Optical imaging spot two-dimensional position measurement precision limit optimization method, device and equipment

Abstract

The application provides a precision limit optimization method, device and equipment for optical imaging image spot two-dimensional position measurement, relates to the technical field of optical imaging precision measurement, and aims to realize precision limit analysis of optical imaging image spot two-dimensional position measurement of a small-size PSF system. The method comprises the following steps: approximating the phase gradient distribution of a PSF in a pixel space according to the energy concentration distribution characteristics of an imaging image spot of a small-size point spread function (PSF) optical system, to obtain an approximate result of the gradient distribution of the PSF; estimating the two-dimensional position measurement precision limit of the imaging image spot of the small-size PSF optical system on an image detector according to the approximate result of the gradient distribution of the PSF; calculating the implementation condition of the minimum value of the two-dimensional position measurement precision limit, and calculating the analytical estimation of the optimal two-dimensional position measurement precision limit according to the implementation condition and the two-dimensional position measurement precision limit.

Description

Technical Field

[0001] This application relates to the field of optical imaging precision measurement technology, and in particular to a method, apparatus and device for optimizing the accuracy limit of two-dimensional position measurement of optical imaging spots. Background Technology

[0002] In the field of optical imaging measurement, the measurement of the two-dimensional position of an image spot directly determines the final measurement accuracy of optical instruments in many applications. For example, in spacecraft navigation, star sensors, as key instruments in attitude measurement systems, directly affect the stability and mission reliability of spacecraft in orbit. Star sensors achieve precise measurement of the three-axis absolute attitude of the spacecraft by performing two-dimensional positioning of stellar image spots and matching them with the star surface. The attitude measurement accuracy of the instrument is almost directly proportional to the positioning accuracy of the stellar image spot. Therefore, high-precision positioning technology for image spots has become a research focus in aerospace navigation, astronomical observation, precision manufacturing, and other related fields.

[0003] For optical imaging precision measurement, the accuracy limit is the lower limit of the standard deviation that cannot be surpassed when measuring the position of the image spot using any unbiased estimation method. It represents the theoretically highest achievable measurement accuracy. Traditional optical imaging measurement systems are mostly based on large-size point spread functions (PSFs) for image spot localization. For large-size PSF optical systems, the imaging localization accuracy limit is mainly related to the number of photoelectrons detected, pixel dark noise, and PSF size. The influence of the PSF at different pixel phases (i.e., its specific position within a pixel) on the accuracy limit is not significant. However, for small-size PSF optical systems, the pixel phase of the image spot significantly affects the accuracy limit. Due to the more concentrated energy distribution of the PSF, its phase gradient at specific pixels is very significant, resulting in a better accuracy limit.

[0004] However, the theoretical analysis of the accuracy limit of small-sized PSF systems is quite complex, and currently, there is a lack of simple and effective analytical estimation formulas or methods. This lack of such methods makes it impossible to systematically understand and quantify the specific optimization effect of pixel phase on the accuracy limit, and even more difficult to guide the active optimization of pixel phase in actual measurements. This situation substantially wastes the potential optimization performance of information theory, making it difficult to overcome existing positioning accuracy bottlenecks. Therefore, it is urgent to establish an analysis method for the accuracy limit of two-dimensional position measurement of optical imaging spots in small-sized PSF optical systems to optimize the accuracy limit. Summary of the Invention

[0005] In view of the above problems, embodiments of this application provide a method, apparatus and device for optimizing the accuracy limit of two-dimensional position measurement of optical imaging spots, so as to overcome the above problems or at least partially solve the above problems.

[0006] A first aspect of this application discloses a method for optimizing the accuracy limit of two-dimensional position measurement of optical imaging spots, the method comprising:

[0007] Based on the energy concentration distribution characteristics of the imaging speckle of a small-size point spread function (PSF) optical system, an approximation of the phase gradient distribution of the PSF in the pixel space is performed to obtain an approximate gradient distribution result of the PSF. The approximate gradient distribution result of the PSF represents the quantitative result of the matching relationship between the PSF gradient distribution and the pixel phase.

[0008] Based on the approximate gradient distribution of the PSF, the limit of the two-dimensional position measurement accuracy of the imaging spot of the small-sized PSF optical system on the image detector is estimated.

[0009] The conditions for achieving the minimum value of the two-dimensional position measurement accuracy limit are calculated, and based on the conditions and the two-dimensional position measurement accuracy limit, an analytical estimate of the optimal accuracy limit of the two-dimensional position measurement is calculated. The conditions and the analytical estimate of the optimal accuracy limit of the two-dimensional position measurement are used to guide the centering measurement of the imaging spot.

[0010] Optionally, the gradient distribution approximation of the PSF includes the gradient distribution approximation of the PSF in the x-direction and the gradient distribution approximation in the y-direction; based on the energy concentration distribution characteristics of the imaging speckle of a small-size point spread function (PSF) optical system, the phase gradient distribution of the PSF in the pixel space is approximated to obtain the gradient distribution approximation result of the PSF, including:

[0011] The energy of the imaging spot of the small-sized PSF optical system is approximated as a two-dimensional energy distribution concentrated in... The function within the pixel window obtains the... The pixel response of four pixels within a pixel window;

[0012] Based on the pixel responses of the four pixels, a first gradient distribution approximation of the PSF in the x-direction is constructed, and a second gradient distribution approximation of the PSF in the y-direction is constructed.

