Method and apparatus for calculating and jointly estimating the precision limits of point target positioning and photometric measurements

Abstract

The application provides a precision limit calculation and joint estimation method and device for point target positioning and photometry, relates to the technical field of optical imaging precision measurement, and aims to solve the problem of inaccurate positioning estimation caused by brightness change of a to-be-measured target. The method comprises the following steps: according to an imaging PSF model of an optical system, a probability density function of a pixel response matrix of an image sensor for imaging a to-be-measured point target about a two-dimensional position of a spot center and an energy coefficient is constructed, wherein the energy coefficient represents the relative brightness of the to-be-measured point target and a modeled point target; according to a log-likelihood function of the probability density function, a joint three-dimensional precision limit of the two-dimensional position of the spot center and the energy coefficient is calculated; based on a maximum likelihood estimation method, the two-dimensional position of the spot center and the energy coefficient are calculated as joint estimation results according to the log-likelihood function of the probability density function, and the precision of the joint estimation results is evaluated through the joint three-dimensional precision limit.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical imaging precision measurement, and in particular to a point target positioning and photometric measurement precision limit calculation and joint estimation method and device. BACKGROUND

[0002] In the field of optical imaging measurement, point target precision positioning technology refers to that a point target optical signal is discretely sampled by a pixel of an image sensor after passing through an optical lens. When the point target is imaged at different positions on the image plane, the energy distribution of the image spot on each pixel is different. According to the response value information output by different pixels, the accurate position of the point target is calculated by cooperating with a sub-pixel centering algorithm. Point target imaging measurement plays an important role in multiple scientific exploration and engineering application fields such as astronomy, biology microscopy, astronomical navigation and precision remote sensing.

[0003] In related technologies, a point spread function (PSF) model of an optical system is usually used to fit imaging data to achieve high-precision positioning. However, the existing method is not accurate in estimating the brightness change of the point target to be measured, which leads to the mismatch between the PSF model and the actual imaging data, and further affects the positioning accuracy. In addition, accurately evaluating the real energy value of the point target itself is also a core requirement in high-precision photometric measurement applications. Therefore, there is an urgent need for a method that can accurately determine the geometric position and photometric information of the target, overcome the mismatch of the PSF model caused by the brightness change of the target, ensure the positioning accuracy, and meet the direct photometric measurement requirements. SUMMARY

[0004] In view of the above problems, the embodiments of the present application provide a point target positioning and photometric measurement precision limit calculation and joint estimation method and device to overcome the above problems or at least partially solve the above problems.

[0005] In a first aspect, the embodiments of the present application disclose a point target positioning and photometric measurement precision limit calculation and joint estimation method, which comprises:

[0006] According to the imaging point spread function (PSF) model of the optical system, a probability density function of a pixel response matrix of an image sensor for imaging a point target to be measured about the two-dimensional position of the image spot center and the energy coefficient is constructed, and the energy coefficient represents the relative brightness of the point target to be measured and the modeling point target;

[0007] According to the log-likelihood function of the probability density function, a joint three-dimensional precision limit of the two-dimensional position of the image spot center and the energy coefficient is calculated;

[0008] Based on the maximum likelihood estimation method, the two-dimensional position of the spot center and the energy coefficient are calculated as joint estimation results according to a log-likelihood function of the probability density function, and the accuracy of the joint estimation results is evaluated by the joint three-dimensional accuracy limit.

[0009] Optionally, according to a point spread function (PSF) model of the optical system, a probability density function of a pixel response matrix of an image sensor imaging a to-be-measured point target with respect to the two-dimensional position of the spot center and the energy coefficient is constructed, including:

[0010] A plurality of frame spot images of a modeling point target are collected at different sub-pixel positions of each pixel in the image sensor of the optical system, and an imaging PSF model of each pixel is constructed according to the plurality of frame spot images of the modeling point target;

[0011] The to-be-measured point target is imaged by an optical lens and an image sensor of the optical system, and a spot image of the to-be-measured point target is collected, and a pixel response matrix of an imaging area is constructed according to the spot image of the to-be-measured point target, the imaging area being an area containing most of the energy information of the spot;

[0012] Based on the feature that the number of photoelectrons generated by a pixel in an imaging process basically obeys a Poisson distribution, the probability density function is constructed according to the imaging PSF model and the pixel response matrix.

[0013] Optionally, a joint three-dimensional accuracy limit of the two-dimensional position of the spot center and the energy coefficient is calculated according to a log-likelihood function of the probability density function, including:

[0014] A Fisher information matrix of a to-be-estimated parameter vector is calculated according to a log-likelihood function of the probability density function, the to-be-estimated parameter vector including an x-coordinate and a y-coordinate of the two-dimensional position of the spot center and the energy coefficient, and an element in the Fisher information matrix being represented as an inverse of an expected value of a second-order partial derivative of the log-likelihood function with respect to the to-be-estimated parameter vector;

[0015] A determinant of the Fisher information matrix is calculated;

[0016] A joint Cramér-Rao lower bound of the two-dimensional position of the spot center and the energy coefficient is calculated according to the determinant, the joint Cramér-Rao lower bound including a Cramér-Rao lower bound of the x-coordinate of the two-dimensional position of the spot center, a Cramér-Rao lower bound of the y-coordinate of the two-dimensional position of the spot center, and a Cramér-Rao lower bound of the energy coefficient;

[0017] The joint Cramér-Rao lower bound is square-rooted to obtain the joint three-dimensional accuracy limit, the joint three-dimensional accuracy limit including an accuracy limit of the x-coordinate of the two-dimensional position of the spot center, an accuracy limit of the y-coordinate of the two-dimensional position of the spot center, and an accuracy limit of the energy coefficient.

