CN110646102A - full-Stokes single photon compression polarization imaging device and method - Google Patents

full-Stokes single photon compression polarization imaging device and method Download PDF

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CN110646102A
CN110646102A CN201910988812.4A CN201910988812A CN110646102A CN 110646102 A CN110646102 A CN 110646102A CN 201910988812 A CN201910988812 A CN 201910988812A CN 110646102 A CN110646102 A CN 110646102A
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CN110646102B (en
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鄢秋荣
李丹
王逸凡
杨逸冰
杨程
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Nanchang University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J11/00—Measuring the characteristics of individual optical pulses or of optical pulse trains
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J4/00—Measuring polarisation of light
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J4/00—Measuring polarisation of light
    • G01J4/04—Polarimeters using electric detection means

Abstract

The invention provides a full-Stokes single-photon compression polarization imaging device and method, aiming at solving the problem of low imaging sensitivity of the existing polarization imaging technology. The micro-polarizer array is attached to the DMD mirror surface, polarization imaging based on a single-pixel imaging technology is achieved, meanwhile, a single-photon detector is adopted to detect light intensity, and ultrahigh imaging sensitivity is achieved.

Description

full-Stokes single photon compression polarization imaging device and method
Technical Field
The invention belongs to the field of weak light imaging and polarization imaging, and relates to a full Stokes single photon compression polarization imaging device and method.
Background
The polarization imaging technology is a technology for imaging by acquiring the polarization state of light waves reflected by the surface of an object. The polarization imaging detection can effectively detect and perceive the target under the conditions of complex background, target shielding, hiding and the like, and meets the application requirements in the fields of security monitoring, remote sensing and remote measuring, photoelectric tracking, target capturing and the like. According to the different technical solutions, various polarization imaging technologies such as time-sharing type, amplitude-dividing type, aperture-dividing type, focus-dividing planar type and interference type have been developed. Due to the low sensitivity of the existing polarization imaging technology, the imaging distance and the imaging quality need to be improved under the conditions of extremely weak light and high scattering medium.
The single photon detection technology is an extremely weak light detection technology with single photon limit sensitivity, and the principle is that after a weak light wave signal enters a single photon detector, the detector outputs a discrete pulse sequence, each pulse indicates that a photon is detected, and then the light intensity is detected by screening and counting the single photon pulses. Single photon detectors such as photomultiplier tubes (PMT), single photon avalanche photodiodes (SPAD), Superconducting Single Photon Detectors (SSPD) and the like belong to point detectors, and in order to realize imaging detection, high-precision optical scanning elements are required to be adopted for scanning imaging, so that the imaging time is long. Single photon detectors with two-dimensional spatial resolution, such as array SPAD, array SSPD, ICCD, EMCCD, etc., are very expensive and have low resolution.
The single-pixel imaging is a novel imaging technology which is based on a compressive sensing theory and adopts a non-position resolution detector to realize two-dimensional imaging. The method comprises the steps of performing random light modulation on an object by adopting a Digital Micromirror Device (DMD), finally converging modulated light on a point detector, and reconstructing a two-dimensional image by utilizing an optical signal received by the detector each time and a pseudo-random code loaded to the DMD. Compared to conventional multi-pixel imaging techniques, single-pixel imaging has two major advantages: firstly, two-dimensional imaging can be realized by only using a point detector, so that the imaging method has low cost, particularly in special wave bands such as infrared and terahertz; and secondly, the point detector in the single-pixel imaging system can simultaneously collect the light intensity of a plurality of pixels, the signal-to-noise ratio is greatly improved, and the ultrahigh sensitivity is realized. The invention provides a method for laminating a micro-polarizer array on a micro-mirror array of a DMD (digital micromirror device), and combining a single-photon detection technology and a single-pixel imaging technology together to realize full Stokes single-photon compression polarization imaging, and the method has the advantages of ultrahigh sensitivity and low cost.
Disclosure of Invention
The invention provides a full-Stokes single-photon compression polarization imaging device and method, aiming at solving the problem of low imaging sensitivity of the existing polarization imaging technology.
The technical scheme of the invention is as follows:
a full Stokes single photon compression polarization imaging device is characterized by comprising:
an imaging lens for imaging an imaging target;
the DMD is arranged on the image surface of the imaging lens and is used for receiving an image formed by the imaging lens; the DMD is made up of U N micromirrors, wherein U, N is the number of micromirrors per row and column of the DMD, respectively;
a micro-polarizer array attached to the mirror surface of the DMD; the micro-polarizer array comprises R multiplied by Q2 multiplied by 2-dimensional micro-polarizing units, each micro-polarizing unit comprises four micro-polarizers with different polarizing angles arranged on the same plane, and the four different polarizing angles are 45 degrees, 90 degrees, 135 degrees and 0 degree clockwise from the upper left corner; dividing the micromirrors of the DMD into 2R × 2Q micromirror combined pixels, one of the micromirror combined pixels including
Figure BDA0002237429490000021
Each micro-polaroid of the micro-polaroid array corresponds to the position of each micro-mirror combined pixel on the DMD one by one; r, Q are each an integer of 1 or more;
the focusing lens is arranged on a reflection light path of the DMD and used for converging the reflection light of the DMD to a photosensitive surface of the single-photon detector;
the single-photon detector is used for converting the collected optical signals into discrete single-photon pulse signals and inputting the discrete single-photon pulse signals into the FPGA-based control and synchronous counting module;
the control and synchronous counting module based on the FPGA is used for outputting a synchronous sampling pulse signal to the DMD controller, counting the single photon pulse signal output by the single photon detector and outputting the single photon pulse signal to an upper computer, and receiving a control instruction from the upper computer;
the upper computer is used for generating an extended measurement matrix and loading the extended measurement matrix to the DMD controller; the extended measurement matrix is composed of numbers 0 and 1, and the turnover of a micromirror in the DMD is controlled through the numbers 0 or 1;
and the DMD controller receives the extended measurement matrix and controls the turnover of the micro-mirror in the DMD when the rising edge of the input synchronous sampling pulse signal pulse is detected.
