Method and system for quickly resolving polarization direction by using Gauss-Newton iteration method

Abstract

The invention discloses a polarization direction rapid resolving method and system using a Gauss-Newton iteration method, and relates to the technical field of polarization detection. Comprising the steps of obtaining a spatial polarization modulation image; obtaining angular distribution data of the gray value of the light intensity image based on the obtained spatial polarization modulation image; based on an extreme value of the angular distribution data, intercepting the angular distribution data by taking the extreme value as a center for Gaussian-Newton iteration; performing Gaussian-Newton iteration on the intercepted angular distribution data to obtain a trigonometric function which describes light intensity distribution and follows the Malus law; by analyzing the phase angle of the trigonometric function, the polarization direction of the optical wave to be measured is calculated. According to the method, optimization fitting is carried out on the actually obtained light intensity angular distribution data through the Gaussian-Newton iteration method, the trigonometric function capable of accurately describing the light intensity distribution rule is obtained, and then the polarization direction of the to-be-measured light wave is calculated through the phase angle of the trigonometric function.

Description

Technical Field

[0001] The present invention relates to the field of polarization detection technology, and in particular to a method and system for quickly calculating a polarization direction using a Gauss-Newton iteration method. Background Art

[0002] Polarization is a basic property of light waves and an important carrier of information. Polarization direction is one of the most important polarization characteristics of light waves. The rapid and accurate measurement of polarization direction has important applications in the fields of sky polarization navigation, optical rotation dispersion analysis, semiconductor thin film detection, photovoltaic solar cells, biochemical detection and analysis, and polarization remote sensing. With the continuous development and maturity of vector light field control and micro-nano processing technology, spatial modulation devices such as vortex wave plates, S-wave plates, and angular polarizers have been processed with high quality and used to build spatial modulation polarization detectors. This type of polarimeter uses spatial modulation devices to modulate the polarization state of light waves to produce a spatially varying light intensity distribution, and obtains information such as polarization direction by analyzing and processing the light intensity modulation image. Spatially modulated polarization detectors do not require mechanical rotating elements or active modulation devices, have simple optical path structures, good stability, fast measurement speed and high accuracy, and are a type of polarization measurement instrument with important engineering application value.

[0003] The basic principles and methods of using spatial modulation devices such as vortex wave plates, S-wave plates and angular polarizers to construct a vector polarized light field and perform spatial modulation to achieve polarization measurement have been studied and reported by many research groups at home and abroad. At the same time, many feasible methods for polarization direction measurement have also been provided. However, the detection speed and accuracy of these methods are not ideal. For example, the polarization direction solution method based on image correlation provided in patent CN108801464A takes about 867ms to achieve a polarization measurement; the polarization direction angle calculation method based on Radon transform provided in patent CN105203102A is also a very time-consuming solution method, and has high requirements on image quality. A small amount of local overexposure or underexposure will lead to a large calculation error; the 2023 document (Wang Fujie et al., Research on the Polarization Direction Solution Method of Light Waves Based on Vector Light Field Spatial Modulation, Acta Physica Sinica) reported and compared four polarization direction solution methods: Radon transform, light intensity modulation curve detection, radial integration and image correlation detection, pointing out that the detection accuracy of the three methods of light intensity modulation curve detection, image correlation detection and radial integration can be better than 0.01°, but the faster light intensity modulation curve detection and radial integration method still require 300-400ms to achieve an effective detection. It can be seen that a faster and more effective polarization direction solution method is developed to meet the urgent needs of realizing fast and high-precision measurement of polarization direction in fields such as polarization navigation, semiconductor thin film and photovoltaic solar cell detection.

[0004] Therefore, it is an urgent problem for those skilled in the art to propose a method and system for quickly calculating the polarization direction using the Gauss-Newton iteration method to solve the difficulties existing in the prior art. Summary of the invention

[0005] In view of this, the present invention provides a method and system for quickly solving the polarization direction using the Gauss-Newton iteration method, which effectively utilizes the characteristic that the change of the spatially modulated light intensity signal along the angular direction basically follows the Malus law, and optimizes and fits the actually acquired light intensity angular distribution data through the Gauss-Newton iteration method to obtain a trigonometric function that can accurately describe the law of light intensity distribution, and then solves and obtains the polarization direction of the light wave to be measured through the phase angle of the trigonometric function.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A method for quickly calculating polarization direction using Gauss-Newton iteration method comprises the following steps:

