Wide-spectrum interferometric star sensor based on eight-wedge beam-splitting assembly and centroid positioning method thereof

Abstract

A broadband interferometric star sensor based on an eight-wedge beam splitter and its centroid positioning method belong to the field of spacecraft attitude measurement technology. To address the problem of decreased single-star measurement accuracy in interferometric star sensors, this invention includes an interferometer assembly, an eight-wedge beam splitter assembly, a focusing assembly, and a detector arranged sequentially. The interferometer assembly consists of two gratings, G1 and G2, spaced a certain distance apart, used to modulate the starlight phase and generate interference fringes. The eight-wedge beam splitter assembly is an array of eight optical wedges used to divide the interference fringes into eight fringe beams. The focusing assembly focuses the fringe beams onto different positions on the detector. The detector is located at the focal plane of the focusing assembly and receives the starlight image. This invention, by employing an eight-wedge beam splitter structure, significantly improves the single-star measurement accuracy of the system in a broadband operating environment.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft attitude measurement technology, specifically relating to a broadband interferometric star sensor based on an eight-wedge beam splitter and its centroid positioning method. Background Technology

[0002] Star sensors are instruments that acquire images of the starry sky and output their attitude in an inertial coordinate system. They possess advantages such as high precision, all-sky autonomous navigation, and no cumulative error, and are currently widely used in platforms such as satellites, missiles, and ships. With the continuous upgrading of various missions, the requirements for the attitude measurement accuracy of star sensors on various platforms are also increasing. Constrained by payload mass and power consumption, the attitude measurement accuracy of traditional star sensors is difficult to further improve. Therefore, improving the measurement accuracy of single stars while maintaining the observation range of the star sensor has become a research hotspot in recent years.

[0003] The computational interferometry method offers a new approach to breaking through the single-star measurement accuracy limits of traditional star sensors. Interferometric star sensors introduce an interferometer component at the front end of the traditional star sensor to modulate the starlight phase, coupling the incident angle information into the image point energy distribution. High-precision starlight incident angles can be calculated through the energy relationships between image points. The effective utilization of starlight phase information by interferometric star sensors enables them to achieve a breakthrough in single-star measurement accuracy by orders of magnitude compared to traditional star sensors with the same field of view.

[0004] Based on the principle of computational interferometry, the Changchun Institute of Optics, Fine Mechanics and Physics proposed an interferometric star sensor device based on a diffraction grating. It mainly consists of two Ronchi gratings, four optical wedges, an imaging lens, and an array detector. Theoretical analysis shows that this structure can significantly improve the accuracy of single-star measurements. However, this design has the following technical limitations: the system only utilizes the ±1st order diffraction light from the grating. Although the Ronchi grating can effectively suppress non-zero even-order diffraction, its suppression effect on zero-order diffraction is insufficient under broadband starlight incident conditions. This key design flaw will lead to a significant decrease in single-star measurement accuracy due to the zero-order diffraction effect when the system operates over a broadband range, ultimately limiting the actual performance of the star sensor. Summary of the Invention

[0005] The problem to be solved by this invention is to improve the single-star measurement accuracy of interferometric star sensors caused by zero-order diffraction of gratings under broadband incident conditions. A broadband interferometric star sensor based on an eight-wedge beam splitter and its centroid positioning method are proposed.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A broadband interferometric star sensor based on an eight-wedge beam splitter includes an interferometer, an eight-wedge beam splitter, a focusing component, and a detector arranged in sequence.

[0008] The interference component consists of two gratings G1 and G2 spaced a certain distance apart, used to modulate the starlight phase and thus generate interference fringes;

[0009] The eight-wedge beam splitter is an array of eight optical wedges used to divide the interference fringes into eight parts of fringe light.

[0010] The focusing component is used to focus the striped light onto different positions of the detector;

[0011] The detector is located at the focal plane of the focusing assembly and is used to capture the image of starlight.