The invention also provides an imaging method based on the full Stokes single photon compression polarization imaging device, which is characterized by comprising the following steps of:
step 1: placing an imaging target in front of an imaging lens, irradiating the imaging target by using extremely weak parallel light, setting the sampling frequency to be F on an upper computer, and setting the sampling frequency of each polarization angle to be M; the irradiation area of the beam of the parallel light is larger than the plane area of the imaging target;
step 2: generating 4 multiplied by M actual measurement matrixes A with the size of R multiplied by Q, then generating 4 multiplied by M extended measurement matrixes B with the size of U multiplied by N through the actual measurement matrixes A, and loading all the extended measurement matrixes B to the DMD controller;
and step 3: the FPGA-based control and synchronous counting module sends a control instruction through an upper computer to generate a measurement starting signal;
and 4, step 4: after the control and synchronous counting module based on the FPGA detects the rising edge of a signal for starting to measure, synchronous sampling pulse signals with the frequency of F and the number of 4M are output to the DMD controller, and each pulse in the synchronous sampling pulse signals represents one-time sampling;
and 5: loading a corresponding extended measurement matrix B to the DMD to control the turnover of a micromirror of the DMD when the DMD controller detects the rising edge of a synchronous sampling pulse signal pulse;
step 6: synchronously with the step 5, when the rising edge of each synchronous sampling pulse signal pulse is detected, the FPGA-based control and synchronous counting module stores the current photon counting value aiResetting a counter in a control and synchronous counting module based on the FPGA;
and 7: counting the single photon pulse signals output by the single photon detector by a control and synchronous counting module based on the FPGA;
and 8: repeating the steps 5-7 until 4M pulses of the synchronous sampling pulse signals are passed, and completing 4M times of sampling;
and step 9: reconstructing a 45 ° polarization image, a 90 ° polarization image, a 0 ° polarization image, a 135 ° polarization image:
the control and synchronous counting module based on FPGA samples the 1 st to Mth time of M photon counting values a1～aMOutputting the M measured values to an upper computer as M measured values of the 45-degree polarization angle, and forming the M measured values into a column vector y1(ii) a Changing the corresponding M extended measurement matrixes B into M measurement row vectors with the size of 1 x (U x N), and combining the M measurement row vectors into a large measurement matrix C with the size of M x (U x N)1Then, the measurement process of the 45 ° polarization angle is:
y1＝C1x1+e (1)
solving the optimal solution x of the formula (1) by a compressed sensing algorithm1Reconstructing a 45-degree polarization image;
m photon counting values a of M +1 to 2M sampling by a control and synchronous counting module based on FPGAM+1～a2MOutputting the M measured values to an upper computer as M measured values of the 90-degree polarization angle, and forming the M measured values into a column vector y2(ii) a Changing the corresponding M extended measurement matrixes B into M measurement row vectors with the size of 1 x (U x N), and combining the M measurement row vectors into a large measurement matrix C with the size of M x (U x N)2Then, the measurement process of the 90 ° polarization angle is:
y2＝C2x2+e (2)
solving the optimal solution x of the formula (2) by a compressed sensing algorithm2Reconstructing a 90-degree polarization image;
m photon counting values a of 2M +1 to 3M sampling by a control and synchronous counting module based on FPGA2M+1～a3MOutputting the M measured values to an upper computer as M measured values of the 0-degree polarization angle, and forming the M measured values into a column vector y3(ii) a Changing the corresponding M extended measurement matrixes B into M measurement row vectors with the size of 1 x (U x N), and combining the M measurement row vectors into one measurement row vector with the size of M x (U x N)Large measurement matrix C3Then, the measurement process of the 0 ° polarization angle is:
y3＝C3x3+e (3)
solving the optimal solution x of the formula (3) by a compressed sensing algorithm3Reconstructing a 0-degree polarization image;
m photon counting values a of 3M + 1-4M sampling by a control and synchronous counting module based on FPGA3M+1～a4MOutputting the M measured values to an upper computer as M measured values of the polarization angle of 135 degrees, and forming the M measured values into a column vector y4(ii) a Changing the corresponding M extended measurement matrixes B into M measurement row vectors with the size of 1 x (U x N), and combining the M measurement row vectors into a large measurement matrix C with the size of M x (U x N)4Then, the measurement process of the 135 ° polarization angle is:
y4＝C4x4+e (4)
solving the optimal solution x of the formula (4) by a compressed sensing algorithm4Reconstructing a 135-degree polarization image;
the above e is the system noise of the whole polarization imaging device;
step 10: the upper computer reconstructs a polarization degree image and a polarization angle image by using the 45-degree polarization image, the 90-degree polarization image, the 0-degree polarization image and the 135-degree polarization image.
