-pixel positioning algorithms, thereby achieving higher reconstruction quality and positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Shown is a schematic structural diagram of a single-photon sub-pixel positioning system based on point spread function encoding reconstruction.

[0026] Reference numerals:

[0027] 1. Imaging module 2. Point spread function encoding component

[0028] 3. Single photon array detector 4. Measurement matrix calculation module

[0029] 5. Decoding and reconstruction positioning module DETAILED DESCRIPTION

[0030] The technical solution of this application is described in detail below with reference to the accompanying drawings.

[0031] The present invention's single-photon sub-pixel localization system based on point spread function encoding and reconstruction utilizes the principle of compressed sensing (CS). CS is a mathematical theory proposed by Donoho, Tao, and Candès. Compared to traditional imaging methods, CS imaging uses a post-processing algorithm to reconstruct sub-sampled signals to obtain an image. This novel mathematical theory breaks the Nyquist sampling theorem, requiring only a far smaller number of signals to be detected to accurately restore the original image. Compressed sensing is mainly divided into three steps: compressed sampling, sparse transformation and algorithmic reconstruction; among them, compressed sampling refers to sampling the signal to be measured far less than the number of signals, and the sampling process is described as y=Ax, where x is a column vector composed of the signal to be measured, A is the measurement matrix, and y is a column vector composed of the measurement results of each detection; sparse transformation refers to selecting a suitable sparse basis Ψ for the signal to be measured x, so that the signal x' is sparse after the sparse transformation x'=Ψx; algorithmic reconstruction refers to the process of using the measurement matrix A, the measurement value y and the sparse basis Ψ, according to its imaging process y=AΨx'+e, to solve the original signal x through the existing compressed sensing reconstruction algorithm.

[0032] Example 1

[0033] refer to Figure 1 , Embodiment 1 of the present invention provides a single-photon sub-pixel positioning system based on point spread function encoding and reconstruction, the system may include an imaging module 1, a point spread function encoding component 2, a single-photon array detector 3, a measurement matrix calculation module 4 and a decoding and reconstruction positioning module 5;

[0034] The imaging module 1 images one or more point targets, places the single-photon array detector 3 on the imaging surface of the imaging module 1, and places the point spread function encoding component 2 between the imaging module 1 and the single-photon array detector 3. The point spread function encoding component 2 performs specific encoding and modulation on the phase information of the target light signal to form a light spot image with a certain spatial distribution on the single-photon array detector 3; the single-photon array detector 3 performs two-dimensional measurement of the light spot and transmits the number of photons measured at each pixel position to the decoding and reconstruction positioning module 5; at the same time, the point spread function encoding component 2 transmits the corresponding phase encoding method to the measurement matrix calculation module 4, the measurement matrix calculation module 4 constructs a measurement matrix according to the phase encoding, and transmits the measurement matrix to the decoding and reconstruction positioning module 5; the decoding and reconstruction positioning module 5 finally obtains the sub-pixel positioning coordinates of the point target to be measured through a compressed sensing reconstruction algorithm based on the measurement matrix constructed by the measurement matrix calculation module 4 and the measurement results of the single-photon array detector 3.

[0035] The above is a description of the overall structure of the single-photon sub-pixel positioning system based on point spread function coding reconstruction of the present invention. The following is a further description of the specific implementation of each component in the single-photon sub-pixel positioning system based on point spread function coding reconstruction.

[0036] The imaging module 1 may include a telephoto lens, a microphoto lens, and a single lens or a lens group.

[0037] The point spread function encoding component 2 is implemented by devices having spatial light modulation capability including a phase plate, a mask plate, a liquid crystal spatial light modulator and a micro-mirror array.

[0038] The phase encoding method of the point spread function encoding component 2 adopts a random matrix, a structured matrix or an optimized design matrix.

[0039] The single photon array detector 3 is a single photon detection device with spatial resolution capability, such as a detector array composed of single photon avalanche diodes (SPADs) or silicon photomultiplier tubes (MPPC / SiPM).