[0008] S1. Acquire image: acquire spatial polarization modulation image;

[0009] S2. Acquiring data: based on the acquired spatial polarization modulation image, obtaining the angular distribution data of the gray value of the intensity image;

[0010] S3. Data interception: Based on the extreme value of the angular distribution data, the angular distribution data is intercepted with the extreme value as the center for Gauss-Newton iteration;

[0011] S4. Obtaining trigonometric functions: performing Gauss-Newton iteration on the intercepted angular distribution data to obtain trigonometric functions that describe the light intensity distribution and follow Malus's law;

[0012] S5. Obtaining results: By analyzing the phase angle of the trigonometric function, the polarization direction of the light wave to be measured is obtained.

[0013] Optionally, the specific content of obtaining the angular distribution data of the grayscale value of the light intensity image based on the acquired spatial polarization modulation image in S2 is:

[0014] Based on the acquired spatial polarization modulation image, a pixel radius of the spatial polarization modulation image is determined, and the spatial polarization modulation image is cropped based on the pixel radius to obtain a circularly symmetrical distribution image;

[0015] The angle calculation step is determined, and the angular distribution data of the grayscale value of the light intensity image is obtained based on the radial integration method.

[0016] Optionally, in S3, based on the extreme value of the angular distribution data, the specific content of intercepting the angular distribution data with the extreme value as the center for Gauss-Newton iteration is:

[0017] Determine the maximum or minimum value of the angular distribution data, select the first maximum or minimum light intensity value, and record it as I max or I min , with I max or I min Centered on the image pixel grayscale value sequence Ioc(θ)={Ioc(0),Ioc(s),Ioc(2s),Ioc(3s),…Ioc(k×s),…Ioc(360)}, 1 / 4 of the data is intercepted for the next Gauss-Newton iteration, where θ is the angle sequence, θ={0,s,2s,3s,…k×s,…360}, 0≤k≤360 / s, and s is the angle interval.

[0018] Optionally, in S4, Gauss-Newton iteration is performed on the intercepted angular distribution data to obtain the specific content of the trigonometric function that describes the light intensity distribution and follows Malus's law:

[0019] Considering that the change of spatial light intensity along the angle direction follows the characteristic of Malus's law, the change law of light intensity I with angle θ in the actual spatial modulation image is expressed as:

[0020] I=a+b[cos(θ+c)] 2 (1)

[0021] Wherein, a is a parameter related to background light interference, b is a parameter related to vignetting effect and exposure conditions, and c is a parameter related to the polarization direction of the light wave to be measured and the initial fast axis direction of the spatial modulation element;

[0022] Using trigonometric function formulas to simplify formula (1):

[0023] I=A+Bcos(2θ+C) (2)

[0024] Wherein, A, B and C are function parameters to be determined by fitting, wherein A=a+b2, B=b2, C=2c; according to the parameter C determined by iterative fitting and the initial fast axis direction of the spatial modulation element, the polarization direction of the light wave to be measured is obtained;

[0025] First, set the iteration number parameter N, the iteration accuracy parameter ε, and the iteration initial parameter a of the three parameters A, B, and C. 0 , b 0 、c 0 ; The Jacobian matrices of parameters A, B, and C are calculated as follows:

[0026]

[0027] Combining the above matrices (3) we can get the Jacobian matrix J of the light intensity I to the parameters A, B, C: f for:

[0028] Jf =[J a ,J b ,J c ] (4)

[0029] Therefore, the iterative error parameter σ is:

[0030] σ=(J f T J f ) -1 J f T r(θ (k) ) (5)

[0031] In the formula, r(θ (k) )=I oc (θ (k) )-I(θ (k) ), that is, the error between the real light intensity data value at the kth iteration and the light intensity value calculated according to the current three parameters A, B, and C. After multiple rounds of iterations less than the number of iterations N, when the second norm of the error parameter σ is less than the accuracy parameter ε, the iterative optimization process terminates;

[0032] The current A r , B r , C r Substituting the three parameters into formula (2), we get the trigonometric function I that describes the light intensity distribution and obeys Malus's law. real :

[0033] I real =A r +B r cos(2θ+C r )(6).