[0012] Furthermore, the spacing between gratings G1 and G2 in the interference assembly is z. t The gratings G1 and G2 have the same period, p. The z-axis is the optical axis of the optical system. The scribe lines of both gratings are perpendicular to the optical axis, and the angle between the scribe lines and the y-axis is ɛ. , where b is the width of a single optical wedge, and the scribe line direction is symmetrical about the y-axis.

[0013] Furthermore, the eight optical wedges of the eight-wedge beam splitter are arranged along the y-axis to apply different deflection directions to the eight parts of starlight. The size of each of the eight optical wedges is a×b, satisfying a=8b, where a and b represent the length of the optical wedge along the x-direction and the length of the optical wedge along the y-direction, respectively. The rear surface of the eight-wedge beam splitter is set as the entrance pupil of the broadband interferometric star sensor based on the eight-wedge beam splitter.

[0014] A method for centroid localization of a broadband interferometric star sensor based on an eight-wedge beam splitter, which is implemented using the aforementioned broadband interferometric star sensor based on an eight-wedge beam splitter, includes the following steps:

[0015] S1. Construct a model relating the starlight incident angle and image point energy of a broadband interferometric star sensor based on an eight-wedge beam splitter;

[0016] S2. Based on the energy distribution of image points obtained by the detector, the coordinates of the image points on the image plane are extracted using the gray-level weighted method, and the gray level of each image point is calculated;

[0017] S3. For the grayscale values ​​of the image points obtained in step S2, determine the image point with the highest grayscale value and extract the centroid coordinates of the image point with the highest grayscale value;

[0018] S4. Based on the centroid coordinates of the image point with the largest gray level obtained in step S4, the geometric optics imaging principle is applied to estimate the starlight incident angle and estimate the starlight phase integer ambiguity.

[0019] S5. Based on the pixel grayscale obtained in step S2, calculate the principal value of the starlight phase, and add the principal value of the phase to the integer phase ambiguity obtained in step S4 to obtain a high-precision starlight phase.

[0020] S6. Calculate the high-precision starlight incident angle from the high-precision starlight phase obtained in step S5 to obtain the high-precision centroid coordinates of the image point.

[0021] Furthermore, the specific implementation method of step S1 includes the following steps:

[0022] S1.1. Calculation of the angular spectrum of starlight after passing through the interferometer and spectrometer components based on the angular spectrum propagation theory. The calculation formula is:

[0023]

[0024] in, This indicates the Fourier transform operation; This represents the complex amplitude of starlight at the front end of the star sensor; This represents the complex amplitude transmittance of grating G1; Let be the transfer function for starlight transmission from the back surface of G1 to G2; This represents the complex amplitude transmittance of grating G2; This indicates the complex amplitude transmittance of the eight-wedge beam splitter; Indicates the convolution operation;

[0025] The formula for calculating the complex amplitude of starlight at the front end of the star sensor is:

[0026]

[0027] in, λ represents the starlight amplitude; j represents the imaginary unit; λ represents the starlight wavelength; α and β represent the complementary angles of the starlight and the x-axis and y-axis of the star sensor, respectively; x and y represent the coordinates of the starlight at the front of the star sensor, respectively.

[0028] The formulas for calculating the complex amplitude transmittance of gratings G1 and G2 are as follows:

[0029]

[0030]

[0031] in, λ is the m-th order diffraction coefficient of grating G1 at wavelength λ; The first grating G2 at wavelength λ Diffraction coefficients;

[0032] The expression for the transfer function of starlight propagating from the back surface of G1 to G2 is:

[0033]

[0034] Among them, f x f represents the spatial frequency of starlight in the x-direction. y This represents the spatial frequency of starlight in the y-direction;

[0035] The expression for the complex amplitude transmittance of the eight-wedge beam splitter is:

[0036]

[0037] in, , Let a and b represent the deflection angles of starlight in the x-direction and y-direction respectively after passing through the nth optical wedge; rect represents a rectangular function, and the relationship between a and b is as shown in the equation. As shown:

[0038]

[0039] The relationship between the light wedge angles is as follows: As shown:

[0040] ;

[0041] S1.2. Combining the formula from step S1.1, we obtain the equation. The expansion formula is as follows:

[0042]

[0043] S1.3. An analysis is conducted on the zero-order diffraction image point generated by starlight passing through an interferometric star sensor. Based on Parseval's theorem, the energy of the zero-order image point generated after starlight passes through the interferometer, the nth optical wedge, and the focusing assembly is:

[0044]

[0045] in, The spectral range of stars;

[0046] The positions of the starlight in the x and y directions at the zero-order image point generated by the detector after passing through the interferometer, the nth optical wedge, and the focusing assembly are:

[0047]

[0048] Where f represents the focal length of the focusing component;

[0049] S1.4. To facilitate the analysis of the zero-order image point energy, intermediate variables are constructed. , , They are respectively:

[0050]

[0051]

[0052]

[0053] in, When m is 1 The value, When m is -1 The value;

[0054] Then we have:

[0055]

[0056] At this point, even if the zeroth-order diffraction of the grating is not zero, equation (16) still holds strictly, and the expression is:

[0057]

[0058] Based on the principle of geometric optics imaging:

[0059]

[0060] At this point, the image point passing through the nth light wedge coincides with the image point passing through the (n+4)th light wedge, thus establishing the relationship between the starlight incident angle and the image point energy.

[0061] Furthermore, the specific implementation method of step S2 includes the following steps:

[0062] S2.1. First, estimate the background noise threshold. The calculation formula is as follows:

[0063]

[0064] Where μ is the mean gray value of the background, and σ is the standard deviation of the gray value of the background;

[0065] Threshold segmentation of the star map;

[0066] S2.2. Perform connected component partitioning on image points based on the scanning method;

[0067] S2.3. Based on the gray-level weighted method, the centroids of the image points are extracted, and the centroid coordinates of the four image points are (x1, y1), (x2, y2), (x3, y3), and (x4, y4), respectively. The gray levels of the four image points are g1, g2, g3, and g4, respectively.

[0068] Furthermore, the specific implementation method of step S3 is to sort the four image points extracted in step S2 by gray level, find the image point with the highest gray level, and its centroid coordinates are (x max y max ).

[0069] Furthermore, the specific implementation method of step S4 is to use the (x) obtained in step S3. max y max Substitution Estimate the angle of starlight incidence , , as shown As shown:

[0070]

[0071] in, , These represent the estimated values ​​of the complementary angles between the starlight and the star sensor along the x-axis and y-axis, respectively.

[0072] Substitute the estimated starlight incident angle into the equation with formula In this process, a rough phase value is obtained. And for the integer ambiguity of the phase An estimate is made, and the specific calculation method is as follows: As shown:

[0073]

[0074] Here, round means rounding to the nearest integer.

[0075] Furthermore, the specific implementation method of step S5 is to substitute the grayscale values ​​of the four pixels extracted in step S2 into the formula. , that is to say , , , Solving the principal values ​​of starlight phase The final starlight phase is obtained by adding the integer ambiguity of the starlight phase to the principal value of the phase. .

[0076] Furthermore, the specific implementation method of step S6 is a simultaneous equation. and To calculate the high-precision starlight incidence angle α, as shown in the equation. As shown,

[0077]

[0078] Then, based on the principle of geometric imaging, high-precision centroid coordinates of the image point are obtained.