[0013] Wherein, the first gradient distribution approximately characterizes the... Within a pixel window, the gradients of the pixel responses of two adjacent pixels along the x-axis are opposite, and the second gradient distribution approximately characterizes the... The gradients of the pixel responses of two adjacent pixels in the y-direction within a pixel window are opposite.

[0014] Optionally, the The four pixels within the pixel window include a first pixel, a second pixel, a third pixel, and a fourth pixel. The first pixel and the second pixel are adjacent to each other horizontally in the x-direction, the third pixel and the fourth pixel are adjacent to each other horizontally in the x-direction, the first pixel and the third pixel are adjacent to each other vertically in the y-direction, and the second pixel and the fourth pixel are adjacent to each other vertically in the y-direction.

[0015] The gradient distribution of PSF in the x-direction is approximately as follows: the gradient of the pixel response of the first pixel in the x-direction is opposite to that of the pixel response of the second pixel in the x-direction; the ratio of the gradient of the pixel response of the first pixel in the x-direction to that of the pixel response of the third pixel in the x-direction is the same as the ratio of the pixel response of the first pixel to that of the third pixel; and the gradient of the pixel response of the third pixel in the x-direction is opposite to that of the pixel response of the fourth pixel in the x-direction.

[0016] The gradient distribution of PSF in the y-direction is approximate, including: the ratio of the gradient of the pixel response of the first pixel in the y-direction to the gradient of the pixel response of the second pixel in the y-direction is the same as the ratio of the pixel response of the first pixel to the pixel response of the second pixel; the gradient of the pixel response of the first pixel in the y-direction is opposite to the gradient of the pixel response of the third pixel in the y-direction; and the ratio of the gradient of the pixel response of the third pixel in the y-direction to the gradient of the pixel response of the fourth pixel in the y-direction is the same as the ratio of the pixel response of the third pixel to the pixel response of the fourth pixel.

[0017] Optionally, based on the approximate gradient distribution of the PSF, the limit of two-dimensional position measurement accuracy of the imaging spot of the small-sized PSF optical system on the image detector is estimated, including:

[0018] According to the Cramer-Rao lower bound theory, calculate the measurement accuracy limit of the first position of the imaging spot in the x direction, and calculate the measurement accuracy limit of the second position of the imaging spot in the y direction.

[0019] Based on the gradient distribution approximation of PSF, the first position measurement accuracy limit and the second position measurement accuracy limit are simplified respectively to obtain the simplified first position measurement accuracy limit and the simplified second position measurement accuracy limit;

[0020] The simplified first position measurement accuracy limit and the simplified second position measurement accuracy limit are superimposed to obtain the two-dimensional position measurement accuracy limit.

[0021] Optionally, calculating the condition for the two-dimensional position measurement accuracy limit to satisfy the minimum value includes:

[0022] For a typical PSF of a two-dimensional Gaussian function, the center of the image spot is located at the... In the case of the intersection of four pixels within a pixel window, the minimum value is determined to satisfy the limit of the two-dimensional position measurement accuracy, thus obtaining the realization condition;

[0023] The implementation conditions include: The pixel responses of the four pixels within the pixel window are equal, and the pixel response of each pixel is equal to the stated value. One-quarter of the sum of the pixel values ​​of the four pixels within the pixel window.

[0024] Optionally, based on the implementation conditions and the two-dimensional position measurement accuracy limit, an analytical estimate of the optimal accuracy limit of the two-dimensional position measurement is calculated, including:

[0025] The significant gradient of the pixel response of the first pixel is determined. The significant gradient of the pixel response of the first pixel represents the maximum rate of change of the first pixel response caused by a small movement of the imaging spot. The magnitude of the pixel response of the first pixel with respect to the gradient in the x direction is the same as that with respect to the gradient in the y direction.

[0026] Substituting the implementation conditions and the significant gradient of the pixel response of the first pixel into the two-dimensional position measurement accuracy limit, an analytical estimate of the optimal accuracy limit of the two-dimensional position measurement is obtained. The analytical estimate of the optimal accuracy limit of the two-dimensional position measurement characterizes the theoretical optimal accuracy that the two-dimensional position measurement can achieve.

[0027] A second aspect of this application discloses a device for optimizing the accuracy limit of two-dimensional position measurement of optical imaging spots, the device comprising:

[0028] An approximation module is used to approximate the phase gradient distribution of the PSF in the pixel space based on the energy concentration distribution characteristics of the imaging spot of a small-sized point spread function (PSF) optical system, and to obtain an approximate gradient distribution result of the PSF. The approximate gradient distribution result of the PSF represents the quantitative result of the matching relationship between the PSF gradient distribution and the pixel phase.

[0029] An estimation module is used to estimate the two-dimensional position measurement accuracy limit of the imaging spot of the small-sized PSF optical system on the image detector based on the approximate gradient distribution result of the PSF;

[0030] The calculation module is used to calculate the conditions for achieving the minimum value of the two-dimensional position measurement accuracy limit, and to calculate the analytical estimate of the optimal accuracy limit of the two-dimensional position measurement based on the conditions and the two-dimensional position measurement accuracy limit. The conditions and the analytical estimate of the optimal accuracy limit of the two-dimensional position measurement are used to guide the centering measurement of the imaging spot.

[0031] A third aspect of this application discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the optical imaging spot two-dimensional position measurement accuracy limit optimization method described in the first aspect of this application.