Further, in step 2, the method for loading the extended measurement matrix B into the DMD controller is as follows:
firstly, changing the generated 4 xM extended measurement matrixes B into row vectors;
then, combining M measurement row vectors corresponding to the 45-degree polarization degree into one large measurement matrix C1Combining M measurement row vectors corresponding to the 90-degree polarization degree into a large measurement matrix C2Combining M measurement row vectors corresponding to the degree of polarization of 0 DEG into a large measurement matrix C3Combining M measurement row vectors corresponding to 135-degree polarization degree into a large measurement matrix C4；
Finally, the large measurement matrix C is divided into1、C2、C3、C4Combined into a total measuring matrix C of size 4 Mx (U × N)And stored in the DMD controller.
Further, the method for generating the extended measurement matrix B in step 2 includes:
step 2.1: generating M extended measurement matrices for 45 degree polarization imaging:
step 2.1.1: generating an actual measurement matrix A for 45-degree polarization imaging45Actual measurement matrix A45Is composed of the numbers 0 and 1, A45Is equal to dimension R × Q of the micro-polarizer array, the actual measurement matrix a45Each element in the micro-polarizer unit is respectively in one-to-one correspondence with the 45-degree micro-polarizers in the micro-polarizer unit;
step 2.1.2: generating an initialization matrix with the dimension equal to the dimension UXN of a micromirror array of the DMD, wherein elements of the initialization matrix correspond to micromirrors one to one; dividing the initialization matrix into 2R multiplied by 2Q unit matrixes, wherein each unit matrix corresponds to the combined pixels of the micro mirrors one by one; according to the corresponding relation of the combined pixels of the 45-degree micro-polarizer and the micro-mirror in the micro-polarizer array, the actual measurement matrix A of 45-degree polarization imaging45Corresponds to a cell matrix in the initialization matrix.
Step 2.1.3: will actually measure the matrix A45Assigning each element value to all elements in the unit matrix in the initialization matrix corresponding to the element, assigning '0' to all elements of other unit matrices in the initialization matrix, and obtaining the initialization matrix which is an extended measurement matrix B for 45-degree polarization imaging45Extended measurement matrix B for 45 degree polarization imaging45Actual measurement matrix A imaged with 45 degree polarization45The corresponding relation is as follows:
Figure BDA0002237429490000051
step 2.1.4: repeating the steps 2.1.1-2.1.3 to generate M extended measurement matrixes for 45-degree polarization imaging;
step 2.2: generating M extended measurement matrices for 90-degree polarization imaging:
m are generated by the same method of the steps 2.1.1-2.1.4Extended measurement matrix B for 90-degree polarization imaging90Extended measurement matrix B for 90-degree polarization imaging90Actual measurement matrix A imaged with 90 degree polarization90The corresponding relation is as follows:
Figure BDA0002237429490000052
step 2.3: generating M extended measurement matrices for 0 degree polarization imaging:
m extended measurement matrixes B for 0-degree polarization imaging are generated by the same method in steps 2.1.1-2.1.40Extended measurement matrix B for 0 degree polarization imaging0Actual measurement matrix A imaged with 0 degree polarization0The corresponding relation is as follows:
Figure BDA0002237429490000053
step 2.4: generating M extended measurement matrices for 135 degree polarization imaging:
m extended measurement matrixes B for 135-degree polarization imaging are generated by the same method in steps 2.1.1-2.1.4135Extended measurement matrix B for 135 degree polarization imaging135Actual measurement matrix A imaged with 135 degree polarization135The corresponding relation is as follows:
Figure BDA0002237429490000054
the above-mentioned i, j indicates the ith row and jth column of the actual measurement matrix a; t1, t2 denote the t1 th row and t2 th column of the extended measurement matrix B, also indicating the pixel position on the DMD.
The invention has the advantages that:
1. high imaging sensitivity
Different from the traditional polarization imaging method for attaching the micro-polarizer array to the CCD, the invention firstly proposes that the micro-polarizer array is attached to the DMD mirror surface, so that the polarization imaging based on the single-pixel imaging technology can be realized, the detector can simultaneously collect the light intensity of a plurality of pixels, and the signal-to-noise ratio is greatly improved. Meanwhile, the detector adopts a single photon detector to detect light intensity, and the imaging sensitivity can be further improved. Therefore, the scheme of the invention has ultrahigh imaging sensitivity.
2. Low cost
Due to the adoption of the single-pixel imaging technology, the two-dimensional single-photon imaging can be realized by using the single-photon point detector without position resolution, so the scheme of the invention has the advantage of low cost.
Drawings
FIG. 1 is a schematic diagram of the principle of the full Stokes single photon compression polarization imaging device.
