Optical payload centroid positioning method reconstructing point target effective point spread function

Abstract

The application discloses an optical load centroid positioning method for reconstructing an effective point spread function of a point target, which is used for establishing an effective point spread function reconstruction model by referring to a star point image and a pixel response function of a to-be-matched star point image position, performing a discrete Fourier transform on the reference star point image, and obtaining a Fourier transform of an average effective point spread function of a load detector pixel plane. An initial centroid offset estimation value between the reference star point image and the to-be-matched star point image is calculated by using a traditional centroid solution algorithm, and then the reference star point image is discretized and moved from a decimal point in the frequency domain according to the initial centroid offset distance. A correlation coefficient between the moved new reference star point image and the to-be-matched star point image is calculated, the centroid offset distance with the maximum correlation coefficient of each digit after the decimal point of the initial offset distance is taken as an initial value for the next digit search, the above process is repeated for iteration until the correlation coefficient no longer changes, and a star point centroid positioning precision better than a millipixel is obtained.

Description

Technical Field

[0001] This invention relates to the field of aerospace applications of optical payloads, and in particular to a method for locating the centroid of an optical payload by reconstructing the effective point spread function of a point target. Background Technology

[0002] Ultra-high precision centroid positioning and angular distance measurement are widely used in fundamental fields such as deep space astronomical navigation, optical aberration autonomous navigation, high-precision space astrometry, high-precision space geodetic mapping, and next-generation high-precision star sensors.

[0003] To improve the accuracy of star centroid positioning, both domestic and international efforts mainly focus on improving star centroid algorithms to achieve higher accuracy in inter-satellite centroid offset estimation, but this only reaches 10. -2 The accuracy is around 1 pixel. Because only the algorithm is improved without considering the shape of the optical system's point spread function or the physical characteristics of the detector itself, truly high-precision spatial measurement and positioning cannot be achieved.

[0004] Current centroid algorithms include Gaussian fitting, median method, derivative method, and adjustable threshold correction moment method. These algorithms only focus on image data processing, limiting the improvement of spatial positioning and angle measurement accuracy, and failing to meet the requirements of sub-milliarsecond or even microarciarsecond space object measurement. Therefore, a new centroid positioning method based on the optical system's point spread function and the detector itself is needed. Summary of the Invention

[0005] This invention aims to at least partially solve one of the technical problems in related technologies. Therefore, the objective of this invention is to provide an optical payload centroid positioning method for reconstructing the effective point spread function, which can achieve star centroid positioning accuracy down to sub-millipixel and inter-star angular distance accuracy down to sub-milliarsecond.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0007] A method for locating the centroid of an optical payload by reconstructing the effective point spread function of a point target includes:

[0008] Step S1: First, based on the pixel response function of the reference star image position, establish an effective point spread function reconstruction model, and perform a discretized Fourier transform on the reference star image to obtain the Fourier transform of the average effective point spread function of the pixel plane of the payload detector.

[0009] Step S2: Next, the initial centroid offset estimate between the reference star image and the star image to be matched is calculated using the traditional centroid solving algorithm;

[0010] Step S3: Then, using the initial centroid offset estimate of the star point, the reference star point image is discretized in the frequency domain and moved digit by digit after the decimal point according to the initial centroid offset distance;

[0011] Step S4: Calculate the correlation coefficient between the new reference star image after the move and the star image to be matched. Use the centroid offset distance with the largest correlation coefficient for each decimal place of the initial offset distance as the initial value for the next search.

[0012] Step S5: Repeat the above process and iterate continuously until the correlation coefficient no longer changes and approaches 1 infinitely, thus obtaining a star centroid positioning accuracy better than that of a millipixel.

[0013] Optionally, in establishing the effective point spread function reconstruction model, the effective point spread function of pixel light intensity is assumed to be the convolution of the point spread function and the pixel response function, and the average effective point spread function is defined as:

[0014]

[0015] Among them, f ps (x,y) is the point spread function. The average pixel response function is given by the Fourier transform of the average effective point spread function, which takes the following form:

[0016]

[0017] Among them, k x ,k y These represent the spatial frequencies of the stripes along the x and y axes, respectively. Based on the detector pixel size *a* and the star image window size *N*, the pixel intensity model is discretized, yielding the pixel effective point spread function reconstruction model as follows:

[0018]

[0019] in Let A be the pixel response function of the star point image to be matched. jl The average effective point spread function is defined as follows:

[0020]

[0021] Based on the model and the pixel response function of the pixel location of the reference star image, a Fourier transform is performed on the pixel value of the reference star image to obtain parameter A. jl .