[0018] Optionally, based on a maximum likelihood estimation method, the spot center two-dimensional position and the energy coefficient are calculated as a joint estimation result according to a log-likelihood function of the probability density function, comprising:

[0019] The spot image of the to-be-measured point target is positioned by a centroid method to obtain an initial spot center two-dimensional position, and an initial energy coefficient is determined according to the imaging PSF model and the pixel response matrix;

[0020] A Jacobian matrix is obtained according to a first-order derivative of the log-likelihood function, and a Hessian matrix is obtained according to a second-order derivative of the log-likelihood function;

[0021] The log-likelihood function is iteratively maximized by using a Newton-Raphson method according to the initial spot center two-dimensional position, the initial energy coefficient, the Jacobian matrix and the Hessian matrix, and the spot center two-dimensional position and the energy coefficient obtained under the condition of meeting an iteration end condition are taken as a joint estimation result.

[0022] Optionally, the initial energy coefficient is determined according to the imaging PSF model and the pixel response matrix, comprising:

[0023] According to the imaging PSF model, the sum of PSF values corresponding to the initial spot center two-dimensional position of all pixels in the imaging area is calculated by interpolation;

[0024] According to the pixel response matrix, the sum of pixel values of all pixels in the imaging area is calculated;

[0025] The initial energy coefficient is obtained according to the ratio of the sum of pixel values to the sum of PSF values.

[0026] Optionally, a plurality of frames of spot images of the modeling point target are collected at different sub-pixel positions of each pixel in an image sensor of the optical system, comprising:

[0027] The motion executor is fixedly connected with the modeling point target, a light source signal of the modeling point target sequentially passes through a parallel light tube of the optical system and the optical lens to reach the image sensor to be imaged as a spot, and the motion executor is controlled to make the spot sub-pixel displacement at each pixel in the image sensor;

[0028] A plurality of frames of spot images of the modeling point target are sampled at each sub-pixel position to obtain a plurality of frames of spot images of the modeling point target at different sub-pixel positions of each pixel.

[0029] Optionally, the imaging PSF model of each pixel is constructed according to the plurality of frames of spot images of the modeling point target, comprising:

[0030] For each pixel, a pixel response value corresponding to each sub-pixel position is calculated according to a plurality of frame images of the modeling point target of different sub-pixel positions of the pixel, and a sampling matrix of the imaging PSF of the pixel is obtained.

[0031] The imaging PSF model of the pixel is obtained by interpolating the sampling matrix of the imaging PSF of the pixel, and the imaging PSF model includes PSF values at any position.

[0032] Optionally, a pixel response matrix is constructed according to the spot image of the point target to be measured, including:

[0033] An imaging area is extracted from the spot image of the point target to be measured.

[0034] A pixel average value of an area other than the imaging area in the spot image of the point target to be measured is taken as a background value, and the background value is removed from the imaging area to obtain the pixel response matrix.

[0035] A second aspect of the embodiment of the present application discloses a precision limit calculation and joint estimation device for point target positioning and photometric measurement, and the device includes:

[0036] A first construction module is configured to construct a probability density function of a pixel response matrix of an image sensor for imaging a point target to be measured with respect to a two-dimensional position of a spot center and an energy coefficient according to an imaging point spread function (PSF) model of an optical system, and the energy coefficient represents a relative brightness of the point target to be measured and a modeling point target.

[0037] A first calculation module is configured to calculate a joint three-dimensional precision limit of the two-dimensional position of the spot center and the energy coefficient according to a log-likelihood function of the probability density function.

[0038] A second calculation module is configured to calculate the two-dimensional position of the spot center and the energy coefficient as a joint estimation result according to the log-likelihood function of the probability density function based on a maximum likelihood estimation method, and to evaluate the precision of the joint estimation result through the joint three-dimensional precision limit.

[0039] A third aspect of the embodiment of the present application discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the point target positioning and photometric measurement precision limit calculation and joint estimation method of the first aspect of the present application when executing the computer program.

[0040] A fourth aspect of the embodiment of the present application discloses a computer readable storage medium having a computer program stored thereon, and the computer program is executed by a processor to implement the steps of the point target positioning and photometric measurement precision limit calculation and joint estimation method of the first aspect of the present application.

[0041] In a fifth aspect, the present application provides a computer program product comprising a computer program which, when executed by a processor, implements the steps of the point target positioning and photometric measurement precision limit calculation and joint estimation method according to the first aspect of the present application.

[0042] The present application has the following advantages:

[0043] In the present application, the joint three-dimensional precision limit of the spot center two-dimensional position and the energy coefficient is derived based on the probability density function of the pixel response matrix of the image sensor imaging the point target to be measured with respect to the spot center two-dimensional position and the energy coefficient, which provides a theoretical basis for the evaluation of the unbiased estimation performance of the point target precision positioning and photometric measurement. And the joint estimation of the position coordinates and the energy coefficient of the point target to be measured is realized by the maximum likelihood estimation method, which can realize the measurement of the radiometric quantity such as the radiant intensity of the point target to be measured on the one hand; on the other hand, it reduces the influence of the brightness change of the point target to be measured on the positioning precision, so as to realize the precision positioning of the point target with different brightness and expand the application range of the imaging PSF. BRIEF DESCRIPTION OF DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the present application, the following will briefly introduce the drawings needed to be used in the description of the present application. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0045] Figure 1 is a step flow chart of a point target positioning and photometric measurement precision limit calculation and joint estimation method provided by the present application;

[0046] Figure 2 is an example diagram of an optical system imaging PSF construction experimental device provided by the present application;

[0047] Figure 3 is a step flow chart of calculating the joint three-dimensional precision limit of the spot center two-dimensional position and the energy coefficient provided by the present application;

[0048] Figure 4 is a step flow chart of a joint estimation method of the spot center two-dimensional position and the energy coefficient provided by the present application;

[0049] Figure 5 is a structural schematic diagram of a point target positioning and photometric measurement precision limit calculation and joint estimation device provided by the present application;

[0050] Figure 6Fig. 1 is a structural schematic diagram of an electronic device provided by an embodiment of the present application. DETAILED DESCRIPTION

[0051] In order to make the above objectives, characteristics and advantages of the present application more apparent, clear and complete, the technical solutions in the embodiments of the present application will be described in detail below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0052] In order to overcome the problem that the brightness change of a point target to be measured makes the PSF model not suitable for actual imaging data, resulting in inaccurate positioning estimation when the point target is precisely positioned based on the imaging PSF, and solve the problem of missing direct photometric measurement, the present application provides a precision limit calculation and joint estimation method for point target positioning and photometric measurement, which supplements the calculation method of the lowest standard deviation that can be reached by joint estimation of two-dimensional positioning and photometric measurement of a point target, and at the same time, supplements the joint estimation method of the lowest standard deviation for precise positioning and photometric measurement of point targets with different brightness, thereby expanding the application range of the imaging PSF.

