A time-series filtering-based wavefront correction method for a survey telescope

Abstract

The present application relates to the field of active optics, and specifically provides a time series filtering-based wavefront correction method for a survey telescope, which obtains time series wavefront data of the telescope through a wavefront curvature sensor, decomposes the time series wavefront data in a spatial domain through Zernike polynomials, forms a time series coefficient sequence for each term of the Zernike polynomials in a time domain, performs frequency domain analysis on each time series coefficient sequence, calculates a power spectrum, uses a Greenwood frequency as a threshold to identify static aberrations, and performs wavefront correction after filtering out dynamic aberrations. The present application effectively separates and filters out high-frequency disturbances introduced by atmospheric turbulence by combining Zernike polynomial decomposition and frequency domain filtering, and accurately realizes low-frequency aberration wavefront correction through active optics.

Description

Technical Field

[0001] This invention belongs to the field of active optics technology, and particularly relates to a wavefront correction method for survey telescopes based on time-series filtering. Background Technology

[0002] The resolution of large-aperture, wide-field-of-view optical survey telescopes is directly proportional to their aperture, and their light-gathering capacity is directly proportional to the square of the aperture. Increasing the system aperture can effectively improve the sensitivity and resolution of survey observations, resulting in higher-quality field-of-view data. In actual observations, imaging aberrations are affected by atmospheric turbulence and telescope-specific factors (such as telescope gravity, temperature variations, and mechanical stress). Random turbulence causes dynamic distortion of the incident wavefront, introducing wavefront errors, while telescope-specific factors also produce static surface shape errors, all contributing to the final image quality. Traditional wavefront correction schemes uniformly filter aberrations introduced by atmospheric turbulence and telescope-specific factors, leading to overcorrection of low-order aberrations and undercorrection of high-order aberrations.

[0003] Therefore, there is an urgent need to design a method that can accurately extract aberrations introduced by the telescope itself and perform wavefront correction on low-frequency aberrations precisely through active optics. Summary of the Invention

[0004] In view of this, the present invention aims to provide a wavefront correction method for survey telescopes based on time-series filtering, which effectively separates and filters out high-frequency disturbances introduced by atmospheric turbulence, and accurately achieves low-frequency aberration wavefront correction through active optics.

[0005] To achieve the above objectives, the technical solution created by this invention is implemented as follows:

[0006] This invention provides a wavefront correction method for sky survey telescopes based on time-series filtering, comprising:

[0007] S1: Obtain the time-series wavefront data of the telescope through the wavefront curvature sensing method;

[0008] S2: Decompose the time-series wavefront data in the spatial domain using Zernike polynomials, and construct a time-series coefficient sequence in the time domain using the coefficients of each term of the Zernike polynomials;

[0009] S3: Perform frequency domain analysis on the time-series coefficient sequence of each term of the Zernike polynomial and calculate the power spectrum of the time-series coefficient sequence of each term;

[0010] S4: Based on the preset atmospheric turbulence characteristic frequency threshold, analyze the power spectrum of each time series coefficient sequence, identify the part of the power spectrum that is higher than the atmospheric turbulence characteristic frequency threshold as dynamic aberration caused by atmospheric turbulence, and identify the part that is lower than the atmospheric turbulence characteristic frequency threshold as static aberration of the telescope itself.

[0011] S5: Filter out dynamic aberrations and perform wavefront correction based on the time-series wavefront data after filtering out dynamic aberrations.

[0012] Preferably, S1: Acquiring time-series wavefront data of the telescope using a wavefront curvature sensing method, including:

[0013] Real-time acquisition of sequenced star images of the target observed by the telescope;

[0014] Based on each frame of star image in the sequence, the wavefront phase corresponding to each frame of star image across the full aperture of the telescope is restored by wavefront curvature sensing method.

[0015] The wavefront phases corresponding to each frame of star image are sorted in the time domain to form time-series wavefront data.

[0016] Preferably, the wavefront phase calculation formula for each frame of star image is as follows:

[0017] ;

[0018] in, For wavefront curvature, For wavefront phase meter, This represents the pre-focal light intensity distribution. This represents the light intensity distribution after focusing. Total light intensity This is the defocusing amount.

[0019] Preferably, in S3, the power spectrum of each term's time-series coefficient sequence is calculated by performing frequency domain analysis on the time-series coefficient sequence of each term using Fast Fourier Transform.

