Method for Detecting the Non-Uniformity of the Curvature Radii of Sub-Mirrors of a Space-Borne Mosaic Telescope

Abstract

A method for detecting the non-uniformity of the curvature radii of the sub-mirrors of a space-based segmented telescope in orbit, belonging to the field of optical detection, includes: collecting point spread function images at different focal plane positions of the segmented space telescope; using the point spread function images as inputs and solving the system wavefront phase distribution by using a phase retrieval algorithm; fitting the sub-aperture wavefront with Zernike polynomials to obtain aberration coefficient values corresponding to various low-order aberrations and obtaining the defocus aberration components contained in the sub-aperture wavefront; decoupling the influence of the non-uniformity error of the sub-mirror curvature radius and the lateral misalignment of other mirrors on the sub-aperture defocus aberration; determining an approximate linear relationship between the sub-aperture defocus aberration and the corresponding non-uniformity error of the sub-mirror curvature radius; and calculating the corresponding non-uniformity error of the sub-mirror curvature radius according to the difference values of the defocus aberrations in the wavefront aberrations of each sub-aperture. The present invention can reduce the main mirror surface error, improve the main mirror surface accuracy, and improve the final imaging performance of the segmented space telescope.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical detection, and particularly relates to a method for on-orbit detecting the non-uniformity of the curvature radii of the sub-mirrors of a segmented telescope. Background Art

[0002] Adopting a segmented primary mirror structure has become an important development trend for future space large-aperture telescopes. Traditional space large-aperture telescopes with a single-piece mirror face great difficulties in aspects such as mirror surface processing, detection, support design and lightweighting, as well as the transportation and launch of the entire mirror body. The emergence of the segmented primary mirror structure provides an effective way to solve these problems.

[0003] In the segmented primary mirror structure of a space telescope, the non-uniformity of the curvature radii of the segmented sub-mirrors (different segmented sub-mirrors have different curvature radii) is one of the key problems affecting the final imaging performance of the segmented space telescope. After the segmented space telescope is deployed in orbit, it needs to go through some complex steps to gradually complete the confocal and co-phasing of different segmented sub-mirrors. And the non-uniformity of the curvature radii of the segmented sub-mirrors, as a special "surface shape error", will reduce the surface shape accuracy after co-phasing.

[0004] Accurate detection of the non-uniformity error of the curvature radii of the segmented sub-mirrors of the primary mirror of a segmented space telescope is a necessary prerequisite for on-orbit correction of the non-uniformity of the curvature radii. At present, the James Webb Space Telescope launched by the United States has the ability to adjust the non-uniformity of the curvature radii of the segmented sub-mirrors. However, the relevant methods for detecting the non-uniformity error of the curvature radii of the segmented sub-mirrors have not been made public, and it is necessary to independently develop relevant methods to solve the problem of on-orbit detection of the non-uniformity error of the curvature radii of the segmented sub-mirrors. Summary of the Invention

[0005] In order to effectively detect the non-uniformity error of the curvature radii of the segmented sub-mirrors of a segmented space telescope, the present invention provides a method for on-orbit detecting the non-uniformity of the curvature radii of the sub-mirrors of a segmented telescope to fill the blank in this field.

[0006] The technical solution adopted by the present invention to solve the above technical problems is as follows:

[0007] The method for on-orbit detecting the non-uniformity of the curvature radii of the sub-mirrors of a segmented telescope according to the present invention includes the following steps:

[0008] Step 1: Collect point spread function images at different focal plane positions of the segmented space telescope;

[0009] Step 2: Taking the point spread function images collected in Step 1 as input, use the phase retrieval algorithm to solve the system wavefront phase distribution and obtain the full-aperture system wavefront aberration;

[0010] Step 3: Use Zernike polynomials to fit the sub-aperture wavefront, obtain the aberration coefficient values corresponding to each low-order aberration, and obtain the defocus aberration component contained in the sub-aperture wavefront;

[0011] Step 4: Decouple the influence of the non-uniformity error of the sub-mirror curvature radius and the lateral misalignment of other mirrors on the sub-aperture defocus aberration;

[0012] Step 5: Determine the approximate linear relationship between the sub-aperture defocus aberration and the corresponding non-uniformity error of the sub-mirror curvature radius;

[0013] Step 6: Calculate the corresponding non-uniformity error of the sub-mirror curvature radius according to the difference values of the defocus aberration in the wave aberration of each sub-aperture.