[0053] Referring to Figure 1 , Fig. 1 is a structural schematic diagram of an electronic device provided by an embodiment of the present application. Figure 1 Fig. 2 is a step flowchart of a precision limit calculation and joint estimation method for point target positioning and photometric measurement provided by an embodiment of the present application. As Figure 1 indicated, the precision limit calculation and joint estimation method for point target positioning and photometric measurement can include steps S110 to S130:

[0054] Step S110: According to an imaging point spread function (PSF) model of an optical system, a probability density function of a pixel response matrix of an image sensor for imaging a point target to be measured about a center position of a spot and an energy coefficient is constructed, wherein the energy coefficient represents the relative brightness of the point target to be measured and a modeling point target.

[0055] In the embodiments of the present application, the imaging PSF model represents the pixel response values of different two-dimensional positions of the center of the spot from the center of the pixel; the probability density function can represent the probability distribution characteristics of the pixel response values in the imaging area in the imaging process, and specifically, the probability density function is a probability density function associated with the center two-dimensional position of the spot of the point target to be measured and the energy coefficient term.

[0056] The two-dimensional position of the image spot center can be represented by a coordinate (x coordinate) of the image spot center in the x direction and a coordinate (y coordinate) in the y direction. The energy coefficient represents the relative brightness of the target to be measured and the modeling target, and can be understood as the energy ratio of the target to be measured and the modeling target.

[0057] Step S120: calculating the joint three-dimensional precision limit of the two-dimensional position of the image spot center and the energy coefficient according to the log-likelihood function of the probability density function.

[0058] The log-likelihood function of the probability density function can be obtained by taking the natural logarithm of the probability density function. According to the log-likelihood function of the probability density function, the joint three-dimensional precision limit of the two-dimensional position of the image spot center and the energy coefficient can be derived according to the Cramer-Rao lower bound theory.

[0059] The precision limit refers to the lower limit of the standard deviation that cannot be exceeded when measuring the position and brightness of the imaging image spot using any unbiased estimation method, representing the highest measurement precision that can be theoretically achieved. The joint three-dimensional precision limit can be used to evaluate the performance of the joint estimation result. Specifically, the joint three-dimensional precision limit of the two-dimensional position of the image spot center and the energy coefficient includes three dimensions of precision limit, i.e. the precision limit of the x coordinate of the two-dimensional position of the image spot center, the precision limit of the y coordinate of the two-dimensional position of the image spot center, and the precision limit of the energy coefficient.

[0060] Step S130: based on the maximum likelihood estimation method, calculating the two-dimensional position of the image spot center and the energy coefficient as the joint estimation result according to the log-likelihood function of the probability density function, and evaluating the precision of the joint estimation result by the joint three-dimensional precision limit.

[0061] In the embodiments of the present application, based on the distribution characteristics of pixel imaging random noise, the maximum likelihood estimation method is used to take the two-dimensional position of the image spot center and the energy coefficient as parameters, and the joint estimation of the position coordinates of the target to be measured and the energy coefficient can be realized by maximizing the log-likelihood function of the probability density function to obtain the two-dimensional position of the image spot center and the energy coefficient.

[0062] The technical scheme of the embodiment of the application is based on the probability density function of the pixel response matrix of the image sensor imaging the target point to deduce the joint three-dimensional precision limit of the two-dimensional position of the spot center and the energy coefficient, thereby providing a theoretical basis for the evaluation of the unbiased estimation performance of the point target precision positioning and photometric measurement. The joint estimation of the position coordinates and the energy coefficient of the target point is realized by the maximum likelihood estimation method, which can realize the measurement of the radiometric quantity, such as the radiance and the illumination of the target point, and reduce the influence of the brightness change of the target point on the positioning precision, thereby realizing the precision positioning of the point target with different brightness and expanding the application range of the imaging PSF.

[0063] In combination with the above embodiment, in an embodiment, the embodiment of the application further provides a precision limit calculation and joint estimation method for point target positioning and photometric measurement. In the method, the step S110 of "constructing the probability density function of the pixel response matrix of the image sensor imaging the target point with respect to the two-dimensional position of the spot center and the energy coefficient according to the imaging point spread function PSF model of the optical system" specifically includes the sub-step S110-1 to the step S110-3:

[0064] The step S110-1 is to collect the spot images of the modeling point target at different sub-pixel positions of each pixel in the image sensor of the optical system, and to construct the imaging PSF model of each pixel according to the spot images of the modeling point target.

[0065] In the embodiment of the application, the spot center of the multiple frames of modeling point target is controlled to move at different sub-pixel positions, so that the spot images of the multiple frames of modeling point target at different sub-pixel positions can be collected. Then, the imaging PSF model of each pixel in the image sensor is constructed based on the spot images of the multiple frames of modeling point target collected at different sub-pixel positions of the pixel.