[0034] Optionally, in S5, the specific content of obtaining the polarization direction of the light wave to be measured by analyzing the phase angle of the trigonometric function is:

[0035] According to parameter C r , and the initial fast axis direction of the spatial modulation element The polarization direction α of the light wave to be measured is obtained, and the specific solution formula is:

[0036]

[0037] Where n is an integer, indicating the periodic adjustment of the phase angle.

[0038] A system for quickly calculating polarization direction using Gauss-Newton iteration method, applying any one of the above-mentioned methods for quickly calculating polarization direction using Gauss-Newton iteration method, comprising: an image acquisition module, a data acquisition module, a data interception module, a trigonometric function acquisition module and a result acquisition module;

[0039] An image acquisition module is connected to the input end of the data acquisition module and is used to acquire a spatial polarization modulated image;

[0040] A data acquisition module is connected to the input end of the interception data module and is used to obtain angular distribution data of the grayscale value of the light intensity image based on the acquired spatial polarization modulation image;

[0041] A data interception module is connected to the input end of the trigonometric function acquisition module and is used for intercepting the angular distribution data based on the extreme value of the angular distribution data and centering on the extreme value for Gauss-Newton iteration;

[0042] A trigonometric function acquisition module is connected to the input end of the result acquisition module and is used to perform Gauss-Newton iteration on the intercepted angular distribution data to obtain a trigonometric function that describes the light intensity distribution and follows Malus's law;

[0043] The result acquisition module is used to solve the polarization direction of the light wave to be measured by analyzing the phase angle of the trigonometric function.

[0044] It can be seen from the above technical solutions that, compared with the prior art, the present invention provides a method and system for quickly calculating the polarization direction using the Gauss-Newton iteration method, which has the following beneficial effects:

[0045] (1) The present invention effectively utilizes the characteristic that the change of the spatially modulated light intensity signal along the angular direction basically follows the Malus law, and optimizes and fits the actually acquired light intensity angular distribution data through the Gauss-Newton iteration method to obtain a trigonometric function that can accurately describe the law of light intensity distribution, and then calculates the polarization direction of the light wave to be measured through the phase angle of the trigonometric function;

[0046] (2) The iterative optimization process of the present invention is fast and efficient, avoiding the time-consuming correlation detection, Radon transformation and other processes in the traditional solution method, and is more suitable for fast and high-precision polarization direction detection, especially for applications with real-time detection requirements;

[0047] (3) The present invention is also insensitive to adverse factors such as image noise, background interference and exposure conditions, and is an excellent method that can be used for rapid and high-precision measurement of the polarization direction of light waves. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0049] Figure 1 A flow chart of a method for quickly calculating polarization direction using Gauss-Newton iteration method provided by the present invention;

[0050] Figure 2 A typical modulated image output by the spatial modulation polarization detection system provided by the present invention;

[0051] Figure 3 The circular symmetrical distribution image obtained after cutting provided by the present invention;

[0052] Figure 4 The angular distribution data of the grayscale value of the light intensity image obtained by radial integration processing provided by the present invention;

[0053] Figure 5 Part of the angular distribution data for Gauss-Newton fitting, which is intercepted with the maximum value as the center, provided by the present invention;

[0054] Figure 6 A trigonometric function curve obtained by Gauss-Newton fitting provided by the present invention;

[0055] Figure 7 A comparison chart of the results of 15 consecutive repeated measurements of the same polarization direction angle provided by the present invention;

[0056] Figure 8 This is a comparison chart of the measurement results of 10 consecutive changes in polarization direction provided by the present invention. DETAILED DESCRIPTION

[0057] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0058] Reference Figure 1 As shown, the present invention discloses a method for quickly calculating the polarization direction using the Gauss-Newton iteration method, comprising the following steps:

[0059] S1. Acquire image: acquire spatial polarization modulation image;

[0060] S2. Acquiring data: based on the acquired spatial polarization modulation image, obtaining the angular distribution data of the gray value of the intensity image;

[0061] S3. Data interception: Based on the extreme value of the angular distribution data, the angular distribution data is intercepted with the extreme value as the center for Gauss-Newton iteration;

[0062] S4. Obtaining trigonometric functions: performing Gauss-Newton iteration on the intercepted angular distribution data to obtain trigonometric functions that describe the light intensity distribution and follow Malus's law;

[0063] S5. Obtaining results: By analyzing the phase angle of the trigonometric function, the polarization direction of the light wave to be measured is obtained.