[0032] A fourth aspect of this application discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the optical imaging spot two-dimensional position measurement accuracy limit optimization method described in the first aspect of this application.

[0033] A fifth aspect of this application discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of the optical imaging spot two-dimensional position measurement accuracy limit optimization method described in the first aspect of this application.

[0034] The embodiments of this application have the following advantages:

[0035] In this embodiment, based on the energy concentration distribution characteristics of the imaging spot in a small-sized PSF optical system, an approximation of the phase gradient distribution of the PSF in the pixel space is made. Based on the approximation of the PSF gradient distribution, the two-dimensional position measurement accuracy limit of the imaging spot on the image detector is estimated, quantifying the matching relationship between the PSF gradient distribution and the pixel phase, and guiding the collaborative optimization of the phase configuration of the optical system and the image detector. By calculating the realization condition for the two-dimensional position measurement accuracy limit to satisfy the minimum value, and based on the realization condition, an analytical estimate of the optimal accuracy limit of the two-dimensional position measurement is calculated. This achieves the analytical estimation and optimization of the optimal accuracy limit of the two-dimensional position measurement, filling the theoretical research gap in improving the two-dimensional positioning accuracy limit of the imaging spot through pixel phase optimization. Based on the realization condition and the analytical estimate of the optimal accuracy limit of the two-dimensional position measurement, the imaging spot centering measurement is guided, utilizing the potential for optimized positioning performance inherent in information theory, making the actual measurement accuracy approach the theoretical optimum, and providing theoretical support and practical path for improving the accuracy of optical imaging measurement applications. Attached Figure Description

[0036] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1This is a flowchart illustrating the steps of a method for optimizing the accuracy limit of two-dimensional position measurement of optical imaging spots according to an embodiment of this application.

[0038] Figure 2 This is a schematic diagram of the image spot energy distribution of a small-sized PSF optical system provided in an embodiment of this application;

[0039] Figure 3 This is a schematic diagram of the maximum gradient of a small-sized PSF provided in an embodiment of this application;

[0040] Figure 4 This is a schematic diagram of the structure of an optical imaging spot two-dimensional position measurement accuracy limit optimization device provided in an embodiment of this application;

[0041] Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0042] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0043] For small-sized PSF optical systems, the concentrated energy distribution of the imaging speckle leads to significant phase gradients at specific pixels, resulting in a superior accuracy limit. However, current technologies have not provided solutions for overcoming existing positioning accuracy bottlenecks by optimizing pixel phase, thus wasting the potential for performance optimization inherent in information theory. Therefore, it is urgent to establish an analysis method for the accuracy limit of two-dimensional position measurement of optical imaging specks in small-sized PSF optical systems. This method would optimize the accuracy limit, guide the design of PSF distribution and measurement phase in optical imaging measurement systems, and provide a pathway to improve the accuracy of optical imaging measurement applications.

[0044] To address this, this application provides a method for optimizing the accuracy limit of two-dimensional position measurement of optical imaging spots. This method, targeting small-sized PSF optical systems, establishes an analytical estimation method for the accuracy limit of two-dimensional position measurement of imaging spots through PSF gradient approximation. It leverages the significant phase gradient of specific pixels in small-sized PSFs to optimize the accuracy limit. This method fills the theoretical research gap in improving the two-dimensional positioning accuracy limit of imaging spots through pixel phase optimization. By quantifying the matching relationship between PSF gradient distribution and pixel phase, it guides the coordinated optimization of the phase configuration of the optical system and image detector, providing theoretical support and a practical path for optical imaging measurement to overcome the traditional positioning accuracy limit bottleneck.

[0045] Reference Figure 1 As shown, Figure 1 This is a flowchart illustrating the steps of a method for optimizing the accuracy limits of two-dimensional position measurement of optical imaging spots, as provided in an embodiment of this application. Figure 1 As shown, the method for optimizing the two-dimensional position measurement accuracy limit of optical imaging spots may include steps S110 to S130:

[0046] Step S110: Based on the energy concentration distribution characteristics of the imaging spot of the small-size point spread function (PSF) optical system, the phase gradient distribution of PSF in the pixel space is approximated to obtain the gradient distribution approximation result of PSF. The gradient distribution approximation result of PSF represents the quantitative result of the matching relationship between PSF gradient distribution and pixel phase.

[0047] Among them, the energy concentration distribution characteristics of the imaging spot of a small-sized PSF optical system can be that the discretized energy distribution of the imaging spot of the small-sized PSF optical system is concentrated in a pixel window composed of several pixels (e.g., (Pixel window). Within this pixel window, as the center of the imaging spot moves across different pixel phases, the gradient distribution of the pixel response of each pixel also changes. By utilizing the energy concentration distribution characteristics of the imaging spot in a small-sized PSF optical system, and by approximating the phase gradient distribution of the PSF in pixel space, the matching relationship between the PSF gradient distribution and the pixel phase can be quantized.

[0048] In an optional embodiment, the gradient distribution approximation result of the PSF includes an approximation of the gradient distribution of the PSF in the x-direction and an approximation of the gradient distribution in the y-direction. Specifically, step S110 may include sub-steps S110-1 to S110-2:

[0049] Step S110-1: The energy of the imaging spot of the small-sized PSF optical system is approximated as a two-dimensional energy distribution and concentrated in... The function within the pixel window obtains the... The pixel response of four pixels within the pixel window.

[0050] Step S110-2: Based on the pixel responses of the four pixels, construct a first gradient distribution approximation of the PSF in the x direction, and construct a second gradient distribution approximation of the PSF in the y direction.