[0066] Specifically, the collection of the spot images of the multiple frames of modeling point target at different sub-pixel positions of each pixel in the image sensor includes: fixing the motion executor with the modeling point target, sequentially passing the light source signal of the modeling point target through the parallel light tube and the optical lens of the optical system to the image sensor to form a spot, and controlling the motion executor to make the spot move at the sub-pixel level in each pixel of the image sensor; and performing multiple frame sampling of the spot of the modeling point target at each sub-pixel position to obtain the multiple frames of spot images of the modeling point target at different sub-pixel positions of each pixel.

[0067] For example, Figure 2An experimental device for constructing the imaging PSF of an optical system is shown. The modeling point target can be an OLED (Organic Light-Emitting Diode) light source, and the motion executor (mechanical motion device) can be a precision turntable or a piezoelectric displacement table, etc. The motion executor is fixedly connected with the modeling point target, so that the fine sub-pixel micro-displacement between the modeling point target light source and the image sensor can be formed under darkroom conditions by controlling the motion executor (i.e. the sub-pixel level micro-displacement of the image spot occurs). In order to reduce the influence of random noise, a plurality of frames of image spot images of the modeling point target are collected (e.g. 50 frames) at each sub-pixel position.

[0068] Specifically, the imaging PSF model of each pixel is constructed according to the plurality of frames of image spot images of the modeling point target, including: for each pixel, the pixel response value corresponding to each sub-pixel position is calculated according to the plurality of frames of image spot images of the modeling point target at different sub-pixel positions of the pixel, to obtain the imaging PSF sampling matrix of the pixel; and the imaging PSF sampling matrix of the pixel is interpolated to obtain the imaging PSF model of the pixel, the imaging PSF model including the PSF value at any position.

[0069] For example, the pixel response value corresponding to each sub-pixel position in the pixel The pixel response value of each frame of image spot image of the modeling point target can be calculated respectively, and the mean value of the pixel response values is calculated according to the pixel response values of each frame of image spot image of the modeling point target, as the pixel response value corresponding to the sub-pixel position, so that the pixel response values corresponding to each sub-pixel position are taken as the elements of the imaging PSF sampling matrix, to obtain the imaging PSF sampling matrix of the pixel The interpolation of the imaging PSF sampling matrix of the pixel can be performed by using the cubic spline interpolation technology to interpolate the discrete imaging PSF sampling matrix to obtain the PSF value at any position between the sampling points, so as to complete the construction of the fine imaging PSF model .

[0070] Step S110-2: The point target to be measured is imaged by the optical lens and the image sensor of the optical system, and the image spot image of the point target to be measured is collected. The pixel response matrix of the imaging area is constructed according to the image spot image of the point target to be measured, the imaging area being an area containing most of the energy information of the image spot.

[0071] In actual measurement, the point target to be measured is imaged by the optical lens and the image sensor of the optical system, and the image spot of the point target to be measured is sampled to obtain the image spot image of the point target to be measured. The image spot image of the point target to be measured collected can be one frame or multiple frames.

[0072] Specifically, a pixel response matrix is constructed according to the spot image of the to-be-measured point target, including: extracting an imaging region from the spot image of the to-be-measured point target; taking the average value of pixels in a region other than the imaging region in the spot image of the to-be-measured point target as a background value, and removing the background value from the imaging region to obtain the pixel response matrix.

[0073] wherein the imaging region is a region containing most of the energy information of the spot, for example, a region containing more than 95% of the energy information of the spot can be extracted as the imaging region. In some embodiments, the imaging region is usually a pixel window.

[0074] It can be understood that if the collected spot image of the to-be-measured point target is multiple frames, the pixel response matrix of each frame of the spot image of the to-be-measured point target can be calculated, and the mean of multiple pixel response matrices is taken as the final pixel response matrix.

[0075] Step S110-3: Based on the feature that the number of photoelectrons generated by the imaging process pixels basically obeys Poisson distribution, the probability density function is constructed according to the imaging PSF model and the pixel response matrix.

[0076] For example, the probability density function of the pixel response matrix of the image sensor for the to-be-measured point target imaging with respect to the two-dimensional position of the spot center and the energy coefficient f can be expressed as:

[0077]

[0078] wherein, represents the imaging region; K represents the pixel gain, that is, the gain coefficient of converting the number of photoelectrons into the pixel value; represents the variance of the dark noise of the image sensor; represents the pixel response matrix, and the pixel response value of the pixel ; represents the imaging PSF model of the pixel . In some embodiments, the pixel gain K and the variance of the dark noise of the image sensor can be obtained by photon transfer method or query manual.

[0079] Through the above implementation process, based on the distribution characteristics of the number of photoelectrons generated by the imaging process pixels and the accurate imaging PSF model of the optical system, the probability density function of the pixel response matrix of the image sensor for the to-be-measured point target imaging with respect to the two-dimensional position of the spot center and the energy coefficient is constructed.

[0080] ​In conjunction with the above embodiments, in one implementation, this application also provides a method for calculating and jointly estimating the accuracy limits of point target localization and photometric measurement. In this method, as... Figure 3 As shown, step S120 above, "calculating the joint three-dimensional accuracy limit of the two-dimensional position of the image spot center and the energy coefficient based on the log-likelihood function of the probability density function," specifically includes sub-steps S120-1 to S120-4:

[0081] Step S120-1: Calculate the Fisher information matrix of the parameter vector to be estimated based on the log-likelihood function of the probability density function. The parameter vector to be estimated includes the x and y coordinates of the two-dimensional position of the image spot center and the energy coefficient. The elements in the Fisher information matrix are represented as the negative of the expected value of the second-order partial derivative of the log-likelihood function with respect to the parameter vector to be estimated.

[0082] Specifically, the log-likelihood function can be obtained by taking the natural logarithm of the probability density function. :

[0083]

[0084] in, This represents the estimated parameter vector, i.e.:

[0085]

[0086] The Fisher information matrix of the parameter vector to be estimated reflects the sensitivity of the probability distribution to changes in the parameters. The Fisher information matrix is ​​a symmetric matrix. For example, the Fisher information matrix of the parameter vector to be estimated... This can be equivalently represented as:

[0087]

[0088] in, Let represent the mathematical expectation, and:

[0089]

[0090] Step S120-2: Calculate the determinant of the Fisher information matrix.