FIG. 2 is a diagram of the relationship of a micro-polarizer array, a DMD micro-mirror array, an actual measurement matrix, and an extended measurement matrix.
FIG. 3 is a timing diagram of the FPGA-based control and synchronization counter module.
FIG. 4 is a reconstruction block diagram of full Stokes single photon compression polarization imaging of the present invention.
Description of reference numerals:
1-an imaging lens; 2-an array of micro-polarizers; 21-a micro-polarizer unit; 211-a micro-polarizer; 3-DMD; 4-a focusing lens; 5-single photon detector.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings
As shown in fig. 1, the full stokes single photon compression polarization imaging device provided by the invention comprises an imaging lens 1, a micro-polarizer array 2, a DMD3, a DMD controller, a focusing lens 4, a single photon detector 5, a control and synchronous counting module based on an FPGA, and an upper computer.
The imaging lens 1 is used to image an imaging target.
The DMD3 is provided on the image plane of the imaging lens 1 and receives an image of a subject formed by the imaging lens 1. The DMD3 is a type of optical switch, and is composed of a plurality of minute mirrors (micromirrors for short), and the number of mirrors is determined by the display resolution of the DMD.
The micro-polarizer array 2 is closely attached to the surface of the DMD3 on the side close to the imaging lens 1. As shown in fig. 2, slight deviationThe vibrating plate array 2 comprises R multiplied by Q micro-polarizing plate units 21 and R, Q which are sequentially and closely arranged and have the sizes of 2 multiplied by 2, and are integers which are more than or equal to 1; each micro-polarizer unit 21 includes four micro-polarizers 211 with different polarization angles arranged on the same plane, and the four different polarization angles are 45 °, 90 °, 135 °, and 0 ° clockwise from the top left corner. The method for closely attaching the micro-polarizer array 2 to the mirror surface of the DMD3 includes: the whole micro-polarizer array 2 is aligned with the edge of the micromirror array on the mirror surface of the DMD3, each micro-polarizer 211 of the micro-polarizer array 2 is arranged corresponding to the position of each micromirror combination pixel on the DMD3, and each micro-polarizer 211 of the micro-polarizer array 2 is covered on the corresponding micromirror combination pixel of the DMD3 in a one-to-one correspondence manner. For example, if the resolution of the micro-polarizer array 2 is R × Q, the micromirror array on the mirror surface of the DMD3 is divided into 2R × 2Q micromirror combination pixels, one micromirror combination pixel corresponds to one micro-polarizer 211, and one micro-polarizer unit 21 of the micro-polarizer array 2 corresponds to four micromirror combination pixels. If the micromirror array on the DMD3 mirror has U N micromirrors, one micromirror combination pixel comprises
Figure BDA0002237429490000071
A micromirror; different DMDs, U, N's value is different, and the DMD of selecting for use, U, N all should be greater than 2, and U, N should be able to divide by 2R and 2Q respectively.
The focusing lens 4 is disposed on the reflected light path of the DMD3 and is used for converging the reflected light of the full-screen mirror (i.e. the surface close to the imaging lens 1 side) of the DMD3 onto the photosensitive surface of the single-photon detector 5.
The single-photon detector 5 is connected with the FPGA-based control and synchronous counting module, converts the collected optical signals into discrete single-photon pulse signals, and inputs the discrete single-photon pulse signals into the FPGA-based control and synchronous counting module.
The control and synchronous counting module based on the FPGA is connected with the DMD controller and outputs synchronous sampling pulse signals to the DMD controller.
The control and synchronous counting module based on the FPGA is connected with the upper computer and used for counting the single photon pulse signals output by the single photon detector 5, outputting the obtained photon counting value to the upper computer and receiving a control instruction from the upper computer.
The upper computer is connected with the DMD controller and is used for generating an extended measurement matrix and loading the extended measurement matrix to the DMD controller; the extended measurement matrix is composed of random numbers 0 and 1, and if the extended measurement matrix is 0, the micro mirror does not turn over; if 1, the micromirrors toggle, thereby effecting the opening and closing of the DMD3, spatially modulating the optical image.
The DMD controller is connected with the DMD3, receives the loaded extended measurement matrix, and controls the turnover of the micro-mirrors in the DMD3 according to the elements '0' and '1' of the extended measurement matrix when the rising edge of the input synchronous sampling pulse signal pulse is detected.
An imaging method based on the full-stokes single photon compression polarization imaging device shown in fig. 1 comprises the following steps:
step 1: placing an imaging target in front of the imaging lens 1, irradiating the imaging target by using extremely weak (because of single photon imaging under the condition of weak light), and the irradiation area of the light beam of the parallel light is larger than the plane area of the imaging target; and setting the sampling frequency to be F and the sampling frequency of each polarization angle to be M on the upper computer.