[0064] Furthermore, in S2, based on the acquired spatial polarization modulation image, the specific content of the angular distribution data of the grayscale value of the light intensity image is obtained as follows:

[0065] Based on the acquired spatial polarization modulation image, a pixel radius of the spatial polarization modulation image is determined, and the spatial polarization modulation image is cropped based on the pixel radius to obtain a circularly symmetrical distribution image;

[0066] The angle calculation step is determined, and the angular distribution data of the grayscale value of the light intensity image is obtained based on the radial integration method.

[0067] Specifically, assume that the acquired spatial polarization modulation image is a digital image Io with N rows and M columns, and the spatial coordinates of any pixel point in the image are (X m , Y n ), the corresponding gray value is Io(X m , Y n ), where 1≤m≤M, 1≤n≤N. First, determine the center point coordinates (X mc , Y nc ), and select the appropriate calculation radius R, then crop the image Io with the center point coordinates as the circle center and R as the radius to obtain the circular symmetrical distribution image Ioc. Then, select the angle calculation step size as s, the angle calculation range is 0° to 360°, then there are 360° / s+1 calculation angles, and the calculation angle sequence composed of them is represented as θ, then θ={0,s,2s,3s,…k×s,…360}, 0≤k≤360 / s; calculate the image pixel gray value sequence at each angle as Ioc(θ), then Ioc(θ)={Ioc(0),Ioc(s),Ioc(2s),Ioc(3s),…Ioc(k×s),…Ioc(360)}, Ioc(θ) is the angular distribution data of the gray value of the intensity image obtained.

[0068] The calculation of the image pixel grayscale value sequence Ioc(θ) at each angle can be achieved through a variety of methods, such as radial integration or interpolation, which can calculate the angular distribution data Ioc(θ) of the image pixel grayscale value at different angles and under a selected radius R.

[0069] Furthermore, in S3, based on the extreme value of the angular distribution data, the specific content of intercepting the angular distribution data with the extreme value as the center for Gauss-Newton iteration is:

[0070] Determine the maximum or minimum value of the angular distribution data, select the first maximum or minimum light intensity value, and record it as I max or I min , with I max or I min Centered on the image pixel grayscale value sequence Ioc(θ)={Ioc(0),Ioc(s),Ioc(2s),Ioc(3s),…Ioc(k×s),…Ioc(360)}, 1 / 4 of the data is intercepted for the next Gauss-Newton iteration, where θ is the angle sequence, θ={0,s,2s,3s,…k×s,…360}, 0≤k≤360 / s, and s is the angle interval.

[0071] Furthermore, in S4, Gauss-Newton iteration is performed on the intercepted angular distribution data to obtain the specific content of the trigonometric function that describes the light intensity distribution and follows Malus's law:

[0072] Considering that the change of spatial light intensity along the angle direction follows the characteristic of Malus's law, the change law of light intensity I with angle θ in the actual spatial modulation image is expressed as:

[0073] I=a+b[cos(θ+c)] 2 (1)

[0074] Wherein, a is a parameter related to background light interference, b is a parameter related to vignetting effect and exposure conditions, and c is a parameter related to the polarization direction of the light wave to be measured and the initial fast axis direction of the spatial modulation element;

[0075] Using trigonometric function formulas to simplify formula (1):

[0076] I=A+Bcos(2θ+C) (2)

[0077] Wherein, A, B and C are function parameters to be determined by fitting, wherein A=a+b2, B=b2, C=2c; according to the parameter C determined by iterative fitting and the initial fast axis direction of the spatial modulation element, the polarization direction of the light wave to be measured is obtained;

[0078] First, set the iteration number parameter N, the iteration accuracy parameter ε, and the iteration initial parameter a of the three parameters A, B, and C. 0 , b 0 、c 0 ; The Jacobian matrices of parameters A, B, and C are calculated as follows:

[0079]

[0080] Combining the above matrices (3) we get the Jacobian matrix J of the light intensity I to the parameters A, B, C: f for:

[0081] J f =[J a ,J b ,J c ] (4)

[0082] Therefore, the iterative error parameter σ is:

[0083] σ=(J f T J f ) -1 J f T r(θ (k) ) (5)

[0084] In the formula, r(θ (k) )=I oc (θ (k) )-I(θ (k) ), that is, the error between the real light intensity data value at the kth iteration and the light intensity value calculated according to the current three parameters A, B, and C. After multiple rounds of iterations less than the number of iterations N, when the second norm of the error parameter σ is less than the accuracy parameter ε, the iterative optimization process terminates;

[0085] The current A r , B r , C r Substituting the three parameters into formula (2), we get the trigonometric function I that describes the light intensity distribution and obeys Malus's law. real :

[0086] I real =A r +B r cos(2θ+C r )(6).