[0091] For example, the determinant of the Fisher information matrix It can be represented as:

[0092]

[0093] in,

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101] Step S120-3: calculating a joint Cramér-Rao lower bound of the two-dimensional position of the spot center and the energy coefficient according to the determinant, the joint Cramér-Rao lower bound comprising a Cramér-Rao lower bound of the x-coordinate of the two-dimensional position of the spot center, a Cramér-Rao lower bound of the y-coordinate of the two-dimensional position of the spot center, and a Cramér-Rao lower bound of the energy coefficient.

[0102] According to the Cramér-Rao lower bound theory, a joint Cramér-Rao lower bound of the two-dimensional position of the spot center and the energy coefficient is calculated according to the determinant. The Cramér-Rao lower bound of the x-coordinate of the two-dimensional position of the spot center may be expressed as:

[0103]

[0104] The Cramér-Rao lower bound of the y-coordinate of the two-dimensional position of the spot center may be expressed as:

[0105]

[0106] The Cramér-Rao lower bound of the energy coefficient may be expressed as:

[0107]

[0108] Step S120-4: taking square roots of the joint Cramér-Rao lower bound to obtain a joint three-dimensional precision limit, the joint three-dimensional precision limit comprising a precision limit of the x-coordinate of the two-dimensional position of the spot center, a precision limit of the y-coordinate of the two-dimensional position of the spot center, and a precision limit of the energy coefficient.

[0109] Specifically, taking square roots of the Cramér-Rao lower bound of the x-coordinate of the two-dimensional position of the spot center obtains a precision limit of the x-coordinate of the two-dimensional position of the spot center (the standard deviation that cannot be exceeded by any unbiased estimation method), that is, the precision limit of the x-coordinate of the two-dimensional position of the spot center represents the optimal positioning precision of the spot center position in the x direction. For example, it can be expressed as:

[0110]

[0111] Taking square root of the Cramér-Rao lower bound of the y coordinate of the two-dimensional position of the spot center, the precision limit of the y coordinate of the two-dimensional position of the spot center is obtained (the standard deviation that any unbiased estimation method cannot be higher than), that is, the precision limit of the y coordinate of the two-dimensional position of the spot center represents the optimal positioning precision of the spot center position in the y direction. Exemplarily, it can be expressed as:

[0112]

[0113] Taking square root of the Cramér-Rao lower bound of the energy coefficient, the precision limit of the energy coefficient is obtained (the standard deviation that any unbiased estimation method cannot be higher than), that is, the precision limit of the energy coefficient represents the optimal precision of the photometric measurement. Exemplarily, it can be expressed as:

[0114]

[0115] Through the above implementation process, the joint three-dimensional precision limit of the two-dimensional position of the spot center and the energy coefficient is derived based on the probability density function of the pixel response matrix of the image sensor for the imaging of the to-be-measured point target about the two-dimensional position of the spot center and the energy coefficient, which provides a theoretical basis for the evaluation of the unbiased estimation performance of the point target precise positioning and photometric measurement.

[0116] In combination with the above embodiments, in an embodiment, the present application also provides a precision limit calculation and joint estimation method for point target positioning and photometric measurement, in which, as shown in Figure 4 the step S130 of "calculating the two-dimensional position of the spot center and the energy coefficient as joint estimation results based on the log-likelihood function of the probability density function according to the maximum likelihood estimation method" specifically includes the sub-step S130-1 to the step S130-3:

[0117] The step S130-1: positioning the spot image of the to-be-measured point target by the centroid method to obtain the initial two-dimensional position of the spot center, and determining the initial energy coefficient according to the imaging PSF model and the pixel response matrix.

[0118] In the present application, the imaging area is extracted from the spot image of the to-be-measured point target, and the centroid method is used to quickly position the imaging area to obtain the initial two-dimensional position of the spot center .

[0119] Specifically, determining the initial energy coefficient according to the imaging PSF model and the pixel response matrix comprises: calculating the sum of PSF values corresponding to the initial spot center two-dimensional position of all pixels in the imaging area by interpolation according to the imaging PSF model; calculating the sum of pixel values of all pixels in the imaging area according to the pixel response matrix; and obtaining the initial energy coefficient according to the ratio of the sum of pixel values to the sum of PSF values.

[0120] wherein the sum of PSF values corresponding to the initial spot center two-dimensional position of all pixels in the imaging area calculated by interpolation can be achieved by a cubic spline interpolation technique. For example, the initial energy coefficient may be represented as:

[0121]

[0122] Step S130-2: obtaining a Jacobian matrix according to the first derivative of the log-likelihood function, and obtaining a Hessian matrix according to the second derivative of the log-likelihood function.

[0123] For example, the Jacobian matrix J and the Hessian matrix H can be represented as:

[0124]

[0125]

[0126] wherein, represents the background value on the pixel .

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133] Step S130-3: iteratively maximizing the log-likelihood function by using the Newton-Raphson method according to the initial spot center two-dimensional position, the initial energy coefficient, the Jacobian matrix and the Hessian matrix, and taking the spot center two-dimensional position and the energy coefficient obtained when the iteration end condition is met as the joint estimation result.

[0134] Specifically, the iteration process can be represented as:

[0135]

[0136] wherein, 、 、 x-coordinate, y-coordinate and energy coefficient obtained by n+1 iteration respectively, 、 、 x-coordinate, y-coordinate and energy coefficient obtained by n iteration respectively, and Jacobi matrix and Hessian matrix obtained by n iteration.

[0137] In the embodiment of the application, the iteration number threshold of the operation is set, and the iteration change threshold of the image spot two-dimensional position coordinate and the energy coefficient is set respectively. The iteration end condition is that the change of the parameter in the iteration is less than the change threshold, or the iteration number is greater than the number threshold. When the iteration end condition is met, the iteration ends, and the image spot center two-dimensional position and the energy coefficient close to the precision limit are output, that is, the target precision positioning result and the photometric result are obtained.