Step 2: as shown in fig. 2, the upper computer first generates 4 × M actual measurement matrices a having a size of R × Q, then generates 4 × M extended measurement matrices B having a size of U × N from the actual measurement matrices a, and loads all the extended measurement matrices B to the DMD controller. The method for loading the extended measurement matrix B into the DMD controller comprises the following steps:
firstly, the generated 4M extended measurement matrices B with size U × N are respectively changed into M row vectors with size 1 × (U × N) (for a single extended measurement matrix B, the element of the next row is sequentially connected with the last element of the previous row, and then the row vector is changed into 1 × (U × N)); then, M measurement row vectors corresponding to the 45-degree polarization degree are sequentially placed line by line according to the generation sequence to form a large measurement matrix C with the size of M x (U x N)1The M measurement line vectors corresponding to the 90-degree polarization degree are sequentially placed line by line according to the generation sequence so as to be combinedInto a large measurement matrix C of size Mx (U × N)2M measurement row vectors corresponding to the degree of polarization of 0 degree are sequentially placed line by line according to the generation sequence to form a large measurement matrix C with the size of M x (U x N)3M measurement row vectors corresponding to 135-degree polarization degree are sequentially placed line by line according to the generation sequence to form a large measurement matrix C with the size of M x (U x N)4(ii) a Finally, the large measurement matrix C is divided into1、C2、C3、C4The total measurement matrix C of size 4M × (U × N) is assembled and stored in the DMD controller.
And step 3: the FPGA-based control and synchronous counting module sends a control instruction through the upper computer to generate a measurement starting signal, and a timing diagram of the FPGA-based control and synchronous counting module is shown in FIG. 3.
And 4, step 4: after the control and synchronous counting module based on the FPGA detects the rising edge of a signal for starting to measure, synchronous sampling pulse signals with the frequency of F and the number of 4M are output to the DMD controller, and each pulse represents one-time sampling.
And 5: every time the DMD controller detects the rising edge of a pulse of a synchronous sampling pulse signal, a corresponding extended measurement matrix B is loaded to the DMD3 to control the turning of the micromirrors thereof (the micromirror corresponding to "1" in the extended measurement matrix B is turned by +12 degrees, and the micromirror corresponding to "0" in the extended measurement matrix B remains unchanged).
Step 6: synchronously with the step 5, when the rising edge of each synchronous sampling pulse signal pulse is detected, the FPGA-based control and synchronous counting module stores the current photon counting value aiAnd then, resetting a counter in the FPGA-based control and synchronous counting module to an internal buffer.
And 7: and the control and synchronous counting module based on the FPGA counts the single photon pulse signals output by the single photon detector 5.
And 8: and (5) repeating the steps 5-7 until 4M pulses of the synchronous sampling pulse signal are passed, and completing 4M times of sampling.
And step 9: reconstructing a 45 ° polarization image, a 90 ° polarization image, a 0 ° polarization image, a 135 ° polarization image:
the control and synchronous counting module based on FPGA samples the 1 st to Mth time of M photon counting values a1～aMThe output is transmitted to an upper computer, and the 45-degree polarization image is reconstructed together with the corresponding M extended measurement matrixes B;
m photon counting values a of M +1 to 2M sampling by a control and synchronous counting module based on FPGAM+1～a2MOutputting the polarization image to an upper computer, and reconstructing a 90-degree polarization image together with the corresponding M extended measurement matrixes B;
m photon counting values a of 2M +1 to 3M sampling by a control and synchronous counting module based on FPGA2M+1～a3MOutputting the polarization image to an upper computer, and reconstructing a 0-degree polarization image together with the corresponding M extended measurement matrixes B;
m photon counting values a of 3M + 1-4M sampling by a control and synchronous counting module based on FPGA3M+1～a4MAnd outputting the polarization image to an upper computer, and reconstructing a 135-degree polarization image together with the corresponding M extended measurement matrixes.
The specific reconstruction process is as follows:
wherein, a1,a2,a3,...a4MRespectively, photon counting values, namely measured values;
y1，y2，y3，y4column vectors of the respective measured values of 45 °, 90 °, 0 °, 135 ° polarization degrees.
FIG. 4 is a block diagram of the reconstruction of full Stokes single photon compression polarization imaging of the present invention, a photon count a if the noise e of the system is taken into accountiCan be considered as the inner product of the ith extended measurement matrix B and the polarization image x for the corresponding polarization angle. After M samples, M measurements are obtained, and the inner product of the large measurement matrix C and the image x can be expressed as:
Figure BDA0002237429490000092
wherein, C1、C2、C3、C4Large measurement matrices of 45 °, 90 °, 0 °, 135 ° polarization degrees, respectively, and the sizes are all M × (U × N).
In general, when x is not necessarily sparse, and x ═ ψ x' and ψ is a sparse transformation matrix, equation (2) can be changed to equation (3):
Figure BDA0002237429490000093
in the compressed sensing theory, in order to solve for x', the solution process is described as a convex optimization problem, namely:
Figure BDA0002237429490000101
wherein: τ is a constant, | | | non-conducting phosphorpRepresents lpNorm, defined as
Figure BDA0002237429490000104
Counting photon by column vector y1，y2，y3，y4And sending the polarization image to an upper computer, and solving the optimal solution x' of the formula (4) through an OMP (orthogonal matching pursuit) or TVLA3 or GPSR (general purpose scanning system) or other compression sensing algorithms to reconstruct the image, namely reconstructing the polarization image of the target signal under the polarization degrees of 45 degrees, 90 degrees, 0 degrees and 135 degrees respectively.