[0051] Wherein, the first gradient distribution approximately characterizes the... Within a pixel window, the gradients of the pixel responses of two adjacent pixels along the x-axis are opposite, and the second gradient distribution approximately characterizes the... The gradients of the pixel responses of two adjacent pixels in the y-direction within a pixel window are opposite.

[0052] In this embodiment, the energy of the imaging spot of the small-sized PSF optical system is approximated as a two-dimensional (x-direction dimension and y-direction dimension) energy distribution concentrated in... The function within the pixel window, namely the PSF energy (energy of the image spot), is distributed in... Within the four pixels of the pixel window, the pixel response of each pixel can be obtained by subtracting the background value from the pixel value.

[0053] The first gradient distribution approximation of the PSF in the x-direction refers to the approximate gradient relationship of the PSF function in the x-direction. Constructing this approximation based on the pixel responses of four pixels can be done by determining the gradient of each pixel's response in the x-direction. Similarly, the second gradient distribution approximation of the PSF in the y-direction refers to the approximate gradient relationship of the PSF function in the y-direction. Constructing this approximation based on the pixel responses of four pixels can also be done by determining the gradient of each pixel's response in the y-direction.

[0054] Because the energy of the imaging spot of a small-sized PSF optical system is approximated as a two-dimensional energy distribution concentrated in... The function is within the pixel window, so the energy of the image spot will not exceed... Pixel window, if the center of the image spot is in When different pixels within a pixel window shift their phase, the gradients of the pixel responses of two adjacent pixels in the same direction will be opposite. For example, for two pixels in the x-direction, if the pixel response of one pixel increases, the pixel response of the other pixel decreases; similarly, for two pixels in the y-direction, if the pixel response of one pixel increases, the pixel response of the other pixel decreases.

[0055] Specifically, the The four pixels within the pixel window include a first pixel, a second pixel, a third pixel, and a fourth pixel. The first pixel and the second pixel are adjacent to each other horizontally in the x-direction, the third pixel and the fourth pixel are adjacent to each other horizontally in the x-direction, the first pixel and the third pixel are adjacent to each other vertically in the y-direction, and the second pixel and the fourth pixel are adjacent to each other vertically in the y-direction.

[0056] The gradient distribution of PSF in the x-direction is approximately as follows: the gradient of the pixel response of the first pixel in the x-direction is opposite to that of the pixel response of the second pixel in the x-direction; the ratio of the gradient of the pixel response of the first pixel in the x-direction to that of the pixel response of the third pixel in the x-direction is the same as the ratio of the pixel response of the first pixel to that of the third pixel; and the gradient of the pixel response of the third pixel in the x-direction is opposite to that of the pixel response of the fourth pixel in the x-direction.

[0057] The gradient distribution of PSF in the y-direction is approximate, including: the ratio of the gradient of the pixel response of the first pixel in the y-direction to the gradient of the pixel response of the second pixel in the y-direction is the same as the ratio of the pixel response of the first pixel to the pixel response of the second pixel; the gradient of the pixel response of the first pixel in the y-direction is opposite to the gradient of the pixel response of the third pixel in the y-direction; and the ratio of the gradient of the pixel response of the third pixel in the y-direction to the gradient of the pixel response of the fourth pixel in the y-direction is the same as the ratio of the pixel response of the third pixel to the pixel response of the fourth pixel.

[0058] like Figure 2 As shown, the four pixels can be represented as follows: First pixel The second pixel The third pixel The fourth pixel Where i represents the row number of the pixel and j represents the column number of the pixel; the pixel responses of the four pixels can be expressed as follows: the pixel response of the first pixel The pixel response of the second pixel The pixel response of the third pixel The pixel response of the fourth pixel ,in It indicates the position of the center of the image spot within the pixel, i.e., the pixel phase.

[0059] For example, the gradient distribution of PSF in the x-direction can be approximately expressed as:

[0060]

[0061] The gradient distribution of PSF in the y-direction can be approximately expressed as:

[0062]

[0063] in, Let be the gradient of the pixel response of the first pixel in the x-direction. This represents the gradient of the second pixel's pixel response with respect to the x-direction. This represents the gradient of the third pixel's pixel response with respect to the x-direction. This represents the gradient of the fourth pixel's pixel response with respect to the x-direction. This represents the gradient of the pixel response of the first pixel with respect to the y-direction. This represents the gradient of the second pixel's pixel response with respect to the y-direction. This represents the gradient of the pixel response of the third pixel with respect to the y-direction. This represents the gradient of the pixel response of the fourth pixel in the y-direction.

[0064] Step S120: Based on the approximate gradient distribution of the PSF, estimate the limit of the two-dimensional position measurement accuracy of the imaging spot of the small-sized PSF optical system on the image detector.

[0065] In this embodiment, the two-dimensional position measurement accuracy limit characterizes the lower limit of the standard deviation (i.e., the theoretically achievable highest measurement accuracy) that cannot be surpassed when measuring the position of the imaging spot in both the x and y directions. Since the gradient distribution approximation of the PSF characterizes the quantized result of the matching relationship between the PSF gradient distribution and the pixel phase, the two-dimensional position measurement accuracy limit of the imaging spot on the image detector of a small-sized PSF optical system can be estimated based on the gradient distribution approximation of the PSF, and the two-dimensional position measurement accuracy limit can be obtained quickly in a simplified manner.