[0079] The beneficial effects of this invention are:

[0080] The broadband interferometric star sensor based on an eight-wedge beam splitter, as described in this invention, suppresses the influence of grating zero-order diffraction on star measurement accuracy by employing an eight-wedge beam splitter structure. This significantly improves the single-star measurement accuracy of the system in a broadband operating environment. This achievement will lay an important theoretical foundation for the system design, performance evaluation, and engineering application of next-generation high-precision star sensors. Furthermore, it can provide reliable technical support for key aspects such as precise landing and orbit maintenance in deep space exploration missions, ultimately effectively improving the level of my country's astronomical navigation technology. Attached Figure Description

[0081] Figure 1 This is a schematic diagram of the structure of a broadband interferometric star sensor based on an eight-wedge beam splitter according to the present invention;

[0082] Figure 2 This is a schematic diagram of the arrangement of the two gratings in the optical system according to the present invention;

[0083] Figure 3 This is a schematic diagram of the three-dimensional structure and thickness distribution along the optical axis of the beam-splitting component described in this invention.

[0084] Figure 4 This is a flowchart of a method for locating the centroid of a broadband interferometric star sensor based on an eight-wedge beam splitter, as described in this invention. Detailed Implementation

[0085] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described specific embodiments are merely a part of the embodiments of the invention, and not all of them. The components of the specific embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations, and the invention may also have other embodiments.

[0086] Therefore, the following detailed description of specific embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected specific embodiments of the invention. All other specific embodiments obtained by those skilled in the art based on these specific embodiments without inventive effort are within the scope of protection of this invention.

[0087] To further understand the invention's content, features, and effects, the following specific embodiments are provided, along with accompanying drawings. Figure 1 -Appendix Figure 4 Detailed explanation is as follows:

[0088] Example 1:

[0089] A broadband interferometric star sensor based on an eight-wedge beam splitter includes an interferometer, an eight-wedge beam splitter, a focusing component, and a detector arranged in sequence.

[0090] The interference component consists of two gratings G1 and G2 spaced a certain distance apart, used to modulate the starlight phase and thus generate interference fringes;

[0091] The eight-wedge beam splitter is an array of eight optical wedges used to divide the interference fringes into eight parts of fringe light.

[0092] The focusing component is used to focus the striped light onto different positions of the detector;

[0093] The detector is located at the focal plane of the focusing assembly and is used to capture the image of starlight.

[0094] Furthermore, the spacing between gratings G1 and G2 in the interference assembly is z. t The gratings G1 and G2 have the same period, p. The z-axis is the optical axis of the optical system. The scribe lines of both gratings are perpendicular to the optical axis, and the angle between the scribe lines and the y-axis is ɛ. , where b is the width of a single optical wedge, and the scribe line direction is symmetrical about the y-axis.

[0095] Furthermore, the eight optical wedges of the eight-wedge beam splitter are arranged along the y-axis to apply different deflection directions to the eight parts of starlight. The size of each of the eight optical wedges is a×b, satisfying a=8b, where a and b represent the length of the optical wedge along the x-direction and the length of the optical wedge along the y-direction, respectively. The rear surface of the eight-wedge beam splitter is set as the entrance pupil of the broadband interferometric star sensor based on the eight-wedge beam splitter.

[0096] Furthermore, the focusing component is used to focus the individual stripes onto different locations on the detector.

[0097] Furthermore, the period of gratings G1 and G2 can be selected as 50 μm, the grating spacing can be selected as 50 mm, and the grating angle α can be selected as 0.0149°; gratings G1 and G2 are Ronchi gratings.

[0098] Furthermore, the beam splitting assembly can be selected as 8 optical wedges arranged along the y-axis, and the size of each optical wedge can be selected as 48mm×12mm;

[0099] Furthermore, the focusing lens group requires no vignetting across the entire field of view.