[0020] Preferably, the atmospheric turbulence characteristic frequency threshold is the Greenwood frequency.

[0021] Preferably, Greenwood frequency The formula for calculation is:

[0022] ;

[0023] in, These are empirical parameters. The average wind speed during the telescope observation process. This is the atmospheric coherence length.

[0024] Preferably, in step S5, the power spectrum after dynamic aberrations are filtered out is inversely transformed to reconstruct the time-series wavefront data after dynamic aberrations are filtered out.

[0025] Preferably, the telescope is a modular telescope, and its mirror surface includes multiple modular sub-mirrors.

[0026] Preferably, the field wavefront of the telescope is reconstructed based on the time-series wavefront data after filtering out dynamic aberrations, and N calibration points are selected on the field wavefront, and the corresponding splicing sub-mirrors for each calibration point are determined.

[0027] Calculate the wavefront eigenvalues ​​for each calibration point;

[0028] Based on the wavefront eigenvalues ​​of each calibration point, wavefront correction is performed sequentially on the corresponding stitched sub-mirrors, and the change in wavefront eigenvalues ​​after wavefront correction is obtained for each stitched sub-mirror.

[0029] A sensitivity matrix is ​​constructed by measuring the change in wavefront eigenvalues ​​corresponding to each calibration point, and wavefront correction is performed on all spliced ​​sub-mirrors based on the sensitivity matrix.

[0030] Preferably, the wavefront eigenvalue S for each calibration point is calculated using the following formula:

[0031] ;

[0032] or, ;

[0033] or, ;

[0034] in, Indicates light intensity. Let M represent the integral variable in the xy plane of the spliced ​​sub-mirror, and M represent the area of ​​the aperture stop region. Indicates the coordinates of the calibration point.

[0035] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0036] This invention utilizes time-series analysis to analyze wavefront curvature sensing results from large-aperture telescopes. It decomposes the time-series wavefront data into Zernike terms of different orders and filters the time-series coefficients at different spatial frequencies using the power spectrum. Furthermore, it filters out dynamic aberrations based on the Greenwood frequency of the atmosphere. By combining Zernike polynomial decomposition with frequency-domain filtering, this invention effectively separates and filters out high-frequency disturbances introduced by atmospheric turbulence. The filtered wavefront data more accurately reflects the actual aberrations of the system, reducing the risk of miscorrection. Moreover, by setting the filtering threshold based on the real-time calculated Greenwood frequency, the system can adaptively adjust the filtering according to different atmospheric conditions, improving the response accuracy of the active optics system. Attached Figure Description

[0037] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0038] Figure 1 This is a flowchart of a survey telescope wavefront correction method based on time-series filtering according to an embodiment of the present invention. Detailed Implementation

[0039] 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 do not constitute a limitation thereof. Similar elements in different embodiments are referred to by associated similar element reference numerals. In the following embodiments, many details are described to facilitate a better understanding of the invention. However, those skilled in the art will readily recognize that some features may be omitted in different situations, or may be replaced by other elements, materials, or methods. In some cases, some operations related to the invention are not shown or described in the specification. This is to avoid obscuring the core parts of the invention with excessive description. For those skilled in the art, detailed description of these related operations is not necessary; they can fully understand the related operations based on the description in the specification and general technical knowledge in the art.

[0040] It should be noted that, unless otherwise specified, the embodiments and features described in this invention can be combined to form various implementations. Furthermore, the order of the steps or actions in the method description can be changed or adjusted in a manner readily apparent to those skilled in the art. Therefore, the various orders in the specification and drawings are merely for the clear description of a particular embodiment and do not imply a mandatory order, unless otherwise stated that a particular order must be followed.

[0041] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0042] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0043] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0044] Please see Figure 1 In one embodiment of the present invention, a survey telescope wavefront correction method based on time-series filtering is provided, comprising:

[0045] S1: Obtain the time-series wavefront data of the telescope through the wavefront curvature sensing method;

[0046] S2: Decompose the time-series wavefront data in the spatial domain using Zernike polynomials, and construct a time-series coefficient sequence in the time domain using the coefficients of each term of the Zernike polynomials;

[0047] S3: Perform frequency domain analysis on the time-series coefficient sequence of each term of the Zernike polynomial and calculate the power spectrum of the time-series coefficient sequence of each term;

[0048] S4: Based on the preset atmospheric turbulence characteristic frequency threshold, analyze the power spectrum of each time series coefficient sequence, identify the part of the power spectrum that is higher than the atmospheric turbulence characteristic frequency threshold as dynamic aberration caused by atmospheric turbulence, and identify the part that is lower than the atmospheric turbulence characteristic frequency threshold as static aberration of the telescope itself.