[0066] In an optional embodiment, the above step S120, "estimating the two-dimensional position measurement accuracy limit of the imaging spot of the small-sized PSF optical system on the image detector based on the approximate gradient distribution result of the PSF," may specifically include sub-steps S120-1 to S120-3:

[0067] Step S120-1: Based on the Cramer-Rao lower bound theory, calculate the measurement accuracy limit of the first position of the imaging spot in the x direction, and calculate the measurement accuracy limit of the second position of the imaging spot in the y direction.

[0068] Ignoring pixel dark noise, the position measurement accuracy limits of the image spot in the x-direction and y-direction can be calculated according to the Cramérault lower bound theory. For example, the first position measurement accuracy limit... Second position measurement accuracy limit They can be represented as:

[0069]

[0070]

[0071] in, and Let Clamer-Rao represent the lower bounds of the variance of the image spot position measurement results in the x and y directions, respectively. express k is an integer between 1 and 4, and K represents the gain of the image detector pixels.

[0072] The accuracy limit of two-dimensional superposition calculation for image spot localization. Represented as:

[0073]

[0074] Step S120-2: Based on the gradient distribution approximation results of PSF, the first position measurement accuracy limit and the second position measurement accuracy limit are simplified respectively to obtain the simplified first position measurement accuracy limit and the simplified second position measurement accuracy limit.

[0075] Specifically, formulas (1) and (2) can be substituted into formula (3) to simplify the first position measurement accuracy limit, resulting in a simplified first position measurement accuracy limit. Substituting formulas (1) and (2) into formula (4) simplifies the first position measurement accuracy limit, resulting in a simplified second position measurement accuracy limit. .

[0076]

[0077]

[0078] Where N represents the number of photoelectrons in the optical imaging spot.

[0079] Step S120-3: Superimpose the simplified first position measurement accuracy limit and the simplified second position measurement accuracy limit to obtain the two-dimensional position measurement accuracy limit.

[0080] Specifically, formulas (6) and (7) can be substituted into formula (5) and superimposed to obtain the two-dimensional position measurement accuracy limit.

[0081]

[0082] Step S130: Calculate the condition for the two-dimensional position measurement accuracy limit to satisfy the minimum value, and calculate the analytical estimate of the optimal accuracy limit of the two-dimensional position measurement based on the condition and the two-dimensional position measurement accuracy limit. The condition and the analytical estimate of the optimal accuracy limit of the two-dimensional position measurement are used to guide the centering measurement of the imaging spot.

[0083] In this embodiment, the condition for achieving the minimum value of the two-dimensional position measurement accuracy limit is the condition for achieving the optimal value of the two-dimensional position measurement accuracy limit. Taking advantage of the significant phase gradient of a small-sized PSF in a specific pixel, the accuracy limit of the two-dimensional position measurement of the imaging spot on the image detector is optimized for a typical two-dimensional Gaussian function PSF optical system (small-sized PSF optical system), and an analytical estimate of the optimal accuracy limit of the two-dimensional position measurement and its realization conditions are given.

[0084] In an optional embodiment, the above step S130 "calculating the condition for the two-dimensional position measurement accuracy limit to satisfy the minimum value" may specifically include sub-step S130-1:

[0085] Step S130-1: For a typical PSF of a two-dimensional Gaussian function, the center of the imaging spot is located at the... In the case of the intersection of four pixels within a pixel window, the minimum value of the two-dimensional position measurement accuracy limit is determined to obtain the implementation condition; wherein, the implementation condition includes: The pixel responses of the four pixels within the pixel window are equal, and the pixel response of each pixel is equal to the stated value. One-quarter of the sum of the pixel values ​​of the four pixels within the pixel window.

[0086] Specifically, for a two-dimensional Gaussian function PSF optical system, the condition for achieving the minimum (optimal) limit of two-dimensional position measurement accuracy can be expressed as:

[0087]

[0088] Where K represents the gain of the image detector pixel, and N represents the number of photoelectrons in the optical imaging spot, then It represents the sum of the pixel values ​​of the four pixels. In other words, it represents the sum of the pixel values ​​at the center of the image spot. Located in the The intersection of four pixels within a pixel window (satisfying) When ), the two-dimensional position measurement accuracy limit can be minimized.

[0089] Furthermore, the above step S130, "calculating the analytical estimate of the optimal accuracy limit of the two-dimensional position measurement based on the implementation conditions and the two-dimensional position measurement accuracy limit," may specifically include sub-steps S130-2 and S130-3:

[0090] Step S130-2: Determine the significant gradient of the pixel response of the first pixel. The significant gradient of the pixel response of the first pixel represents the maximum rate of change of the first pixel response caused by a small movement of the imaging spot, and the magnitude of the gradient of the pixel response of the first pixel with respect to the x-direction is the same as that with respect to the y-direction.

[0091] Step S130-3: Substitute the implementation conditions and the significant gradient of the pixel response of the first pixel into the two-dimensional position measurement accuracy limit to obtain an analytical estimate of the optimal accuracy limit of the two-dimensional position measurement. The analytical estimate of the optimal accuracy limit of the two-dimensional position measurement characterizes the theoretical optimal accuracy that the two-dimensional position measurement can achieve.

[0092] In this embodiment of the application, the center of the imaging spot is located at The phase gradient of the first pixel's pixel response is most significant at the intersection of four pixels within a pixel window; thus, the significant gradient of the first pixel's pixel response is obtained. For example... Figure 3 As shown, this illustrates the case where a small-sized PSF achieves the maximum gradient.