[0100] Example 2:

[0101] A method for centroid localization of a broadband interferometric star sensor based on an eight-wedge beam splitter, implemented using the broadband interferometric star sensor based on an eight-wedge beam splitter as described in Example 1, includes the following steps:

[0102] S1. Construct a model relating the starlight incident angle and image point energy of a broadband interferometric star sensor based on an eight-wedge beam splitter;

[0103] Furthermore, the specific implementation method of step S1 includes the following steps:

[0104] S1.1. Calculation of the angular spectrum of starlight after passing through the interferometer and spectrometer components based on the angular spectrum propagation theory. The calculation formula is:

[0105]

[0106] in, This indicates the Fourier transform operation; This represents the complex amplitude of starlight at the front end of the star sensor; This represents the complex amplitude transmittance of grating G1; Let be the transfer function for starlight transmission from the back surface of G1 to G2; This represents the complex amplitude transmittance of grating G2; This indicates the complex amplitude transmittance of the eight-wedge beam splitter; Indicates the convolution operation;

[0107] The formula for calculating the complex amplitude of starlight at the front end of the star sensor is:

[0108]

[0109] in, λ represents the starlight amplitude; j represents the imaginary unit; λ represents the starlight wavelength; α and β represent the complementary angles of the starlight and the x-axis and y-axis of the star sensor, respectively; x and y represent the coordinates of the starlight at the front of the star sensor, respectively.

[0110] The formulas for calculating the complex amplitude transmittance of gratings G1 and G2 are as follows:

[0111]

[0112]

[0113] in, λ is the m-th order diffraction coefficient of grating G1 at wavelength λ; The first grating G2 at wavelength λ Diffraction coefficients;

[0114] The expression for the transfer function of starlight propagating from the back surface of G1 to G2 is:

[0115]

[0116] Among them, f x f represents the spatial frequency in the x-direction. y Indicates the spatial frequency in the y-direction;

[0117] The expression for the complex amplitude transmittance of the eight-wedge beam splitter is:

[0118]

[0119] in, , Let a and b represent the deflection angles of starlight in the x-direction and y-direction respectively after passing through the nth optical wedge; rect represents a rectangular function, and the relationship between a and b is as shown in the equation. As shown:

[0120]

[0121] The relationship between the light wedge angles is as follows: As shown:

[0122] ;

[0123] S1.2. Combining the formula from step S1.1, we obtain the equation. The expansion formula is as follows:

[0124]

[0125] S1.3. An analysis is conducted on the zero-order diffraction image point generated by starlight passing through an interferometric star sensor. Based on Parseval's theorem, the energy of the zero-order image point generated after starlight passes through the interferometer, the nth optical wedge, and the focusing assembly is:

[0126]

[0127] Where T is the stellar color temperature; M is the apparent star size. Spectral irradiance of stars; The spectral range of stars;

[0128] The positions of the starlight in the x and y directions at the zero-order image point generated by the detector after passing through the interferometer, the nth optical wedge, and the focusing assembly are:

[0129]

[0130] Where f represents the focal length of the focusing component;

[0131] When only considering the 0th and ±1st order diffraction of the grating, let (m,n) represent the image points formed on the image plane by the m-th order diffraction produced by G1 and the n-th order diffraction produced by G2, respectively. Then, after the starlight passes through the interference assembly, any optical wedge, and the focusing lens group, it will produce a total of nine diffraction image points: (-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 0), (0, +1), (1, -1), (1, 0), and (1, 1). When the incident starlight is in a broad spectrum, due to the dispersion effect of the grating, the six higher-order diffraction points (-1, -1), (-1, 0), (0, -1), (0, 1), (1, 0), and (1, 1) will have obvious tails, which greatly increases the detection difficulty compared to the three zero-order diffraction points (-1, 1), (0, 0), and (1, -1). Therefore, only the zero-order diffraction points generated by the starlight passing through the interferometric star sensor are analyzed.

[0132] S1.4. To facilitate the analysis of the zero-order image point energy, intermediate variables are constructed. , , They are respectively:

[0133]

[0134]

[0135]

[0136] in, When m is 1 The value, When m is -1 The value;

[0137] Then we have:

[0138]

[0139] At this point, even if the zeroth-order diffraction of the grating is not zero, equation (16) still holds strictly, and the expression is:

[0140]

[0141] Based on the principle of geometric optics imaging:

[0142]

[0143] At this point, the image point passing through the nth light wedge coincides with the image point passing through the (n+4)th light wedge, thus establishing the relationship between the starlight incident angle and the image point energy.