[0014] Further, the specific operation steps of Step 3 are as follows:

[0015] Step S3.1: Represent the measured sub-aperture wavefront with an n-term Zernike polynomial as:

[0016] W(x,y) = q1Z1(x,y) + q2Z2(x,y) +... + q n Z n (x,y) (1)

[0017] In the formula, W represents the wave aberration value, Z n represents the nth Zernike polynomial, q n represents the corresponding Zernike coefficient in the nth Zernike polynomial, and (x,y) represents the position coordinates of the pupil plane;

[0018] Step S3.2: Represent formula (1) in matrix form as:

[0019] W(x,y) = q T Z (2)

[0020] In the formula, q represents the vector containing each Zernike coefficient, the superscript T represents the transpose of the matrix, and Z represents the Zernike polynomial matrix.

[0021] Step S3.3: Suppose there are m discrete measurement data points W i (x i ,y i ), i = 1, 2,..., m; let a ij = Z j (x i ,y i ), j = 1, 2,..., n, m > n, substitute the above formula (1) and formula (2), and obtain an inconsistent system of equations:

[0022]

[0023] Step S3.4: Formula (3) is represented in matrix form as:

[0024] Aq = w (4)

[0025] where A = (a ij ) is an m×n matrix, q = [q1, q 2, ..., q n T , w = [W1, W 2, ..., W m T ;

[0026] Step S3.5: Solve the inconsistent equations using the least squares criterion to obtain the aberration coefficient values corresponding to the defocus aberration:

[0027] q = (A T A) -1 A T w (5)

[0028] where the superscript T represents the transpose of the matrix.

[0029] Furthermore, the specific operation steps of Step Four are as follows:

[0030] Step S4.1: The full-aperture coma produces the same coma components in different sub-apertures. Take the average of the coma components of each sub-aperture to obtain the sub-aperture coma value:

[0031]

[0032] where N represents the number of segmented sub-mirrors in the primary mirror structure of the segmented space telescope, represents the x-direction coma coefficient of the i-th sub-aperture, represents the y-direction coma coefficient of the i-th sub-aperture;

[0033] Step S4.2: According to the relationship between the sub-aperture coma and the full-aperture coma, obtain the full-aperture coma value:

[0034]

[0035] where k represents the ratio of the full-aperture size to the sub-aperture size, C7 represents the x-direction full-aperture coma coefficient, and C8 represents the y-direction full-aperture coma coefficient;

[0036] The defocus aberration value derived from the full-aperture coma in the i-th sub-aperture is:

[0037]

[0038] where · represents the dot product of vectors, and ​​respectively represent the ratios of the distances between the centers of the \(i\)-th sub-aperture and the full-aperture center in the \(x\) and \(y\) directions to the full-aperture radius;

[0039] Step S4.3: Remove the defocus aberration component derived from the full-aperture coma from the sub-aperture defocus aberration. The remaining is the defocus aberration component caused by the non-uniformity error of the sub-mirror curvature radius:

[0040]

[0041] In the formula, represents the total defocus aberration component in the \(i\)-th sub-aperture, represents the defocus aberration component derived from the full-aperture coma in the \(i\)-th sub-aperture, represents the defocus aberration component caused by the non-uniformity error of the sub-mirror curvature radius in the \(i\)-th sub-aperture, that is, the part derived from the full-aperture coma is removed from the total defocus aberration component.

[0042] Further, the specific operation steps of Step Five are as follows:

[0043] Introduce a change amount of the non-uniformity error of the sub-mirror curvature radius in the optical simulation software, extract the change amount of the defocus aberration of the off-axis subsystem. The ratio of the change amount of the non-uniformity error of the sub-mirror curvature radius to the change amount of the defocus aberration of the off-axis subsystem is the coefficient of the linear relationship, and thus the approximate linear relationship between the sub-aperture defocus aberration and the corresponding non-uniformity error of the sub-mirror curvature radius is determined.

[0044] Further, the specific operation steps of Step Six are as follows:

[0045] Based on the approximate linear relationship between the sub-aperture defocus aberration and the corresponding non-uniformity error of the sub-mirror curvature radius obtained in Step Five, divide the sub-aperture defocus aberration value by the coefficient of the linear relationship obtained in Step Five to obtain the corresponding non-uniformity error of the sub-mirror curvature radius; count and record the non-uniformity errors of the curvature radius errors of each sub-mirror.