Step 10: the upper computer utilizes the 45-degree polarization image, the 90-degree polarization image, the 0-degree polarization image and the 135-degree polarization image to reconstruct a polarization degree image and a polarization angle image:
the polarized images at different angles can obtain light intensities I at different angles45°、I90°、I0°、I135°
The polarization state S of the target can be represented by the stokes vector as equation (5), and typically V ═ 0:
S＝[I,Q,U,V]T＝[I0°+I90°,I0°-I90°,I45°-I135°,0] (5)
and (3) obtaining the value of the polarization degree P and the polarization angle alpha of the target according to the formula (6), wherein the value range of P is 0 to 1, the value of alpha is 0 to pi, obtaining a polarization degree image according to the polarization degree of each pixel, obtaining a polarization angle image according to the polarization angle of each pixel, and realizing image reconstruction of compressed sensing polarization imaging.
Figure BDA0002237429490000103
The generating step of the extended measurement matrix B in the step 2 is as follows:
step 2.1: generating M extended measurement matrices for 45 degree polarization imaging:
step 2.1.1: as shown in FIG. 2, the upper computer generates an actual measurement matrix A for 45-degree polarization imaging45(actual measurement matrix A)45Is random, either 1 or 0), the actual measurement matrix a45Is equal to dimension R × Q of the micro-polarizer array 2, the actual measurement matrix a45Each of which corresponds one-to-one to the 45-degree micro-polarizer 211 in the micro-polarizer unit 21.
Step 2.1.2: generating an initialization matrix with the dimension equal to the dimension U multiplied by N of a micromirror array of the DMD3, wherein elements of the initialization matrix correspond to the micromirrors one to one; dividing the initialization matrix into 2R multiplied by 2Q unit matrixes, wherein each unit matrix corresponds to the combined pixels of the micro mirrors one by one; according to the corresponding relation of the combined pixels of the 45-degree micro-polarizer and the micro-mirror in the micro-polarizer array 21, the actual measurement matrix A of the 45-degree polarization imaging45Corresponds to a cell matrix in the initialization matrix.
Step 2.1.3: will actually measure the matrix A45Assigning each element value to all elements in the unit matrix in the initialization matrix corresponding to the element, assigning '0' to all elements of other unit matrices in the initialization matrix, and obtaining the initialization matrix which is an extended measurement matrix B for 45-degree polarization imaging45(ii) a And, an extended measurement matrix B for 45-degree polarization imaging45And 45 degree polarization imagingActual measurement matrix A of45The corresponding relation is as follows:
where i, j denotes the actual measurement matrix A45Row i and column j; t1, t2 denotes the extended measurement matrix B45Row t1 and column t2, also indicate pixel locations on the DMD, e.g., (1,1) are the elements located in the first row and column t;
step 2.1.4: repeating steps 2.1.1-2.1.3 generates M extended measurement matrices for 45 degree polarization imaging.
Step 2.2: generating M extended measurement matrices for 90-degree polarization imaging:
m extended measurement matrixes B for 90-degree polarization imaging are generated by the same method in steps 2.1.1-2.1.490Extended measurement matrix B for 90-degree polarization imaging90Actual measurement matrix A imaged with 90 degree polarization90The corresponding relation is as follows:
Figure BDA0002237429490000112
where i, j denotes the actual measurement matrix A90Row i and column j; t1, t2 denotes the extended measurement matrix B90Row t1 and column t2, also indicate pixel locations on the DMD;
step 2.3: generating M extended measurement matrices for 0 degree polarization imaging:
m extended measurement matrixes B for 0-degree polarization imaging are generated by the same method in steps 2.1.1-2.1.40Extended measurement matrix B for 0 degree polarization imaging0Actual measurement matrix A imaged with 0 degree polarization0The corresponding relation is as follows:
Figure BDA0002237429490000113
where i, j denotes the actual measurement matrix A0Row i and column j; t1, t2 denote extended measurementsMatrix B0Row t1 and column t2, also indicate pixel locations on the DMD;
step 2.4: generating M extended measurement matrices for 135 degree polarization imaging:
m extended measurement matrixes B for 135-degree polarization imaging are generated by the same method in steps 2.1.1-2.1.4135Extended measurement matrix B for 135 degree polarization imaging135Actual measurement matrix A imaged with 135 degree polarization135The corresponding relation is as follows:
Figure BDA0002237429490000121
where i, j denotes the actual measurement matrix A135Row i and column j; t1, t2 denotes the extended measurement matrix B135Row t1 and column t2 also indicate the pixel location on the DMD.
In step 2, an actual measurement matrix for 0-degree, 90-degree or 135-degree polarization imaging may be generated first, and only 45 degrees is taken as an example.