[0093] For example, the significant gradient of the pixel response of the first pixel can be expressed as:

[0094]

[0095] Where r represents the radius of the two-dimensional Gaussian function in pixels.

[0096] Finally, by substituting formulas (9) and (10) into the two-dimensional position measurement accuracy limit of formula (8), an analytical estimate of the optimal accuracy limit of two-dimensional position measurement is obtained. For example, the analytical estimate of the optimal accuracy limit of two-dimensional position measurement... It can be represented as:

[0097]

[0098] It is understandable that the analytical estimation of the optimal accuracy limit of two-dimensional position measurement is equivalent to achieving the optimal measurement accuracy by satisfying the measurement conditions of formulas (9) and (10). At this point, the optimal accuracy can be achieved. In actual imaging spot centering measurement, the measurement method can be guided based on the conditions, and the analytical estimation of whether the actual accuracy can reach the optimal accuracy limit of two-dimensional position measurement can be evaluated.

[0099] The technical solution implemented in this application approximates the phase gradient distribution of the PSF in pixel space based on the energy concentration distribution characteristics of the imaging spot in a small-sized PSF optical system. Based on the approximate gradient distribution of the PSF, the two-dimensional position measurement accuracy limit of the imaging spot on the image detector is estimated, quantifying the matching relationship between the PSF gradient distribution and the pixel phase, and guiding the collaborative optimization of the phase configuration of the optical system and the image detector. By calculating the realization condition for the two-dimensional position measurement accuracy limit to satisfy the minimum value, and based on the realization condition, an analytical estimate of the optimal accuracy limit of the two-dimensional position measurement is calculated. This achieves the analytical estimation and optimization of the optimal accuracy limit of the two-dimensional position measurement, filling the theoretical research gap in improving the two-dimensional positioning accuracy limit of the imaging spot through pixel phase optimization. Based on the realization condition and the analytical estimate of the optimal accuracy limit of the two-dimensional position measurement, the centering measurement of the imaging spot is guided, utilizing the potential for optimized positioning performance inherent in information theory, making the actual measurement accuracy approach the theoretical optimum, and providing theoretical support and practical path for improving the accuracy of optical imaging measurement applications.

[0100] This application embodiment also provides a device for optimizing the accuracy limit of two-dimensional position measurement of optical imaging spots, referring to... Figure 4 As shown, Figure 4 This is a schematic diagram of a device for optimizing the accuracy of two-dimensional position measurement of optical imaging spots according to an embodiment of this application. The device includes:

[0101] The approximation module 410 is used to approximate the phase gradient distribution of PSF in pixel space based on the energy concentration distribution characteristics of the imaging spot of the small-size point spread function PSF optical system, and obtain the gradient distribution approximation result of PSF. The gradient distribution approximation result of PSF represents the quantitative result of the matching relationship between PSF gradient distribution and pixel phase.

[0102] The estimation module 420 is used to estimate the two-dimensional position measurement accuracy limit of the imaging spot of the small-sized PSF optical system on the image detector based on the gradient distribution approximation result of the PSF;

[0103] The calculation module 430 is used to calculate the conditions for achieving the minimum value of the two-dimensional position measurement accuracy limit, and to calculate the analytical estimate of the optimal accuracy limit of the two-dimensional position measurement based on the conditions and the two-dimensional position measurement accuracy limit. The conditions and the analytical estimate of the optimal accuracy limit of the two-dimensional position measurement are used to guide the centering measurement of the imaging spot.

[0104] In an optional embodiment, the gradient distribution approximation result of the PSF includes an approximation of the gradient distribution of the PSF in the x-direction and an approximation of the gradient distribution in the y-direction; the approximation module includes:

[0105] The energy distribution approximation module is used to approximate the energy of the imaging spot of the small-sized PSF optical system as a two-dimensional energy distribution concentrated in... The function within the pixel window obtains the... The pixel response of four pixels within a pixel window;

[0106] The construction module is configured to construct a first gradient distribution approximation of the PSF in the x-direction and a second gradient distribution approximation of the PSF in the y-direction based on the pixel responses of the four pixels; wherein the first gradient distribution approximation characterizes the pixel responses of the four pixels. Within a pixel window, the gradients of the pixel responses of two adjacent pixels along the x-axis are opposite, and the second gradient distribution approximately characterizes the... The gradients of the pixel responses of two adjacent pixels in the y-direction within a pixel window are opposite.

[0107] In one optional embodiment, the estimation module includes:

[0108] The accuracy limit module is used to calculate the accuracy limit of the first position measurement of the imaging spot in the x-direction and the accuracy limit of the second position measurement of the imaging spot in the y-direction, based on the Cramer-Rao lower bound theory.

[0109] The simplification module is used to simplify the first position measurement accuracy limit and the second position measurement accuracy limit according to the gradient distribution approximation result of PSF, respectively, to obtain the simplified first position measurement accuracy limit and the simplified second position measurement accuracy limit;

[0110] The superposition module is used to superimpose the simplified first position measurement accuracy limit and the simplified second position measurement accuracy limit to obtain the two-dimensional position measurement accuracy limit.