[0144] Furthermore, without increasing the number of image points, the measurement accuracy of the interferometric star sensor in the broadband band was improved by introducing an eight-wedge beam splitter.

[0145] S2. Based on the energy distribution of image points obtained by the detector, the coordinates of the image points on the image plane are extracted using the gray-level weighted method, and the gray level of each image point is calculated;

[0146] Furthermore, the specific implementation method of step S2 includes the following steps:

[0147] S2.1. First, estimate the background noise threshold. The calculation formula is as follows:

[0148]

[0149] Where μ is the mean gray value of the background, and σ is the standard deviation of the gray value of the background;

[0150] Threshold segmentation of the star map;

[0151] S2.2. Perform connected component partitioning on image points based on the scanning method;

[0152] S2.3. Based on the gray-level weighted method, the centroids of the image points are extracted, and the centroid coordinates of the four image points are (x1, y1), (x2, y2), (x3, y3), and (x4, y4), respectively. The gray levels of the four image points are g1, g2, g3, and g4, respectively.

[0153] S3. For the grayscale values ​​of the image points obtained in step S2, determine the image point with the highest grayscale value and extract the centroid coordinates of the image point with the highest grayscale value;

[0154] Furthermore, the specific implementation method of step S3 is to sort the four image points extracted in step S2 by gray level, find the image point with the highest gray level, and its centroid coordinates are (x max y max ).

[0155] S4. Based on the centroid coordinates of the image point with the largest gray level obtained in step S4, the geometric optics imaging principle is applied to estimate the starlight incident angle and estimate the starlight phase integer ambiguity.

[0156] Furthermore, the specific implementation method of step S4 is to use the (x) obtained in step S3. max y max Substitution Estimate the angle of starlight incidence , , as shown As shown:

[0157]

[0158] in, , These represent the estimated values ​​of the complementary angles between the starlight and the star sensor along the x-axis and y-axis, respectively.

[0159] Substitute the estimated starlight incident angle into the equation with formula In this process, a rough phase value is obtained. And for the integer ambiguity of the phase An estimate is made, and the specific calculation method is as follows: As shown:

[0160]

[0161] Here, round means rounding to the nearest integer.

[0162] S5. Based on the pixel grayscale obtained in step S2, calculate the principal value of the starlight phase, and add the principal value of the phase to the integer phase ambiguity obtained in step S4 to obtain a high-precision starlight phase.

[0163] Furthermore, the specific implementation method of step S5 is to substitute the grayscale values ​​of the four pixels extracted in step S2 into the formula. , that is to say , , , Solving the principal values ​​of starlight phase The final starlight phase is obtained by adding the integer ambiguity of the starlight phase to the principal value of the phase. .

[0164] S6. Calculate the high-precision starlight incident angle from the high-precision starlight phase obtained in step S5 to obtain the high-precision centroid coordinates of the image point.

[0165] Furthermore, the specific implementation method of step S6 is a simultaneous equation. and To calculate the high-precision starlight incidence angle α, as shown in the equation. As shown,

[0166]

[0167] Then, based on the principle of geometric imaging, high-precision centroid coordinates of the image point are obtained.

[0168] It should be noted that relational terms such as "first" and "second" are used merely 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 apparatus 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 apparatus. 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 apparatus that includes said element.

[0169] Although this application has been described above with reference to specific embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of this application. In particular, as long as there is no structural conflict, the features in the specific embodiments disclosed in this application can be combined with each other in any way. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, this application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A method for centroid localization of a broadband interferometric star sensor based on an eight-wedge beam splitter, characterized in that, Includes the following steps: S1. Construct a model relating the starlight incident angle and image point energy of a broadband interferometric star sensor based on an eight-wedge beam splitter; The specific implementation method of step S1 includes the following steps: S1.