Claims (4)

1. A full Stokes single photon compression polarization imaging device is characterized by comprising:
an imaging lens (1) for imaging an imaging target;
a DMD (3) which is arranged on the image surface of the imaging lens (1) and is used for receiving the image formed by the imaging lens (1); DMD (3) is made up of UxN micromirrors, U, N being the number of micromirrors per row and column, respectively, of the DMD;
a micro-polarizer array (2) bonded to the mirror surface of the DMD (3); the micro-polarizer array (2) comprises R multiplied by Q2 multiplied by 2-dimensional micro-polarizing units (21), each micro-polarizer unit (21) comprises four micro-polarizers (211) with different polarizing angles, which are arranged on the same plane, and the four polarizing angles are 45 degrees, 90 degrees, 135 degrees and 0 degrees clockwise from the upper left corner; dividing the micromirrors of said DMD (3) into 2R x 2Q micromirror combination pixels, one of said micromirror combination pixels comprising
Figure FDA0002237429480000011
Each micro-polarizer (211) of the micro-polarizer array (2) and each micro-mirror combined pixel position on the DMD (3) are arranged in a one-to-one correspondence mode; r, Q are each an integer of 1 or more;
the focusing lens (4) is arranged on a reflection light path of the DMD (3) and is used for converging the reflection light of the DMD (3) to a photosensitive surface of the single-photon detector (5);
the single-photon detector (5) is used for converting the collected optical signals into discrete single-photon pulse signals and inputting the discrete single-photon pulse signals into the FPGA-based control and synchronous counting module;
the control and synchronous counting module based on the FPGA is used for outputting a synchronous sampling pulse signal to the DMD controller, counting the single photon pulse signal output by the single photon detector (5), outputting the single photon pulse signal to an upper computer, and receiving a control instruction from the upper computer;
the upper computer is used for generating an extended measurement matrix and loading the extended measurement matrix to the DMD controller; the extended measurement matrix is composed of numbers 0 and 1, and the turnover of the micro-mirror in the DMD (3) is controlled through the number 0 or 1;
and the DMD controller receives the extended measurement matrix and controls the turnover of the micro-mirrors in the DMD (3) when the rising edge of the input synchronous sampling pulse signal pulse is detected.
2. The imaging method of the full stokes single photon compression polarization imaging device according to claim 1, comprising the following steps:
step 1: placing an imaging target in front of an imaging lens (1), irradiating the imaging target by using extremely weak parallel light, setting the sampling frequency to be F on an upper computer, and setting the sampling frequency of each polarization angle to be M; the irradiation area of the beam of the parallel light is larger than the plane area of the imaging target;
step 2: generating 4 multiplied by M actual measurement matrixes A with the size of R multiplied by Q, then generating 4 multiplied by M extended measurement matrixes B with the size of U multiplied by N through the actual measurement matrixes A, and loading all the extended measurement matrixes B to the DMD controller;
and step 3: the FPGA-based control and synchronous counting module sends a control instruction through an upper computer to generate a measurement starting signal;
and 4, step 4: after the control and synchronous counting module based on the FPGA detects the rising edge of a signal for starting to measure, synchronous sampling pulse signals with the frequency of F and the number of 4M are output to the DMD controller, and each pulse in the synchronous sampling pulse signals represents one-time sampling;
and 5: when the DMD controller detects the rising edge of a synchronous sampling pulse signal pulse, a corresponding extended measurement matrix B is loaded on the DMD (3) to control the turnover of a micro mirror of the DMD controller;
step 6: synchronously with the step 5, when the rising edge of each synchronous sampling pulse signal pulse is detected, the FPGA-based control and synchronous counting module stores the current photon counting value aiResetting a counter in a control and synchronous counting module based on the FPGA;
and 7: the control and synchronous counting module based on the FPGA counts the single photon pulse signals output by the single photon detector (5);
and 8: repeating the steps 5-7 until 4M pulses of the synchronous sampling pulse signals are passed, and completing 4M times of sampling;
and step 9: reconstructing a 45 ° polarization image, a 90 ° polarization image, a 0 ° polarization image, a 135 ° polarization image:
the control and synchronous counting module based on FPGA samples the 1 st to Mth time of M photon counting values a1～aMOutputting the M measured values to an upper computer as M measured values of the 45-degree polarization angle, and forming the M measured values into a column vector y1(ii) a Changing the corresponding M extended measurement matrixes B into M measurement row vectors with the size of 1 x (U x N), and combining the M measurement row vectors into a large measurement matrix C with the size of M x (U x N)1Then, the measurement process of the 45 ° polarization angle is:
y1＝C1x1+e (1)
solving the optimal solution x of the formula (1) by a compressed sensing algorithm1Reconstructing a 45-degree polarization image;
based on FPThe control and synchronous counting module of GA counts M photon counting values a of M +1 to 2M sampling timesM+1～a2MOutputting the M measured values to an upper computer as M measured values of the 90-degree polarization angle, and forming the M measured values into a column vector y2(ii) a Changing the corresponding M extended measurement matrixes B into M measurement row vectors with the size of 1 x (U x N), and combining the M measurement row vectors into a large measurement matrix C with the size of M x (U x N)2Then, the measurement process of the 90 ° polarization angle is:
y2＝C2x2+e (2)
solving the optimal solution x of the formula (2) by a compressed sensing algorithm2Reconstructing a 90-degree polarization image;
m photon counting values a of 2M +1 to 3M sampling by a control and synchronous counting module based on FPGA2M+1～a3MOutputting the M measured values to an upper computer as M measured values of the 0-degree polarization angle, and forming the M measured values into a column vector y3(ii) a Changing the corresponding M extended measurement matrixes B into M measurement row vectors with the size of 1 x (U x N), and combining the M measurement row vectors into a large measurement matrix C with the size of M x (U x N)3Then, the measurement process of the 0 ° polarization angle is:
y3＝C3x3+e (3)
solving the optimal solution x of the formula (3) by a compressed sensing algorithm3Reconstructing a 0-degree polarization image;
m photon counting values a of 3M + 1-4M sampling by a control and synchronous counting module based on FPGA3M+1～a4MOutputting the M measured values to an upper computer as M measured values of the polarization angle of 135 degrees, and forming the M measured values into a column vector y4(ii) a Changing the corresponding M extended measurement matrixes B into M measurement row vectors with the size of 1 x (U x N), and combining the M measurement row vectors into a large measurement matrix C with the size of M x (U x N)4Then, the measurement process of the 135 ° polarization angle is:
y4＝C4x4+e (4)
by compressing the sensing algorithm, solving(4) Of (2) an optimal solution x4Reconstructing a 135-degree polarization image;
the e is system noise of the whole full Stokes single photon compression polarization imaging device;
step 10: the upper computer reconstructs a polarization degree image and a polarization angle image by using the 45-degree polarization image, the 90-degree polarization image, the 0-degree polarization image and the 135-degree polarization image.