[0111] In one optional embodiment, the computing module includes:

[0112] The condition determination module is used to determine the location of the imaging spot center within the specified range. In the case of the intersection of four pixels within a pixel window, the minimum value of the two-dimensional position measurement accuracy limit is determined to obtain the implementation condition; wherein, the implementation condition includes: The pixel responses of the four pixels within the pixel window are equal, and the pixel response of each pixel is equal to the stated value. One-quarter of the sum of the pixel values ​​of the four pixels within the pixel window.

[0113] In one optional embodiment, the computing module includes:

[0114] The significant gradient determination module is used to determine the significant gradient of the pixel response of the first pixel. The significant gradient of the pixel response of the first pixel represents the maximum rate of change of the first pixel response caused by a small movement of the imaging spot, and the magnitude of the pixel response of the first pixel with respect to the gradient in the x direction and the gradient with respect to the y direction are the same.

[0115] The calculation module is used to substitute the implementation conditions and the significant gradient of the pixel response of the first pixel into the two-dimensional position measurement accuracy limit to obtain an analytical estimate of the optimal accuracy limit of the two-dimensional position measurement. The analytical estimate of the optimal accuracy limit of the two-dimensional position measurement characterizes the theoretical optimal accuracy that the two-dimensional position measurement can achieve.

[0116] This application also provides an electronic device, see embodiments thereof. Figure 5 , Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 5 As shown, the electronic device 500 includes a memory 510 and a processor 520. The memory 510 and the processor 520 are connected via a bus for communication. The memory 510 stores a computer program that can run on the processor 520 to implement the steps of the optical imaging spot two-dimensional position measurement accuracy limit optimization method described in the embodiments of this application.

[0117] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the optical imaging spot two-dimensional position measurement accuracy limit optimization method described in this application embodiment.

[0118] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the optical imaging spot two-dimensional position measurement accuracy limit optimization method described in this application embodiment.

[0119] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0120] This application describes embodiments of methods and apparatus according to flowchart illustrations and / or block diagrams. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations 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, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0121] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0122] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0123] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0124] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0125] The above provides a detailed description of the method, apparatus, and device for optimizing the accuracy limit of two-dimensional position measurement of optical imaging spots provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for optimizing the accuracy limits of two-dimensional position measurement of optical imaging spots, characterized in that, The method includes: Based on the energy concentration distribution characteristics of the imaging spot of a small-sized PSF optical system, the phase gradient distribution of the PSF in the pixel space is approximated to obtain the approximate gradient distribution result of the PSF. The approximate gradient distribution result of the PSF represents the quantitative result of the matching relationship between the PSF gradient distribution and the pixel phase. Based on the approximate gradient distribution of the PSF, the limit of the two-dimensional position measurement accuracy of the imaging spot of the small-sized PSF optical system on the image detector is estimated. The conditions for achieving the minimum value of the two-dimensional position measurement accuracy limit are calculated, and based on the conditions and the two-dimensional position measurement accuracy limit, an analytical estimate of the optimal accuracy limit of the two-dimensional position measurement is calculated. The conditions and the analytical estimate of the optimal accuracy limit of the two-dimensional position measurement are used to guide the centering measurement of the imaging spot. The gradient distribution approximation of the PSF includes the gradient distribution approximation of the PSF in the x-direction and the gradient distribution approximation in the y-direction. Based on the energy concentration distribution characteristics of the imaging speckle of the small-sized PSF optical system, the phase gradient distribution of the PSF in the pixel space is approximated to obtain the gradient distribution approximation result of the PSF, including: approximating the energy of the imaging speckle of the small-sized PSF optical system as a two-dimensional energy distribution concentrated in... The function within the pixel window obtains the... The pixel responses of four pixels within a pixel window; based on the pixel responses of the four pixels, a first gradient distribution approximation of the PSF in the x-direction is constructed, and a second gradient distribution approximation of the PSF in the y-direction is constructed; wherein, the first gradient distribution approximation characterizes the pixel responses of the four pixels within the pixel window; Within a pixel window, the gradients of the pixel responses of two adjacent pixels along the x-axis are opposite, and the second gradient distribution approximately characterizes the... The gradients of the pixel responses of two adjacent pixels in the y-direction within a pixel window are opposite. Based on the approximate gradient distribution of the PSF, the two-dimensional position measurement accuracy limit of the imaging spot of the small-sized PSF optical system on the image detector is estimated, including: calculating the first position measurement accuracy limit of the imaging spot in the x-direction and the second position measurement accuracy limit of the imaging spot in the y-direction according to the Cramer-Rao lower bound theory; simplifying the first position measurement accuracy limit and the second position measurement accuracy limit according to the approximate gradient distribution of the PSF to obtain the simplified first position measurement accuracy limit and the simplified second position measurement accuracy limit; and superimposing the simplified first position measurement accuracy limit and the simplified second position measurement accuracy limit to obtain the two-dimensional position measurement accuracy limit.