[0040] The decoding and reconstruction positioning module 4 adopts any one of the following algorithms to implement compressed sensing reconstruction: CVX convex optimization reconstruction algorithm, matching pursuit algorithm MP, orthogonal matching pursuit algorithm OMP, basis pursuit algorithm BP, greedy reconstruction algorithm, LASSO, LARS, GPSR, Bayesian estimation algorithm, magic, IST, TV, StOMP, CoSaMP, LBI, SP, l1_ls, smp algorithm, SpaRSA algorithm, TwIST algorithm, l0 reconstruction algorithm, l1 reconstruction algorithm, l2 reconstruction algorithm, least squares method, maximum likelihood method, logistic regression algorithm, ridge regression algorithm, Lasso algorithm, gradient descent algorithm, and deep learning solution algorithms including CNN network, UNet network, and ISTA-Net network.

[0041] Example 2

[0042] The above is a structural description of the single-photon sub-pixel positioning system based on point spread function encoding and reconstruction of the present invention. The working process of the single-photon sub-pixel positioning system based on point spread function encoding and reconstruction is described below.

[0043] Embodiment 2 of the present invention provides a single-photon sub-pixel positioning method based on point spread function coding reconstruction, which is implemented based on the above system and includes:

[0044] The imaging module 1 images one or more point target signals;

[0045] The point spread function encoding component 2 is placed between the imaging module 1 and the imaging surface, and encodes and modulates the phase of the target signal according to a preset encoding method, and transmits the corresponding encoding method to the measurement matrix calculation module 4;

[0046] The single-photon array detector 3 is placed on the imaging surface of the imaging module 1. After the target passes through the imaging module 1 and the point spread function encoding component 2, a light spot image with a certain spatial distribution is formed on the single-photon array detector 3. The single-photon array detector 3 performs two-dimensional measurement of the light spot and transmits the photon count measured at each pixel position to the decoding and reconstruction positioning module 4.

[0047] The measurement matrix calculation module 4 divides the detection area of ​​the single photon array detector 3 into a grid of m×n pixels, where m≥M, n≥N, and M×N is the pixel size of the single photon array detector 3. According to the encoding method of the point spread function encoding component 2, the pixel coordinates of the theoretical point target on the detector plane are calculated as (x i ,y j ) produces a spot image I with a pixel size of M×N k , where i≤m, j≤n, by traversing all possible cases of the target pixel coordinates (xi, yj), the spot images I1, I2, ..., I that should be generated theoretically when located at different pixel coordinates are obtained. k ,...,I m×n , stretch the m×n spot images into m×n (M×N)×1 column vectors respectively, and splice the above column vectors into a matrix A with a pixel size of (M×N)×(m×n) as the measurement matrix and transmit it to the decoding and reconstruction positioning module 5;

[0048] The decoding and reconstruction positioning module 5 subtracts the dark count noise at the corresponding pixel position of the single-photon array detector 3 from the number of photons at each pixel position in the measurement result of the single-photon array detector 3, and then stretches the subtraction result into a column as the measurement value y. According to the measurement matrix A constructed by the measurement matrix calculation module 4, the equation y=Aθ is solved by the compressed sensing reconstruction algorithm, where θ is a column vector of size (m×n)×1 formed by stretching the high-resolution image. A high-resolution image is obtained by reshaping θ into a matrix of m×n pixels, and the coordinates (x i ,y j ) as the sub-pixel coordinates of the target point to be measured.

[0049] Finally, it should be noted that the above embodiments are intended only to illustrate the technical solutions of this application and are not intended to limit the scope of the present invention. Although this application has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions to the technical solutions of this application do not depart from the spirit and scope of the technical solutions of this application and should be encompassed by the claims of this application.

Claims

1. A single-photon sub-pixel positioning system based on point spread function encoding reconstruction, characterized in that: The system comprises an imaging module (1), a point spread function encoding component (2), a single photon array detector (3), a measurement matrix calculation module (4) and a decoding and reconstruction positioning module (5); wherein, The imaging module (1) is used to image one or more point targets; The single-photon array detector (3) is located on the imaging surface of the imaging module (1) and is used to perform two-dimensional measurement of the light spot and transmit the number of photons measured at each pixel position to the decoding and reconstruction positioning module (5); The point spread function encoding component (2) is located between the imaging module (1) and the single photon array detector (3), and is used to encode and modulate the phase information of the target light signal so as to form a light spot image with a certain spatial distribution on the single photon array detector (3); and also transmit the corresponding phase encoding mode to the measurement matrix calculation module (4); The measurement matrix calculation module (4) is used to construct a measurement matrix according to phase encoding and transmit the measurement matrix to the decoding and reconstruction positioning module (5); The decoding and reconstruction positioning module (5) obtains the sub-pixel positioning coordinates of the target point to be measured through a compressed sensing reconstruction algorithm based on the measurement matrix constructed by the measurement matrix calculation module (4) and the measurement results of the single-photon array detector (3).