[0138] Specifically, the iteration number threshold can be set to 5 times, the iteration change threshold of the image spot two-dimensional position coordinate is set to 0.002 pixels, and the iteration change threshold of the energy coefficient is set to 0.001. In the embodiment, the algorithm usually converges after 2-4 iterations.

[0139] Through the above implementation process, the joint estimation of the target position coordinate and the energy coefficient of the to-be-measured point is realized based on the maximum likelihood estimation method. On the one hand, the photometric quantity such as the radiation quantity and the illumination of the to-be-measured target can be measured; on the other hand, the influence of the brightness change of the to-be-measured target on the positioning precision is reduced, so that the precision positioning of the point target with different brightness is realized, and the application range of the imaging PSF is expanded.

[0140] Based on the same inventive concept, the embodiment of the application also provides a precision limit calculation and joint estimation device for point target positioning and photometric measurement. Referring to FIG. 10, Figure 5 , Figure 5 is a structural schematic diagram of a precision limit calculation and joint estimation device for point target positioning and photometric measurement provided by the embodiment of the application. The device comprises:

[0141] A first construction module 510 is configured to construct, according to an imaging point spread function (PSF) model of an optical system, a probability density function of a pixel response matrix of an image sensor for imaging a to-be-measured point target about an image spot center two-dimensional position and an energy coefficient. The energy coefficient represents the relative brightness of the to-be-measured point target and the modeled point target.

[0142] The first calculation module 520 is configured to calculate a joint three-dimensional precision limit of the two-dimensional position of the spot center and the energy coefficient according to a log-likelihood function of the probability density function.

[0143] The second calculation module 530 is configured to calculate the two-dimensional position of the spot center and the energy coefficient as a joint estimation result according to the log-likelihood function of the probability density function based on a maximum likelihood estimation method, and evaluate the precision of the joint estimation result by the joint three-dimensional precision limit.

[0144] In an optional embodiment, the first construction module comprises:

[0145] The first construction submodule is configured to collect a plurality of spot images of a modeling point target at different sub-pixel positions of each pixel in an image sensor of the optical system, and construct an imaging PSF model of each pixel according to the plurality of spot images of the modeling point target.

[0146] The second construction submodule is configured to image a to-be-tested point target by an optical lens and an image sensor of the optical system, collect a spot image of the to-be-tested point target, and construct a pixel response matrix of an imaging area according to the spot image of the to-be-tested point target, the imaging area being an area containing most energy information of the spot.

[0147] The third construction submodule is configured to construct the probability density function according to the imaging PSF model and the pixel response matrix based on the feature that the number of photoelectrons generated by a pixel in an imaging process substantially obeys a Poisson distribution.

[0148] In an optional embodiment, the first calculation module comprises:

[0149] The first calculation submodule is configured to calculate a Fisher information matrix of a to-be-estimated parameter vector according to a log-likelihood function of the probability density function, the to-be-estimated parameter vector comprising an x-coordinate and a y-coordinate of the two-dimensional position of the spot center and the energy coefficient, and an element in the Fisher information matrix being represented as an inverse of an expected value of a second-order partial derivative of the log-likelihood function with respect to the to-be-estimated parameter vector.

[0150] The second calculation submodule is configured to calculate a determinant of the Fisher information matrix.

[0151] The third calculation submodule is configured to calculate a joint Cramér-Rao lower bound of the two-dimensional position of the spot center and the energy coefficient according to the determinant, the joint Cramér-Rao lower bound comprising a Cramér-Rao lower bound of the x-coordinate of the two-dimensional position of the spot center, a Cramér-Rao lower bound of the y-coordinate of the two-dimensional position of the spot center, and a Cramér-Rao lower bound of the energy coefficient.

[0152] A fourth calculating sub-module is configured to square root the joint Cramer-Rao lower bound to obtain the joint three-dimensional precision limit, which includes a precision limit of a two-dimensional position x coordinate of a spot center, a precision limit of a two-dimensional position y coordinate of the spot center, and a precision limit of an energy coefficient.

[0153] In an alternative embodiment, the second calculating module comprises:

[0154] A fifth calculating sub-module is configured to position the spot image of the to-be-measured point target by a centroid method to obtain an initial two-dimensional position of the spot center, and determine an initial energy coefficient according to the imaging PSF model and the pixel response matrix.

[0155] A sixth calculating sub-module is configured to obtain a Jacobian matrix according to a first-order derivative of the log-likelihood function, and obtain a Hessian matrix according to a second-order derivative of the log-likelihood function.

[0156] A seventh calculating sub-module is configured to iteratively maximize the log-likelihood function by a Newton-Raphson method according to the initial two-dimensional position of the spot center, the initial energy coefficient, the Jacobian matrix and the Hessian matrix, and obtain a two-dimensional position of the spot center and an energy coefficient obtained when an iteration end condition is met as joint estimation results.

[0157] In an alternative embodiment, the fifth calculating sub-module comprises:

[0158] An initial energy coefficient calculating sub-module is configured to calculate a sum of PSF values corresponding to the initial two-dimensional position of the spot center of all pixels in the imaging region according to the imaging PSF model, calculate a sum of pixel values of all pixels in the imaging region according to the pixel response matrix, and obtain the initial energy coefficient according to a ratio of the sum of the pixel values to the sum of the PSF values.

[0159] In an alternative embodiment, the first constructing sub-module comprises:

[0160] An image collecting sub-module is configured to fix a motion executor with a modeling point target, sequentially pass light source signals of the modeling point target through a parallel light tube of the optical system and an optical lens to the image sensor to form a spot, control the motion executor to make the spot sub-pixel shift in each pixel of the image sensor, and collect multiple frames of spot images of the modeling point target at each sub-pixel position to obtain multiple frames of spot images of the modeling point target at different sub-pixel positions of each pixel.