[0087] Furthermore, in S5, by analyzing the phase angle of the trigonometric function, the specific content of the polarization direction of the light wave to be measured is calculated as follows:

[0088] According to parameter C r , and the initial fast axis direction of the spatial modulation element The polarization direction α of the light wave to be measured is obtained, and the specific solution formula is:

[0089]

[0090] Where n is an integer, indicating the periodic adjustment of the phase angle.

[0091] Example 1

[0092] Acquire a spatial polarization modulated image; based on the acquired spatial polarization modulated image, obtain angular distribution data of the grayscale value of the light intensity image; based on the extreme value of the angular distribution data, intercept the angular distribution data with the extreme value as the center for Gauss-Newton iteration; perform Gauss-Newton iteration on the intercepted angular distribution data to obtain a trigonometric function that describes the light intensity distribution and follows Malus's law; and solve and obtain the polarization direction of the light wave to be measured by analyzing the phase angle of the trigonometric function.

[0093] Figure 2 The modulated image output by a typical spatial modulation polarization detection system is 2048*2048 pixels in size. The coordinates of the image center are (1017, 1003). The calculated pixel radius R=400 is selected. The circular symmetrical distribution image obtained after cropping is as follows: Figure 3 If the angle calculation step is selected as 1°, there are 361 calculation angles in total. The radial integration method is used to obtain the angular distribution data of 361 light intensity image gray values. The results are shown in Figure 4 shown.

[0094] The first maximum value of the angular distribution of light intensity is found to be 0.7802. 45 intensity data are selected around the maximum value, for a total of 91 data (corresponding to an angle range of 129°-219°) for Gauss-Newton fitting. The selected data are as follows: Figure 5 shown.

[0095] The above data were fitted with Gauss-Newton iteration, with the number of iterations parameter N = 500 and the iteration accuracy parameter ε = 10 -8 , iterate the initial parameter a 0 =0.2, b 0 =0.8, c 0 =0.1, the three parameters A obtained after iterative calculation r , B r and C r They are 0.5712, 0.2095 and 0.2345 respectively. The trigonometric function obtained by iteration is as follows Figure 6 As shown. Using the formula The direction angle is calculated and converted into radians, and the polarization direction angle of the light wave to be measured is 6.718°. The entire iterative solution process takes about 3.5ms, and the computing platform is a Lenovo Thinkpad laptop (P15, I7-10750H@2.6GHz, 32GB, Win10).

[0096] Example 2

[0097] In order to verify the actual effect of the polarization direction detection method provided by the present invention, an experimental system for detecting the polarization direction of light waves was built, and spatially modulated polarization images under different states were collected to verify the specific performance of the algorithm. At the same time, the code of the image correlation algorithm was written for result verification and performance comparison. First, the polarization direction of the incident linear polarized light wave was kept unchanged, and the digital camera was controlled to collect one image every 1 second, and 15 images were collected continuously for calculation and analysis. Figure 7 It is the result of repeated measurement of a certain polarization direction angle in an embodiment of the present invention. The average measurement time of the Gauss-Newton iteration method is about 3.5ms (the computing platform is the same as above), the average value of 15 measurements is 128.866°, the standard deviation is 0.015°, and the maximum error of any two results in 15 measurements is 0.048°; the average measurement time of the image correlation method is about 396ms (the computing platform is the same as above, the image size is 600*600, the angle range and accuracy of the correlation search are 0.2° and 0.01° respectively), the average value of 15 measurements is 128.695°, the standard deviation is 0.004°, and the maximum error of any two results in 15 measurements is 0.016°. In this embodiment, the solution time of the Gauss-Newton iteration method is 2 orders of magnitude less than that of the image correlation method, but the stability of the calculation result is slightly worse than that of the image correlation method. This is mainly because the correlation method uses a large amount of image pixel data and has stronger anti-interference ability, but the price paid is that the amount of calculation is large and very time-consuming.