2. The method according to claim 1, characterized in that, The The four pixels within the pixel window include a first pixel, a second pixel, a third pixel, and a fourth pixel. The first pixel and the second pixel are adjacent to each other horizontally in the x-direction, the third pixel and the fourth pixel are adjacent to each other horizontally in the x-direction, the first pixel and the third pixel are adjacent to each other vertically in the y-direction, and the second pixel and the fourth pixel are adjacent to each other vertically in the y-direction. The gradient distribution of PSF in the x-direction is approximately as follows: the gradient of the pixel response of the first pixel in the x-direction is opposite to that of the pixel response of the second pixel in the x-direction; the ratio of the gradient of the pixel response of the first pixel in the x-direction to that of the pixel response of the third pixel in the x-direction is the same as the ratio of the pixel response of the first pixel to that of the third pixel; and the gradient of the pixel response of the third pixel in the x-direction is opposite to that of the pixel response of the fourth pixel in the x-direction. The gradient distribution of PSF in the y-direction is approximate, including: the ratio of the gradient of the pixel response of the first pixel in the y-direction to the gradient of the pixel response of the second pixel in the y-direction is the same as the ratio of the pixel response of the first pixel to the pixel response of the second pixel; the gradient of the pixel response of the first pixel in the y-direction is opposite to the gradient of the pixel response of the third pixel in the y-direction; and the ratio of the gradient of the pixel response of the third pixel in the y-direction to the gradient of the pixel response of the fourth pixel in the y-direction is the same as the ratio of the pixel response of the third pixel to the pixel response of the fourth pixel.

3. The method according to claim 1, characterized in that, The conditions for achieving the minimum value of the two-dimensional position measurement accuracy limit are calculated, including: For a typical PSF of a two-dimensional Gaussian function, the center of the image spot is located at the... In the case of the intersection of four pixels within a pixel window, the minimum value is determined to satisfy the limit of the two-dimensional position measurement accuracy, thus obtaining the realization condition; The implementation conditions include: The pixel responses of the four pixels within the pixel window are equal, and the pixel response of each pixel is equal to the stated value. One-quarter of the sum of the pixel values ​​of the four pixels within the pixel window.

4. The method according to claim 3, characterized in that, Based on the aforementioned implementation conditions and the two-dimensional position measurement accuracy limit, an analytical estimate of the optimal accuracy limit for two-dimensional position measurement is calculated, including: The significant gradient of the pixel response of the first pixel is determined. The significant gradient of the pixel response of the first pixel represents the maximum rate of change of the first pixel response caused by a small movement of the imaging spot. The magnitude of the pixel response of the first pixel with respect to the gradient in the x direction is the same as that with respect to the gradient in the y direction. Substituting the implementation conditions and the significant gradient of the pixel response of the first pixel into the two-dimensional position measurement accuracy limit, an analytical estimate of the optimal accuracy limit of the two-dimensional position measurement is obtained. The analytical estimate of the optimal accuracy limit of the two-dimensional position measurement characterizes the theoretical optimal accuracy that the two-dimensional position measurement can achieve.

5. A device for optimizing the accuracy of two-dimensional position measurement of optical imaging spots, characterized in that, The device includes: An approximation module is used to approximate the phase gradient distribution of the PSF in the pixel space based on the energy concentration distribution characteristics of the imaging spot of a small-sized PSF optical system, and obtain an approximate gradient distribution result of the PSF. The approximate gradient distribution result of the PSF represents the quantitative result of the matching relationship between the PSF gradient distribution and the pixel phase. An estimation module is used to estimate the two-dimensional position measurement accuracy limit of the imaging spot of the small-sized PSF optical system on the image detector based on the approximate gradient distribution result of the PSF; The calculation module is used to calculate the conditions for achieving the minimum value of the two-dimensional position measurement accuracy limit, and to calculate the analytical estimate of the optimal accuracy limit of the two-dimensional position measurement based on the conditions and the two-dimensional position measurement accuracy limit. The conditions and the analytical estimate of the optimal accuracy limit of the two-dimensional position measurement are used to guide the centering measurement of the imaging spot. The gradient distribution approximation of the PSF includes the gradient distribution approximation of the PSF in the x-direction and the gradient distribution approximation in the y-direction. Based on the energy concentration distribution characteristics of the imaging speckle of the small-sized PSF optical system, the phase gradient distribution of the PSF in the pixel space is approximated to obtain the gradient distribution approximation result of the PSF, including: approximating the energy of the imaging speckle of the small-sized PSF optical system as a two-dimensional energy distribution concentrated in... The function within the pixel window obtains the... The pixel responses of four pixels within a pixel window; based on the pixel responses of the four pixels, a first gradient distribution approximation of the PSF in the x-direction is constructed, and a second gradient distribution approximation of the PSF in the y-direction is constructed; wherein, the first gradient distribution approximation characterizes the pixel responses of the four pixels within the pixel window; Within a pixel window, the gradients of the pixel responses of two adjacent pixels along the x-axis are opposite, and the second gradient distribution approximately characterizes the... The gradients of the pixel responses of two adjacent pixels in the y-direction within a pixel window are opposite. Based on the approximate gradient distribution of the PSF, the two-dimensional position measurement accuracy limit of the imaging spot of the small-sized PSF optical system on the image detector is estimated, including: calculating the first position measurement accuracy limit of the imaging spot in the x-direction and the second position measurement accuracy limit of the imaging spot in the y-direction according to the Cramer-Rao lower bound theory; simplifying the first position measurement accuracy limit and the second position measurement accuracy limit according to the approximate gradient distribution of the PSF to obtain the simplified first position measurement accuracy limit and the simplified second position measurement accuracy limit; and superimposing the simplified first position measurement accuracy limit and the simplified second position measurement accuracy limit to obtain the two-dimensional position measurement accuracy limit.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the optical imaging spot two-dimensional position measurement accuracy limit optimization method according to any one of claims 1-4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the method for optimizing the accuracy limit of two-dimensional position measurement of optical imaging spots as described in any one of claims 1-4.

8. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method for optimizing the accuracy limit of two-dimensional position measurement of optical imaging spots as described in any one of claims 1-4.

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