[0046] The beneficial effects of the present invention are:

[0047] A method for on-orbit detecting the non-uniformity of the curvature radii of each sub-mirror of a segmented telescope according to the present invention can provide a necessary prerequisite for on-orbit correction of the non-uniformity of the curvature radii of each segmented sub-mirror of the primary mirror of a segmented space telescope, can effectively solve the technical problem of on-orbit detection of the non-uniformity error of the curvature radii of each segmented sub-mirror, can reduce the surface shape error of the primary mirror, improve the surface shape accuracy of the primary mirror, and improve the final imaging performance of the segmented space telescope. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1Flow chart of a method for detecting the non - uniformity of the curvature radii of the sub - mirrors of a space - based segmented telescope in orbit according to the present invention. Detailed implementation manners

[0049] The present invention will be further described in detail below with reference to the accompanying drawings.

[0050] As Figure 1 shown, a method for detecting the non - uniformity of the curvature radii of the sub - mirrors of a space - based segmented telescope in orbit according to the present invention is mainly applied to adjusting the image quality of a space - based segmented telescope in orbit. The specific steps are as follows:

[0051] Step 1: Since the non - uniformity of the curvature radii between the segmented sub - mirrors in the main mirror structure of a space - based segmented telescope will affect the system wavefront aberration, the detection can start from the system wavefront aberration. First, collect the point - spread function images at different focal plane positions of the space - based segmented telescope for the next step of calculating the system wavefront aberration.

[0052] Step 2: Using the point - spread function images at different focal planes collected in Step 1 as input, use the phase - retrieval algorithm to solve the system wavefront phase distribution and obtain the full - aperture system wavefront aberration; among them, the phase - retrieval algorithm used is a commonly used method for on - orbit wavefront detection of space telescopes, which can use the (off) - focal plane image to recover the image phase and then iteratively solve the system wavefront phase distribution.

[0053] The sub - aperture wavefront includes: non - common - phase error and continuous aberrations such as defocus and astigmatism. Among them, the non - common - phase error includes: Piston error and Tip - tilt error, corresponding to the first three terms of the Zernike polynomial. Therefore, by fitting the sub - aperture wavefront with the Zernike polynomial, the aberration coefficient values corresponding to each low - order aberration (defocus, astigmatism, coma, etc.) can be obtained, and the defocus aberration component included in the sub - aperture wavefront, corresponding to the fourth term of the Zernike polynomial, can be obtained.

[0054] The specific operation steps are as follows:

[0055] Step S3.1: Represent the measured sub - aperture wavefront with an n - term Zernike polynomial as:

[0056] W(x,y)=q1Z1(x,y)+q2Z2(x,y)+...+q n Z n (x,y) (1)

[0057] In the formula, W represents the wave aberration value, Z n represents the n - th Zernike polynomial, q n represents the corresponding Zernike coefficient in the n - th Zernike polynomial, and (x,y) represents the pupil - plane position coordinates; preferably, the Zernike polynomial can take the first 9 terms, that is, n = 9.

[0058] Step S3.2: Formula (1) can be expressed in matrix form as:

[0059] W(x, y) = q T Z(2)

[0060] where q represents a vector containing various Zernike coefficients, the superscript T represents the transpose of the matrix, and Z represents the Zernike polynomial matrix.

[0061] Step S3.3: Suppose there are m discrete measurement data points W i (x i , y i ), i = 1, 2,..., m; let a ij = Z j (x i , y i ), j = 1, 2,..., n, m > n, substitute the above formulas (1) and (2), and obtain an inconsistent system of equations:

[0062]

[0063] Step S3.4: Formula (3) can be expressed in matrix form as:

[0064] Aq = w (4)

[0065] where Α = (a ij ) is an m×n matrix, q = [q1, q 2, ..., q n T , w = [W1, W 2, ..., W m T ;

[0066] Step S3.5: Generally, there is no solution in the usual sense for the inconsistent system of equations, that is, for any n-dimensional vector q, generally Aq - w ≠ O. At this time, the least squares criterion is used to solve the parameters, and the aberration coefficient value corresponding to the defocus aberration can be obtained.

[0067] q = (A T A) -1 A T w (5)

[0068] where the superscript T represents the transpose of the matrix.

[0069] Step Four: Decouple the influence of the non-uniformity error of the sub-mirror curvature radius and the lateral misalignment of other mirrors on the sub-aperture defocus aberration.