[0098] Example 3

[0099] In order to further verify the calculation accuracy and speed of the solution method provided by the present invention at different polarization direction angles, a PRM1Z8 stepper motor produced by Thorlabs is used to drive the polarizer to rotate to the angle to be measured. In the experiment, one image is collected at each polarization direction angle for calculation and analysis, and then the motor drives the polarizer to rotate 1°, and another image is collected for calculation and analysis. The motor rotates 10 times continuously to collect a total of 11 images. This experiment is analyzed by comparing the polarization angle difference (1°) between the two images before and after. There are a total of 10 angles with a step interval of 1° that need to be measured, and then the iterative fitting method and image correlation method provided by the present invention are used for calculation and comparison. Figure 8The results of 10 measurements of continuously changing polarization directions in the embodiment of the present invention. The average measurement time using the Gauss-Newton iteration method is still 3.5ms (the computing platform is the same as above), the average value of 10 measurements is 0.998°, the standard deviation is 0.016°, and the maximum error in 10 measurements is 0.034°; the average measurement time using the image correlation method is 396ms (the computing platform is the same as above, the image size is 600*600, the angle range and accuracy of the correlation search are 0.2° and 0.01° respectively), the average value of 10 measurements is 1.012°, the standard deviation is 0.025°, and the maximum error in 10 measurements is 0.057°. In this embodiment, the mean and standard deviation calculated by the Gauss-Newton iteration fitting method and the traditional image correlation method are basically the same, and the measurement result of the Gauss-Newton iteration method is slightly better, and the calculation speed is very fast. Under the same computing platform, it can almost be improved by 2 orders of magnitude compared with the image correlation method, which is very suitable for applications where rapid real-time measurement of polarization direction is required.

[0100] and Figure 1 Corresponding to the method described above, the embodiment of the present invention also provides a system for quickly calculating the polarization direction using the Gauss-Newton iteration method, for Figure 1 The specific implementation of the method includes: obtaining an image module, obtaining a data module, intercepting a data module, obtaining a trigonometric function module and obtaining a result module;

[0101] An image acquisition module is connected to the input end of the data acquisition module and is used to acquire a spatial polarization modulated image;

[0102] A data acquisition module is connected to the input end of the interception data module and is used to obtain angular distribution data of the grayscale value of the light intensity image based on the acquired spatial polarization modulation image;

[0103] A data interception module is connected to the input end of the trigonometric function acquisition module and is used for intercepting the angular distribution data based on the extreme value of the angular distribution data and centering on the extreme value for Gauss-Newton iteration;

[0104] A trigonometric function acquisition module is connected to the input end of the result acquisition module and is used to perform Gauss-Newton iteration on the intercepted angular distribution data to obtain a trigonometric function that describes the light intensity distribution and follows Malus's law;

[0105] The result acquisition module is used to solve the polarization direction of the light wave to be measured by analyzing the phase angle of the trigonometric function.

[0106] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0107] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for quickly calculating the polarization direction using the Gauss-Newton iteration method, characterized in that: The following steps are involved: S1. Acquire image: acquire spatial polarization modulation image; S2. Acquiring data: based on the acquired spatial polarization modulation image, obtaining the angular distribution data of the gray value of the intensity image; S3. Data interception: Based on the extreme value of the angular distribution data, the angular distribution data is intercepted with the extreme value as the center for Gauss-Newton iteration; S4. Obtaining trigonometric functions: performing Gauss-Newton iteration on the intercepted angular distribution data to obtain trigonometric functions that describe the light intensity distribution and follow Malus's law; S5. Obtaining results: By analyzing the phase angle of the trigonometric function, the polarization direction of the light wave to be measured is obtained.

2. The method for quickly calculating the polarization direction using the Gauss-Newton iteration method according to claim 1, characterized in that: In S2, based on the acquired spatial polarization modulation image, the specific content of the angular distribution data of the grayscale value of the light intensity image is obtained as follows: Based on the acquired spatial polarization modulation image, a pixel radius of the spatial polarization modulation image is determined, and the spatial polarization modulation image is cropped based on the pixel radius to obtain a circularly symmetrical distribution image; The angle calculation step is determined, and the angular distribution data of the grayscale value of the light intensity image is obtained based on the radial integration method.