1. Calculation of the angular spectrum of starlight after passing through the interferometer and spectrometer components based on the angular spectrum propagation theory. The calculation formula is: in, This indicates the Fourier transform operation; This represents the complex amplitude of starlight at the front end of the star sensor; This represents the complex amplitude transmittance of grating G1; Let be the transfer function for starlight transmission from the back surface of G1 to G2; This represents the complex amplitude transmittance of grating G2; This indicates the complex amplitude transmittance of the eight-wedge beam splitter; * indicates the convolution operation. The formula for calculating the complex amplitude of starlight at the front end of the star sensor is: in, λ represents the starlight amplitude; j represents the imaginary unit; λ represents the starlight wavelength; α and β represent the complementary angles of the starlight and the star sensor's x-axis and y-axis, respectively; x and y represent the coordinates of the starlight at the front end of the star sensor, respectively; a and b represent the lengths of the optical wedge along the x-direction and the y-direction, respectively. The formulas for calculating the complex amplitude transmittance of gratings G1 and G2 are as follows: in, λ is the m-th order diffraction coefficient of grating G1 at wavelength λ; The first grating G2 at wavelength λ The diffraction coefficient is α; α is the angle between the grating lines of the two gratings and the y-axis; p is the grating period. The expression for the transfer function of starlight propagating from the back surface of G1 to G2 is: Among them, f x f represents the spatial frequency of starlight in the x-direction. y Represents the spatial frequency of starlight in the y-direction; z t The spacing between gratings G1 and G2 in the interference assembly; The expression for the complex amplitude transmittance of the eight-wedge beam splitter is: in, , Let a and b represent the deflection angles of starlight in the x-direction and y-direction respectively after passing through the nth optical wedge; rect represents a rectangular function, and the relationship between a and b is as shown in the equation. As shown: The relationship between the light wedge angles is as follows: As shown: ； S1.

2. Combining the formula from step S1.1, we obtain the equation. The expansion formula is as follows: Where α and β represent the complementary angles of the angle between the starlight and the x-axis and the y-axis of the star sensor, respectively; S1.

3. An analysis is conducted on the zero-order diffraction image point generated by starlight passing through an interferometric star sensor. Based on Parseval's theorem, the energy of the zero-order image point generated after starlight passes through the interferometer, the nth optical wedge, and the focusing assembly is: in, The spectral range of stars; The positions of the starlight in the x and y directions at the zero-order image point generated by the detector after passing through the interferometer, the nth optical wedge, and the focusing assembly are: Where f represents the focal length of the focusing component; S1.

4. To facilitate the analysis of the zero-order image point energy, intermediate variables are constructed. , , They are respectively: in, When m is 1 The value, When m is -1 The value; Then we have: At this point, even if the zeroth-order diffraction of the grating is not zero, equation (16) still holds strictly, and the expression is: Based on the principle of geometric optics imaging: At this point, the image point formed by the nth light wedge coincides with the image point formed by the (n+4)th light wedge, thus establishing the relationship between the starlight incident angle and the image point energy. S2. Based on the energy distribution of image points obtained by the detector, the coordinates of the image points on the image plane are extracted using the gray-level weighted method, and the gray level of each image point is calculated; S3. For the grayscale values ​​of the image points obtained in step S2, determine the image point with the highest grayscale value and extract the centroid coordinates of the image point with the highest grayscale value; S4. Based on the centroid coordinates of the image point with the largest gray level obtained in step S4, the geometric optics imaging principle is applied to estimate the starlight incident angle and estimate the starlight phase integer ambiguity. S5. Based on the pixel grayscale obtained in step S2, calculate the principal value of the starlight phase, and add the principal value of the phase to the integer phase ambiguity obtained in step S4 to obtain a high-precision starlight phase. S6. Calculate the high-precision starlight incident angle from the high-precision starlight phase obtained in step S5 to obtain the high-precision centroid coordinates of the image point.

2. The centroid localization method for a broadband interferometric star sensor based on an eight-wedge beam splitter according to claim 1, characterized in that, The specific implementation method of step S2 includes the following steps: S2.