[0161] In an alternative embodiment, the first constructing sub-module comprises:

[0162] The PSF model calculation submodule is configured to calculate, for each pixel, a pixel response value corresponding to each sub-pixel position according to a plurality of frame spot images of the modeled point target at different sub-pixel positions of the pixel, and obtain an imaging PSF sampling matrix of the pixel; and interpolate the imaging PSF sampling matrix of the pixel to obtain an imaging PSF model of the pixel, wherein the imaging PSF model includes PSF values at any position.

[0163] In an optional embodiment, the second construction submodule includes:

[0164] The pixel response matrix calculation submodule is configured to extract an imaging area from the spot image of the point target to be measured; take an average value of pixels in an area other than the imaging area in the spot image of the point target to be measured as a background value, and remove the background value from the imaging area to obtain the pixel response matrix.

[0165] The embodiments of the present application further provide an electronic device, which refers to Figure 6 , Figure 6 is a structural schematic diagram of an electronic device provided by the embodiments of the present application. As shown in Figure 6 , the electronic device 600 includes a memory 610 and a processor 620, the memory 610 and the processor 620 are in communication connection through a bus, the memory 610 stores a computer program, the computer program can run on the processor 620, and then the steps of the point target positioning and photometric precision limit calculation and joint estimation method described in the embodiments of the present application are implemented.

[0166] The embodiments of the present application further provide a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the steps of the point target positioning and photometric precision limit calculation and joint estimation method described in the embodiments of the present application.

[0167] The embodiments of the present application further provide a computer program product, which includes a computer program, and the computer program is executed by a processor to implement the steps of the point target positioning and photometric precision limit calculation and joint estimation method described in the embodiments of the present application.

[0168] Each of the embodiments in the present specification is described in a progressive manner, and each embodiment focuses on the difference from other embodiments, and the same and similar parts between each embodiment can be referred to each other.

[0169] The embodiments of the present application are described with reference to the flowcharts and / or block diagrams of the methods, apparatuses (systems) according to the embodiments of the present application. It is understood that each flow and / or block in the flowcharts and / or block diagrams, and a combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or a processor of other programmable data processing terminals to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing terminals generate a device implemented in the flowcharts and / or block diagrams of the methods, apparatuses (systems) according to the embodiments of the present application. Figure 1 one or more flows and / or blocks in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks in the flowcharts and / or block diagrams.

[0170] These computer program instructions can also be stored in a computer readable memory capable of directing the computer or other programmable data processing terminal to work in a specific manner, so that the instructions stored in the computer readable memory produce a manufactured product including instruction devices, which implement the functions specified in one or more flows and / or blocks in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks in the flowcharts and / or block diagrams.

[0171] These computer program instructions can also be loaded into a computer or other programmable data processing terminal, so that a series of operation steps are performed on the computer or other programmable terminal to produce a computer implemented process, so that the instructions executed on the computer or other programmable terminal provide steps for implementing the functions specified in one or more flows and / or blocks in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks in the flowcharts and / or block diagrams.

[0172] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications to the embodiments once they know the basic inventive concept. Therefore, the appended claims are intended to be interpreted as including all the preferred embodiments and all the changes and modifications falling within the scope of the embodiments of the present application.

[0173] Finally, it is to be understood that the phraseology or terminology such as "first" and "second" etc. used herein is merely intended to differentiate one entity or operation from another entity or operation, without necessarily requiring or implying any actual such relationship or order between such entities or operations. Moreover, the terms "comprising", "including", or any other closure, are intended to cover the non-exclusive inclusion such that a process, method, article, or apparatus that comprises a list of elements does not include those elements solely, but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without more limitations, the element defined by the statement "comprising a" does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0174] The above describes in detail the precision limit calculation and joint estimation method and device of a point target positioning and photometric measurement provided by the present application. The principles and implementation modes of the present application are described by using specific examples. The above description of the embodiments is only used to help understand the method of the present application and its core idea. Meanwhile, for those skilled in the art, according to the idea of the present application, the specific implementation mode and application range will be changed. In summary, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A method of precision limit calculation and joint estimation of point target positioning and photometric measurements, characterized in that, The method comprises: According to the imaging point spread function PSF model of the optical system, a probability density function of a pixel response matrix of an image sensor imaging a to-be-measured point target with respect to a two-dimensional position of a spot center and an energy coefficient is constructed, the energy coefficient representing a relative brightness of the to-be-measured point target and a modeling point target; According to a log-likelihood function of the probability density function, a joint three-dimensional precision limit of the two-dimensional position of the spot center and the energy coefficient is calculated; Based on a maximum likelihood estimation method, the two-dimensional position of the spot center and the energy coefficient are calculated as a joint estimation result according to the log-likelihood function of the probability density function, and the precision of the joint estimation result is evaluated through the joint three-dimensional precision limit; According to the imaging point spread function PSF model of the optical system, a probability density function of a pixel response matrix of an image sensor imaging a to-be-measured point target with respect to a two-dimensional position of a spot center and an energy coefficient is constructed, the energy coefficient representing a relative brightness of the to-be-measured point target and a modeling point target; A plurality of spot images of the modeling point target are collected at different sub-pixel positions of each pixel in the image sensor of the optical system, and an imaging PSF model of each pixel is constructed according to the plurality of spot images of the modeling point target; A to-be-measured point target is imaged through an optical lens and an image sensor of the optical system, and a spot image of the to-be-measured point target is collected, a pixel response matrix of an imaging region is constructed according to the spot image of the to-be-measured point target, the imaging region being a region containing most energy information of the spot; Based on the feature that the number of photoelectrons generated by a pixel in an imaging process basically obeys a Poisson distribution, the probability density function is constructed according to the imaging PSF model and the pixel response matrix.