[0070] ​​Since the non-uniformity error of the sub-mirror curvature radius and the lateral misalignment (such as eccentricity, tilt) of other mirrors (such as the secondary mirror) will also generate sub-aperture defocus aberration. Among them, the lateral misalignment of other mirrors will introduce full-aperture coma, thus deriving sub-aperture defocus aberration and coma. Therefore, when using the sub-aperture defocus aberration caused by the non-uniformity error of the sub-mirror curvature radius to solve the non-uniformity error of the sub-mirror curvature radius, it is necessary to decouple the influence of the non-uniformity error of the sub-mirror curvature radius and the lateral misalignment of other mirrors on the sub-aperture defocus aberration. The basic principle of decoupling is: Since the full-aperture coma introduced by the lateral misalignment of other mirrors not only derives defocus aberration in the sub-aperture, but also derives coma, and the sub-aperture coma generated by the non-uniformity error of the sub-mirror curvature radius can be ignored. Therefore, decoupling can be carried out according to this difference. First, use the sub-aperture coma to solve the full-aperture coma, then use the full-aperture coma to solve the defocus aberration generated in each sub-aperture, and finally remove this part of the sub-aperture defocus aberration.

[0071] The specific operation steps are as follows:

[0072] Step S4.1: The full-aperture coma generates the same coma component in different sub-apertures. Take the average of the coma components of each sub-aperture to obtain the sub-aperture coma value:

[0073]

[0074] In the formula, N represents the number of each spliced sub-mirror in the main mirror structure of the segmented space telescope, represents the x-direction coma Zernike coefficient (the 7th Zernike coefficient) of the i-th sub-aperture, represents the y-direction coma Zernike coefficient (the 8th Zernike coefficient) of the i-th sub-aperture.

[0075] Step S4.2: According to the relationship between the sub-aperture coma and the full-aperture coma, the full-aperture coma value can be obtained:

[0076]

[0077] In the formula, k represents the ratio of the full-aperture size to the sub-aperture size, C7 represents the x-direction full-aperture coma coefficient, and C8 represents the y-direction full-aperture coma coefficient.

[0078] The defocus aberration value derived by the full-aperture coma in the i-th sub-aperture is:

[0079]

[0080] In the formula, · represents the vector dot product, and They respectively represent the ratios of the distances between the centers of the \(i\)-th sub-aperture and the full-aperture center in the \(x\) and \(y\) directions to the radius of the full-aperture. It can be seen from Equation (8) that the full-aperture coma aberration derives different defocus aberration values in different sub-apertures.

[0081] Step S4.3: Remove the defocus aberration component derived from the full-aperture coma aberration from the sub-aperture defocus aberration. The remaining is the defocus aberration component caused by the non-uniformity error of the sub-mirror curvature radius:

[0082]

[0083] In the formula, represents the total defocus aberration component in the \(i\)-th sub-aperture, represents the defocus aberration component derived from the full-aperture coma aberration in the \(i\)-th sub-aperture, represents the defocus aberration component caused by the non-uniformity error of the sub-mirror curvature radius in the \(i\)-th sub-aperture, that is, the part derived from the full-aperture coma aberration is removed from the total defocus aberration component.

[0084] Step Five: Determine the approximate linear relationship between the sub-aperture defocus aberration and the non-uniformity error of the corresponding sub-mirror curvature radius.

[0085] Each sub-mirror in the main mirror structure of the segmented space telescope and other mirrors in the system form an off-axis subsystem. When the curvature radius of the sub-mirror is changed, defocus aberration will be introduced. Within a certain range, the change amount of the introduced defocus aberration is linearly related to the change amount of the non-uniformity error of the sub-mirror curvature radius. Accordingly, in the optical simulation software, a small change amount of the non-uniformity error of the sub-mirror curvature radius can be introduced, and then the change amount of the defocus aberration of the off-axis subsystem can be extracted. The ratio of the change amount of the non-uniformity error of the sub-mirror curvature radius to the change amount of the defocus aberration of the off-axis subsystem is the coefficient of the linear relationship, and thus the approximate linear relationship between the sub-aperture defocus aberration and the non-uniformity error of the corresponding sub-mirror curvature radius can be determined. Among them, the ratio of the change amount of the non-uniformity error of the sub-mirror curvature radius to the change amount of the defocus aberration of the off-axis subsystem is the sensitivity of the sub-aperture defocus aberration to the non-uniformity error of the corresponding sub-mirror curvature radius.

[0086] Step Six: Calculate the non-uniformity error of the corresponding sub-mirror curvature radius according to the difference value of the defocus aberration in the wave aberration of each sub-aperture.

[0087] Based on the approximate linear relationship between the sub-aperture defocus aberration obtained in Step Five and the non-uniformity error of the corresponding sub-mirror curvature radius, divide the sub-aperture defocus aberration value by the coefficient of the linear relationship obtained in Step Five (the ratio of the change in the non-uniformity error of the sub-mirror curvature radius to the change in the defocus aberration of the off-axis subsystem). Thus, the sub-aperture defocus aberration value can be converted into the curvature radius value of the corresponding sub-mirror, that is, the non-uniformity error of the curvature radius of the corresponding sub-mirror is obtained; then, simply count and record the non-uniformity error of the curvature radius error of each sub-mirror.