1. First, estimate the background noise threshold. The calculation formula is as follows: Where μ is the mean gray value of the background, and σ is the standard deviation of the gray value of the background; Threshold segmentation of the star map; S2.

2. Perform connected component partitioning on image points based on the scanning method; S2.

3. Based on the gray-level weighted method, the centroids of the image points are extracted, and the centroid coordinates of the four image points are (x1, y1), (x2, y2), (x3, y3), and (x4, y4), respectively. The gray levels of the four image points are g1, g2, g3, and g4, respectively.

3. The centroid localization method for a broadband interferometric star sensor based on an eight-wedge beam splitter according to claim 2, characterized in that, The specific implementation method of step S3 is to sort the four image points extracted in step S2 by gray level, find the image point with the largest gray level, and mark its centroid coordinates as (x max y max ).

4. The centroid localization method for a broadband interferometric star sensor based on an eight-wedge beam splitter according to claim 3, characterized in that, The specific implementation method of step S4 is to use the (x) obtained in step S3. max y max Substitution Estimate the angle of starlight incidence , , as shown As shown: in, , These represent the estimated values ​​of the complementary angles between the starlight and the star sensor along the x-axis and y-axis, respectively. Substitute the estimated starlight incident angle into the equation with formula In this process, a rough phase value is obtained. And for the integer ambiguity of the phase An estimate is made, and the specific calculation method is as follows: As shown: Here, round means rounding to the nearest integer.

5. The centroid localization method for a broadband interferometric star sensor based on an eight-wedge beam splitter according to claim 4, characterized in that, The specific implementation method of step S5 is to input the grayscale values ​​of the four pixels extracted in step S2 into the formula. , that is to say , , , Solving the principal values ​​of starlight phase The final starlight phase is obtained by adding the integer ambiguity of the starlight phase to the principal value of the phase. .

6. The centroid localization method for a broadband interferometric star sensor based on an eight-wedge beam splitter according to claim 5, characterized in that, The specific implementation method of step S6 is a simultaneous equation. and To calculate the high-precision starlight incidence angle α, as shown in the equation. As shown, Then, based on the principle of geometric imaging, high-precision centroid coordinates of the image point are obtained.

7. A broadband interferometric star sensor based on an eight-wedge beam splitter, realizing the centroid localization method of a broadband interferometric star sensor based on an eight-wedge beam splitter as described in any one of claims 1-6, characterized in that, It includes an interference assembly, an eight-wedge beam splitter assembly, a focusing assembly, and a detector arranged in sequence; The interference component consists of two gratings G1 and G2 spaced a certain distance apart, used to modulate the starlight phase and thus generate interference fringes; The eight-wedge beam splitter is an array of eight optical wedges used to divide the interference fringes into eight parts of fringe light. The focusing component is used to focus the striped light onto different positions of the detector; The detector is located at the focal plane of the focusing assembly and is used to capture the image of starlight.

8. A broadband interferometric star sensor based on an eight-wedge beam splitter according to claim 7, characterized in that, The spacing between gratings G1 and G2 in the interference assembly is z. t The gratings G1 and G2 have the same period, p. The z-axis is the optical axis of the optical system. The scribe lines of both gratings are perpendicular to the optical axis, and the angle between the scribe lines and the y-axis is ɛ. , where b is the width of a single optical wedge, and the scribe line direction is symmetrical about the y-axis.

9. A broadband interferometric star sensor based on an eight-wedge beam splitter according to claim 8, characterized in that, The eight optical wedges of the eight-wedge beam splitter are arranged along the y-axis to apply different deflection directions to the eight parts of starlight. The size of each of the eight optical wedges is a×b, satisfying a=8b, where a and b represent the length of the optical wedge along the x-direction and the length of the optical wedge along the y-direction, respectively. The rear surface of the eight-wedge beam splitter is set as the entrance pupil of the broadband interferometric star sensor based on the eight-wedge beam splitter.

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