2. The single-photon sub-pixel positioning system based on point spread function encoding reconstruction according to claim 1, characterized in that: The imaging module (1) is a telephoto lens, a microscopic lens, a single lens or a lens group.

3. The single-photon sub-pixel positioning system based on point spread function encoding reconstruction according to claim 1, characterized in that: The point spread function encoding component (2) is implemented by a device having spatial light phase modulation capability, including a phase plate, a mask plate and a liquid crystal spatial light modulator.

4. The single-photon sub-pixel positioning system based on point spread function encoding reconstruction according to claim 1, characterized in that: The phase encoding method of the point spread function encoding component (2) adopts a random matrix, a structured matrix or an optimized design matrix.

5. The single-photon sub-pixel positioning system based on point spread function encoding reconstruction according to claim 1, characterized in that: The single-photon array detector (3) is a single-photon detection device with spatial resolution capability, comprising a single-photon avalanche diode array or a silicon photomultiplier tube.

6. The single-photon sub-pixel positioning system based on point spread function encoding reconstruction according to claim 1, characterized in that: The decoding and reconstruction positioning module (4) adopts any one of the following algorithms to realize compressed sensing reconstruction: CVX convex optimization reconstruction algorithm, matching pursuit algorithm MP, orthogonal matching pursuit algorithm OMP, basis pursuit algorithm BP, greedy reconstruction algorithm, LASSO, LARS, GPSR, Bayesian estimation algorithm, magic, IST, TV, StOMP, CoSaMP, LBI, SP, l1_ls, smp algorithm, SpaRSA algorithm, TwIST algorithm, l0 reconstruction algorithm, l1 reconstruction algorithm, l2 reconstruction algorithm, least squares method, maximum likelihood method, logistic regression algorithm, ridge regression algorithm, Lasso algorithm or gradient descent algorithm, and deep learning solution algorithm including CNN network, UNet network or ISTA-Net network.

7. A single-photon sub-pixel localization method based on point spread function encoding reconstruction, implemented based on the system of any one of claims 1-6, comprising: The imaging module (1) images one or more point target signals; The point spread function encoding component (2) performs encoding modulation on the phase of the target signal according to a preset encoding method, and transmits the corresponding encoding method to the measurement matrix calculation module (4); The single-photon array detector (3) forms a light spot image with a certain spatial distribution on the single-photon array detector (3) after the point target to be measured passes through the imaging module (1) and the point spread function encoding component (2); the single-photon array detector (3) performs two-dimensional measurement on the light spot and transmits the number of photons measured at each pixel position to the decoding and reconstruction positioning module (4); The measurement matrix calculation module (4) divides the detection area of ​​the single photon array detector (3) into a grid of m×n pixels, wherein m≥M, n≥N, and M×N is the pixel scale of the single photon array detector (3), and calculates the pixel coordinates (x i ,y j ) produces a spot image I with a pixel size of M×N k , where i≤m, j≤n; by traversing the target pixel coordinates (x i ,y j ) for all possible cases, and obtain the spot images I1, I2, ..., I that should be generated theoretically when located at different pixel coordinates. k ,...,I m×n ; Stretching the m×n spot images into m×n (M×N)×1 column vectors respectively, and splicing the above column vectors into a matrix A with a pixel size of (M×N)×(m×n) as a measurement matrix and transmitting it to the decoding and reconstruction positioning module (5); The decoding and reconstruction positioning module (5) subtracts the dark count noise at the corresponding pixel position of the single-photon array detector (3) from the number of photons at each pixel position in the measurement result of the single-photon array detector (3), and then stretches the subtraction result into a column as a measurement value y, and solves the equation y=Aθ by a compressed sensing reconstruction algorithm based on the measurement matrix A constructed by the measurement matrix calculation module (4), wherein θ is a column vector of size (m×n)×1 formed by stretching the high-resolution image, and obtains a high-resolution image by reshaping θ into a matrix of m×n pixels, and extracts the coordinates (x i ,y j ) as the sub-pixel coordinates of the target point to be measured.

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