[0022] Optionally, during the discretization of the reference star image in the frequency domain, the pixel response function term in the effective point spread function reconstruction model is subjected to a Taylor expansion, which can be expressed as:

[0023]

[0024] Where, q mnThe flat-field response nonuniformity of pixel (m,n), (Δx) mn ,Δy mn ) represents the deviation between the actual center position and the ideal center position of pixel (m,n).

[0025] Discretizing the reference star image and shifting it in the frequency domain yields a discrete star image offset by a certain position, which can be represented as:

[0026]

[0027] in, The pixel response function after translation. The reference star image is discretized and then shifted (Δx). c ,Δy c The output value of pixel (m,n) on the discrete star point image obtained by distance.

[0028] Optionally, in step S3, the ideal coordinates and measurement coordinates are calibrated using the film constant method, and the calibrated ideal coordinates are projected and converted into celestial coordinates.

[0029] Optionally, when calculating the correlation coefficient between the reference star image and the star image to be matched, a new reference star image with a certain positional offset is generated one decimal place after the initial star centroid offset value. The correlation coefficient between the new reference star image and the star image to be matched is calculated. The offset value with the largest correlation coefficient is taken as the initial offset distance to the second decimal place. The offset is increased by 0.01 step by step, and this is repeated 10 times. The offset distance when the correlation coefficient is the largest is calculated. The above process is repeated, and the decimal point continues to move one place to the next until the calculated correlation coefficient no longer changes, thus obtaining a star centroid positioning accuracy better than millipixels.

[0030] Optionally, the correlation coefficient between the new reference star image after the movement and the star image to be matched is calculated:

[0031]

[0032] Where S represents the reference star image, S corr Indicates the star point image to be matched, g p , and g pcorr , These represent the grayscale values ​​of the pixels in the reference star image and the grayscale values ​​in the star image to be matched, respectively.

[0033] This invention mainly proposes an optical payload centroid positioning method for reconstructing the effective point spread function, which provides technical support for applications requiring ultra-high precision centroid positioning and angular distance measurement.

[0034] This invention has at least one of the following technical effects:

[0035] (1) This invention proposes a method for reconstructing the effective point spread function of star point images, which can get rid of the influence of detector manufacturing process, pixel spatial arrangement, physical size change, ambient temperature and other factors on the centroid positioning accuracy of star points, and the centroid positioning accuracy reaches sub-millipixel.

[0036] (2) This invention proposes a method of shifting the reference star image in the frequency domain and then using the correlation coefficient to continuously update iteratively, which can improve the positioning accuracy and the efficiency of star centroid positioning calculation.

[0037] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0038] Figure 1 This is a schematic flowchart of an optical payload centroid localization method for reconstructing the effective point spread function of a point target according to the present invention. Detailed Implementation

[0039] The following describes this embodiment in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0040] This invention provides a method for locating the centroid of an optical payload by reconstructing the effective point spread function of a point target. This method enables the optical payload telescope to achieve star point location and angular distance measurement accuracy better than millipixels. The method flow is as follows: Figure 1 As shown in the flowchart, the following steps 1 to 5 are described in detail.

[0041] Step 1: Establish an effective point spread function reconstruction model using the pixel response functions of the reference star image and the star image to be matched.

[0042] First, the light intensity distribution formula is converted into a point spread function, which gives the formula:

[0043] g mn (x c ,y c )=∫∫dxdyf ps (x,y)Q(x+x c -ma,y+y c -na)

[0044] =f eps (ma-x c ,na-yc )

[0045] In the formula, (m,n) are the row and column coordinates of the pixel, (x c ,y c Let ) be the centroid coordinates of the point spread function, Q(x,y) be the pixel response function, and g be the centroid coordinates. mn (x c ,y c The center of the point spread function is located at (x). c ,y c The output value of pixel (m,n) at position f, where a is the pixel size and f is the output value of pixel (m,n). ps (x,y) is the point spread function, f eps (x,y) is the effective point spread function, which is the convolution of the point spread function and the pixel response function. Meanwhile, the origin of Q(x,y) is at the center of the pixel, while f... ps The origin of the coordinate system (x, y) is at the center of the point spread function.