2. The method of claim 1, wherein, According to a log-likelihood function of the probability density function, a joint three-dimensional precision limit of the two-dimensional position of the spot center and the energy coefficient is calculated, comprising: According to the log-likelihood function of the probability density function, a Fisher information matrix of a to-be-estimated parameter vector is calculated, the to-be-estimated parameter vector including an x-coordinate and a y-coordinate of the two-dimensional position of the spot center and the energy coefficient, and an element in the Fisher information matrix being represented as an inverse of an expected value of a second-order partial derivative of the log-likelihood function with respect to the to-be-estimated parameter vector; The determinant of the Fisher information matrix is calculated; According to the determinant, a joint Cramér-Rao lower bound of the two-dimensional position of the spot center and the energy coefficient is calculated, the joint Cramér-Rao lower bound including a Cramér-Rao lower bound of the x-coordinate of the two-dimensional position of the spot center, a Cramér-Rao lower bound of the y-coordinate of the two-dimensional position of the spot center, and a Cramér-Rao lower bound of the energy coefficient; The joint Cramér-Rao lower bound is square-rooted to obtain the joint three-dimensional precision limit, the joint three-dimensional precision limit including a precision limit of the x-coordinate of the two-dimensional position of the spot center, a precision limit of the y-coordinate of the two-dimensional position of the spot center, and a precision limit of the energy coefficient.

3. The method of claim 1, wherein, Based on a maximum likelihood estimation method, the two-dimensional position of the spot center and the energy coefficient are calculated as a joint estimation result according to the log-likelihood function of the probability density function, comprising: locating the spot image of the to-be-measured point target by a centroid method to obtain an initial spot center two-dimensional position, and determining an initial energy coefficient according to the imaging PSF model and the pixel response matrix; obtaining a Jacobian matrix according to a first derivative of the log-likelihood function, and obtaining a Hessian matrix according to a second derivative of the log-likelihood function; iteratively maximizing the log-likelihood function by a Newton-Raphson method according to the initial spot center two-dimensional position, the initial energy coefficient, the Jacobian matrix and the Hessian matrix, and taking a spot center two-dimensional position and an energy coefficient obtained under a condition that an iteration end condition is met as a joint estimation result.

4. The method of claim 3, wherein, determining an initial energy coefficient according to the imaging PSF model and the pixel response matrix, comprising: calculating a sum of PSF values corresponding to the initial spot center two-dimensional position of all pixels in the imaging region by interpolation according to the imaging PSF model; calculating a sum of pixel values of all pixels in the imaging region according to the pixel response matrix; obtaining the initial energy coefficient according to a ratio of the sum of the pixel values to the sum of the PSF values.

5. The method of claim 1, wherein, acquiring multiple frames of spot images of a modeling point target at different sub-pixel positions of each pixel in an image sensor of the optical system, comprising: fixing a motion executor with the modeling point target, sequentially passing light source signals of the modeling point target through a parallel light tube of the optical system and the optical lens to the image sensor to be imaged as a spot, and performing sub-pixel level displacement of the spot at each pixel in the image sensor by controlling the motion executor; sampling multiple frames of spot images of the modeling point target at each sub-pixel position to obtain multiple frames of spot images of the modeling point target at different sub-pixel positions of each pixel.

6. The method of claim 5, wherein, constructing an imaging PSF model of each pixel according to the multiple frames of spot images of the modeling point target, comprising: for each pixel, calculating a pixel response value corresponding to each sub-pixel position according to the multiple frames of spot images of the modeling point target at different sub-pixel positions of the pixel to obtain an imaging PSF sampling matrix of the pixel; interpolating the imaging PSF sampling matrix of the pixel to obtain the imaging PSF model of the pixel, the imaging PSF model comprising a PSF value at an arbitrary position.

7. The method of claim 1, wherein, constructing a pixel response matrix according to the spot image of the to-be-measured point target, comprising: extracting an imaging region from the spot image of the to-be-measured point target; taking an average value of pixels in a region other than the imaging region in the spot image of the to-be-measured point target as a background value, and removing the background value from the imaging region to obtain the pixel response matrix.

8. An apparatus for precision limit calculation and joint estimation of point target positioning and photometric measurements, characterized by The apparatus comprises: a first constructing module configured to construct, according to an imaging point spread function (PSF) model of an optical system, a probability density function of a pixel response matrix of an image sensor with respect to a spot center two-dimensional position and an energy coefficient for imaging a to-be-measured point target, the energy coefficient representing a relative brightness of the to-be-measured point target and a modeling point target; The method comprises the following steps: constructing a probability density function of a pixel response matrix of an image sensor imaging a point target to be measured with respect to a two-dimensional position of a spot center and an energy coefficient according to a point spread function (PSF) model of an optical system, including: collecting a plurality of spot images of a modeling point target at different sub-pixel positions of each pixel in the image sensor of the optical system, and constructing an imaging PSF model of each pixel according to the plurality of spot images of the modeling point target; imaging a point target to be measured through an optical lens and an image sensor of the optical system, collecting a spot image of the point target to be measured, and constructing a pixel response matrix of an imaging area according to the spot image of the point target to be measured, the imaging area being an area containing most of the energy information of the spot; based on the characteristic that the number of photoelectrons generated by a pixel in an imaging process basically obeys a Poisson distribution, constructing the probability density function according to the imaging PSF model and the pixel response matrix; a first calculation module configured to calculate a joint three-dimensional precision limit of the two-dimensional position of the spot center and the energy coefficient according to a log-likelihood function of the probability density function; a second calculation module configured to calculate the two-dimensional position of the spot center and the energy coefficient as a joint estimation result according to the log-likelihood function of the probability density function based on a maximum likelihood estimation method, and evaluate the precision of the joint estimation result through the joint three-dimensional precision limit.

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the steps of the point target positioning and photometric precision limit calculation and joint estimation method of any one of claims 1-7 when executing the computer program.

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