3. The imaging method of the full stokes single photon compression polarization imaging device according to claim 2, wherein:
in step 2, the method for loading the extended measurement matrix B into the DMD controller is as follows:
firstly, changing the generated 4 xM extended measurement matrixes B into row vectors;
then, combining M measurement row vectors corresponding to the 45-degree polarization degree into one large measurement matrix C1Combining M measurement row vectors corresponding to the 90-degree polarization degree into a large measurement matrix C2Combining M measurement row vectors corresponding to the degree of polarization of 0 DEG into a large measurement matrix C3Combining M measurement row vectors corresponding to 135-degree polarization degree into a large measurement matrix C4；
Finally, the large measurement matrix C is divided into1、C2、C3、C4The total measurement matrix C of size 4M × (U × N) is assembled and stored in the DMD controller.
4. The imaging method of the full stokes single photon compression polarization imaging device according to claim 2, wherein:
the method for generating the extended measurement matrix B in the step 2 comprises the following steps:
step 2.1: generating M extended measurement matrices for 45 degree polarization imaging:
step 2.1.1: generating an actual measurement matrix A for 45-degree polarization imaging45Actual measurement matrix A45Is composed of the numbers 0 and 1, A45Is equal to dimension R × Q of the micro-polarizer array (2), the actual measurement matrix A45Each element ofRespectively correspond to the 45-degree micro-polarizers (211) in the micro-polarizer unit (21) one by one;
step 2.1.2: generating an initialization matrix with the dimension equal to the dimension U multiplied by N of a micro mirror array of the DMD (3), wherein elements of the initialization matrix correspond to micro mirrors one to one; dividing the initialization matrix into 2R multiplied by 2Q unit matrixes, wherein each unit matrix corresponds to the combined pixels of the micro mirrors one by one; according to the corresponding relation of the 45-degree micro-polarizer and the micro-mirror combined pixel in the micro-polarizer array (21), the actual measurement matrix A of 45-degree polarization imaging45One matrix element of (a) corresponds to one unit matrix in the initialization matrix;
step 2.1.3: will actually measure the matrix A45Assigning each element value to all elements in the unit matrix in the initialization matrix corresponding to the element, assigning '0' to all elements of other unit matrices in the initialization matrix, and obtaining the initialization matrix which is an extended measurement matrix B for 45-degree polarization imaging45Extended measurement matrix B for 45 degree polarization imaging45Actual measurement matrix A imaged with 45 degree polarization45The corresponding relation is as follows:
step 2.1.4: repeating the steps 2.1.1-2.1.3 to generate M extended measurement matrixes for 45-degree polarization imaging;
step 2.2: generating M extended measurement matrices for 90-degree polarization imaging:
m extended measurement matrixes B for 90-degree polarization imaging are generated by the same method in steps 2.1.1-2.1.490Extended measurement matrix B for 90-degree polarization imaging90Actual measurement matrix A imaged with 90 degree polarization90The corresponding relation is as follows:
Figure FDA0002237429480000042
step 2.3: generating M extended measurement matrices for 0 degree polarization imaging:
by the steps of2.1.1-2.1.4, M extended measurement matrices B for 0 degree polarization imaging0Extended measurement matrix B for 0 degree polarization imaging0Actual measurement matrix A imaged with 0 degree polarization0The corresponding relation is as follows:
step 2.4: generating M extended measurement matrices for 135 degree polarization imaging:
m extended measurement matrixes B for 135-degree polarization imaging are generated by the same method in steps 2.1.1-2.1.4135Extended measurement matrix B for 135 degree polarization imaging135Actual measurement matrix A imaged with 135 degree polarization135The corresponding relation is as follows:
Figure FDA0002237429480000051
the above-mentioned i, j indicates the ith row and jth column of the actual measurement matrix a; t1, t2 denote the t1 th row and t2 th column of the extended measurement matrix B, also indicating the pixel position on the DMD.
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