[0046] Furthermore, let the effective point spread function of pixel light intensity be the convolution of the point spread function and the pixel response function, and define the average effective point spread function as:

[0047]

[0048] in The average pixel response function is given by the Fourier transform of the average effective point spread function, which takes the following form:

[0049]

[0050] Where k x ,k y Let be the spatial frequencies of the stripes on the x and y axes, respectively. Furthermore, based on the detector pixel size *a* and the star image window size *N*, the pixel intensity model is discretized, yielding the pixel effective point spread function reconstruction model as follows:

[0051]

[0052] in Let A be the pixel response function of the star point image to be matched. jl The average effective point spread function is defined as follows:

[0053]

[0054] Based on the model and the pixel response function of the pixel location of the reference star image, a Fourier transform is performed on the pixel value of the reference star image to obtain parameter A. jl .

[0055] Step 2: Calculate the initial centroid offset estimate between the reference star image and the star image to be matched. Using the star image centroid calculation method, it can be expressed as:

[0056]

[0057] Where x mn ,y mn g represents the pixel plane coordinates. mn This represents the pixel grayscale value. By using a star-point centroid method, an initial centroid offset can be obtained, achieving sub-pixel accuracy.

[0058] Step 3: Using the initial centroid offset estimate, discretize the reference star image in the frequency domain and shift it digit by digit according to the initial centroid offset distance. Perform a Taylor expansion on the pixel response function term in the effective point spread function reconstruction model, which can be expressed as:

[0059]

[0060] Where q mn The flat-field response nonuniformity of pixel (m,n), (Δx) mn ,Δy mn The value represents the deviation between the actual center position and the ideal center position of a pixel.

[0061] Discretizing the reference star image and shifting it in the frequency domain yields a discrete star image offset by a certain position, which can be represented as:

[0062]

[0063] in, The pixel response function after translation. The reference star image is discretized and then shifted (Δx). c ,Δy c The output value of pixel (m,n) on the discrete star point image obtained by distance.

[0064] Step 4: Calculate the correlation coefficient between the new reference star image after the movement and the star image to be matched:

[0065]

[0066] Where S represents the reference star image, S corr Indicates the star point image to be matched, g p , and g pcorr , These represent the grayscale values ​​of the pixels in the reference star image and the grayscale values ​​in the star image to be matched, respectively.

[0067] Step 5: First, increment the initial star point centroid offset value by one decimal place, stepping by 0.1, and then increase it sequentially to generate a new reference star point image with a certain positional offset. Calculate the correlation coefficient between the new reference star point image after the movement and the star point image to be matched. Take the offset value with the largest correlation coefficient as the initial offset distance to the second decimal place, and continue to step and increase it sequentially. Calculate the offset distance when the correlation coefficient is the largest. Repeat the above process, moving the decimal point one place to the next, until the calculated correlation coefficient no longer changes, to obtain a star point centroid positioning accuracy better than millipixels.

[0068] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A method for locating the centroid of an optical payload by reconstructing the effective point spread function of a point target, characterized in that, include: Step S1: Based on the pixel response function of the reference star image position, establish an effective point spread function reconstruction model, perform discretized Fourier transform on the reference star image, and obtain the Fourier transform of the average effective point spread function of the pixel plane of the payload detector. Step S2: Calculate the initial centroid offset estimate between the reference star image and the star image to be matched using the traditional centroid solving algorithm; Step S3: Using the initial centroid offset estimate of the star point, discretize the reference star point image in the frequency domain and move it digit by digit after the decimal point according to the initial centroid offset distance; Step S4: Calculate the correlation coefficient between the new reference star image after the movement and the star image to be matched: in, Indicates a reference star image. This represents the star point image to be matched. and These represent the grayscale values ​​of the pixels in the reference star image and the grayscale values ​​in the star image to be matched, respectively. The centroid offset distance with the largest correlation coefficient for each decimal place of the initial offset distance is used as the initial value for the next search. Step S5: First, increment the initial star point centroid offset value by one decimal place, step by 0.1, and increase it 10 times to generate a new reference star point image after the movement. Calculate the correlation coefficient between the new reference star point image and the star point image to be matched. Take the offset value with the largest correlation coefficient as the initial offset distance to the second decimal place, and continue to increment by 0.01, increasing it 10 times. Calculate the offset distance when the correlation coefficient is the largest. Repeat the above process, iterating continuously, with the decimal point moving one place to the next until the calculated correlation coefficient no longer changes and infinitely approaches 1, thus obtaining a star point centroid positioning accuracy better than millipixels.

Images