[0088] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for on-orbit detecting the non-uniformity of the curvature radii of the sub-mirrors of a spliced telescope, characterized in that, It includes the following steps: Step 1: Collect the point spread function images at different focal plane positions of the segmented space telescope; Step 2: Using the point spread function images collected in Step 1 as the input, solve the system wavefront phase distribution by the phase retrieval algorithm to obtain the full-aperture system wavefront aberration; Step 3: Fit the sub-aperture wavefront with Zernike polynomials to obtain the aberration coefficient values corresponding to each low-order aberration, and obtain the defocus aberration component included in the sub-aperture wavefront; Step S3.1: Represent the measured sub-aperture wavefront with an n-term Zernike polynomial as: W(x,y) = q1Z1(x,y) + q2Z2(x,y) +... + q n Z n (x,y)(1) Where W represents the wave aberration value, and Z n represents the n-th Zernike polynomial, and q n represents the corresponding Zernike coefficient in the n-th Zernike polynomial, and (x, y) represents the position coordinates on the pupil plane; Step S3.2: Represent formula (1) in matrix form as: W(x,y) = q T Z(2) In the formula, q represents the vector containing each Zernike coefficient, the superscript T represents the transpose of the matrix, and Z represents the Zernike polynomial matrix; Step S3.3: There are m discrete measurement data points W i (x i , y i ), i = 1, 2,..., m; Let a ij = Z j (x i , y i ), j = 1, 2,..., n, m > n, substitute into the above formulas (1) and (2) to obtain a system of contradictory equations: Step S3.4: Represent formula (3) in matrix form as: Aq = w (4) where Α = (a ij ) is an m×n matrix, q = [q1, q2,..., q n T , w = [W1, W2,..., W m T ;​​ Step S3.5: Solve the inconsistent equations using the least squares criterion to obtain the aberration coefficient value corresponding to the defocus aberration: q = (A T A) -1 A T w(5) In the formula, the superscript T represents the transpose of the matrix; Step 4: Decouple the influence of the non-uniformity error of the sub-mirror curvature radius and the lateral misalignment of other mirrors on the sub-aperture defocus aberration; Step S4.1: The full-aperture coma produces the same coma component in different sub-apertures. Take the average of the coma components of each sub-aperture to obtain the sub-aperture coma value; In the formula, N represents the number of each segmented mirror in the segmented space telescope primary mirror structure, represents the coma coefficient in the x direction of the i-th sub-aperture, represents the coma coefficient in the y direction of the i-th sub-aperture; Step S4.2: According to the relationship between the sub-aperture coma and the full-aperture coma, obtain the full-aperture coma value: In the formula, k represents the ratio of the full-aperture size to the sub-aperture size, C7 represents the full-aperture coma coefficient in the x direction, and C8 represents the full-aperture coma coefficient in the y direction; The defocus aberration value derived from the full-aperture coma in the i-th sub-aperture is: where · represents the dot product of vectors, and respectively represent the ratios of the distances between the centers of the i-th sub-aperture and the full-aperture center in the x and y directions to the radius of the full-aperture; Step S4.3: Remove the defocus aberration component derived from the full-aperture coma from the sub-aperture defocus aberration. The remaining is the defocus aberration component caused by the non-uniformity error of the sub-mirror curvature radius; In the formula, represents the total defocus aberration component in the i-th sub-aperture, represents the defocus aberration component derived from the full-aperture coma in the i-th sub-aperture, represents the defocus aberration component caused by the non-uniformity error of the sub-mirror curvature radius in the i-th sub-aperture, that is, the part derived from the full-aperture coma is removed from the total defocus aberration component; Step 5: Determine the approximate linear relationship between the sub-aperture defocus aberration and the non-uniformity error of the corresponding sub-mirror curvature radius; Introduce a change amount of the non-uniformity error of the sub-mirror curvature radius in the optical simulation software, extract the change amount of the defocus aberration of the off-axis subsystem. The ratio of the change amount of the non-uniformity error of the sub-mirror curvature radius to the change amount of the defocus aberration of the off-axis subsystem is the coefficient of the linear relationship. Thus, determine the approximate linear relationship between the sub-aperture defocus aberration and the non-uniformity error of the corresponding sub-mirror curvature radius; Step 6: Calculate the non-uniformity error of the corresponding sub-mirror curvature radius according to the difference value of the defocus aberration in the wave aberration of each sub-aperture.

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