3. The method for quickly calculating the polarization direction using the Gauss-Newton iteration method according to claim 1, characterized in that: In S3, based on the extreme value of the angular distribution data, the specific content of intercepting the angular distribution data with the extreme value as the center for Gauss-Newton iteration is: Determine the maximum or minimum value of the angular distribution data, select the first maximum or minimum light intensity value, and record it as I max or I min , with I max or I min Centered on the image pixel grayscale value sequence Ioc(θ)={Ioc(0),Ioc(s),Ioc(2s),Ioc(3s),…Ioc(k×s),…Ioc(360)}, 1 / 4 of the data is intercepted for the next Gauss-Newton iteration, where θ is the angle sequence, θ={0,s,2s,3s,…k×s,…360}, 0≤k≤360 / s, and s is the angle interval.

4. The method for quickly calculating the polarization direction using the Gauss-Newton iteration method according to claim 1, characterized in that: In S4, the intercepted angular distribution data is subjected to Gauss-Newton iteration, and the specific content of the trigonometric function that describes the light intensity distribution and follows Malus's law is obtained as follows: Considering that the change of spatial light intensity along the angle direction follows the characteristic of Malus's law, the change law of light intensity I with angle θ in the actual spatial modulation image is expressed as: I=a+b[cos(θ+c)] 2 (1) Wherein, a is a parameter related to background light interference, b is a parameter related to vignetting effect and exposure conditions, and c is a parameter related to the polarization direction of the light wave to be measured and the initial fast axis direction of the spatial modulation element; Using trigonometric function formulas to simplify formula (1): I=A+Bcos(2θ+C) (2) Wherein, A, B and C are function parameters to be determined by fitting, wherein A=a+b / 2, B=b / 2, C=2c; according to the parameter C determined by iterative fitting and the initial fast axis direction of the spatial modulation element, the polarization direction of the light wave to be measured is obtained; First, set the iteration number parameter N, the iteration accuracy parameter ε, and the iteration initial parameters a0, b0, and c0 of the three parameters A, B, and C; calculate the Jacobian matrices of the parameters A, B, and C respectively as follows: Combining the above matrices (3) we get the Jacobian matrix J of the light intensity I to the parameters A, B, C: f for: I f =[J a ,J b ,J c ] (4) Therefore, the iterative error parameter σ is: In the formula, r(θ (k) )=I oc (θ (k) )-I(θ (k) ), that is, the error between the real light intensity data value at the kth iteration and the light intensity value calculated according to the current three parameters A, B, and C. After multiple rounds of iterations less than the number of iterations N, when the second norm of the error parameter σ is less than the accuracy parameter ε, the iterative optimization process terminates; The current A r , B r , C r Substituting the three parameters into formula (2), we get the trigonometric function I that describes the light intensity distribution and obeys Malus's law. real : I real =A r +B r cos(2θ+C r ) (6)。 5. The method for quickly calculating the polarization direction using the Gauss-Newton iteration method according to claim 1 or 4, characterized in that: In S5, by analyzing the phase angle of the trigonometric function, the specific content of the polarization direction of the light wave to be measured is solved as follows: According to parameter C r , and the initial fast axis direction of the spatial modulation element The polarization direction α of the light wave to be measured is obtained, and the specific solution formula is: Where n is an integer, indicating the periodic adjustment of the phase angle.

6. A system for quickly calculating polarization direction using Gauss-Newton iteration method, characterized in that: A method for quickly calculating the polarization direction using the Gauss-Newton iteration method as described in any one of claims 1 to 5, comprising: an image acquisition module, a data acquisition module, a data interception module, a trigonometric function acquisition module, and a result acquisition module; An image acquisition module is connected to the input end of the data acquisition module and is used to acquire a spatial polarization modulated image; A data acquisition module is connected to the input end of the interception data module and is used to obtain angular distribution data of the grayscale value of the light intensity image based on the acquired spatial polarization modulation image; A data interception module is connected to the input end of the trigonometric function acquisition module and is used for intercepting the angular distribution data based on the extreme value of the angular distribution data and centering on the extreme value for Gauss-Newton iteration; A trigonometric function acquisition module is connected to the input end of the result acquisition module and is used to perform Gauss-Newton iteration on the intercepted angular distribution data to obtain a trigonometric function that describes the light intensity distribution and follows Malus's law; The result acquisition module is used to solve the polarization direction of the light wave to be measured by analyzing the phase angle of the trigonometric function.

Images