[0049] S5: Filter out dynamic aberrations and perform wavefront correction based on the time-series wavefront data after filtering out dynamic aberrations.

[0050] Among them, the survey telescope is a modular telescope, whose mirror surface consists of multiple modular sub-mirrors, which are spliced ​​together to form the entire primary mirror surface.

[0051] The process of acquiring time-series wavefront data in step S1 is as follows: the wavefront sensor of the survey telescope acquires a sequence of star images of the target observed by the telescope at a preset sampling frequency. The sequence of star images includes multiple frames of star images that are continuous in time.

[0052] For each frame of a star image sequence, the wavefront phase corresponding to each frame across the telescope's full aperture is reconstructed using a wavefront curvature sensing method. The basic principle of this method is based on the local curvature change of the wavefront at the pupil, calculating wavefront information based on the changes in light intensity distribution between the in-focus and out-of-focus images. Specifically, the wavefront curvature change is estimated based on the difference in light intensity distribution between the in-focus and out-of-focus areas, yielding the wavefront phase corresponding to each frame across the telescope's full aperture as follows:

[0053] ;

[0054] in, For wavefront curvature, For wavefront phase meter, This represents the pre-focal light intensity distribution. This represents the light intensity distribution after focusing. Total light intensity This is the defocusing amount.

[0055] By arranging the wavefront phases corresponding to each frame of star image in chronological order on the time axis, time-series wavefront data can be obtained.

[0056] In step S2, the time-series wavefront data obtained in step S1 is decoupled spatially and temporally, and decomposed in the spatial domain into a set of time-series coefficients corresponding to orthogonal basis functions, which are Zernike polynomials. The coefficients of each term of the Zernike polynomial represent different spatial frequency aberrations. The coefficients of each term of the Zernike polynomial are arranged in the time domain to form a time-series coefficient sequence. Each term of the Zernike polynomial can constitute a time-series coefficient sequence, and each time-series coefficient sequence includes multiple time-domain discrete coefficients of a certain order of the Zernike polynomial.

[0057] In step S3, the time-series coefficient sequence is transformed from the time domain to the frequency domain for characterization, and the distribution of the wavefront phase in the frequency domain is analyzed. A Fast Fourier Transform (FFT) is performed on the time-series coefficient sequence generated for each order term of the Zernike polynomial to achieve frequency domain analysis. Based on the FFT results, the power spectral density estimate of each sequence is calculated, i.e., the power spectrum of each time-series coefficient sequence is obtained, which reflects the distribution of the wave energy of each order coefficient at different time frequencies.

[0058] In step S4, after obtaining the power spectrum of each time-series coefficient sequence, aberration analysis and filtering are performed using a preset atmospheric turbulence characteristic frequency threshold. Specifically, the preset atmospheric turbulence characteristic frequency threshold uses the Greenwood frequency. The formula for calculation is:

[0059] ;

[0060] in, These are empirical parameters. The average wind speed during the telescope observation process. This is the atmospheric coherence length.

[0061] Using Greenwood frequency The power spectrum of each time-series coefficient sequence is divided, and frequencies higher than the Greenwood frequency are selected from the power spectrum. Partially identified as dynamic aberrations caused by atmospheric turbulence. Frequency in the power spectrum below the Greenwood frequency... The partial identification is due to the static aberration of the telescope itself. This part of the static aberration needs to be corrected by wavefront through an active optics system, which avoids the problem of traditional blind uniform correction.

[0062] In step S5, frequencies in the power spectrum higher than the Greenwood frequency are... The dynamic aberrations are filtered out, retaining the target frequency band. The power spectrum after dynamic aberration removal is then subjected to an inverse fast Fourier transform. The frequency domain information of each Zernike mode is converted into time domain data, and wavefront reconstruction is performed using the time-series wavefront data after dynamic aberration removal. The reconstructed wavefront data is used as the wavefront error signal and input to the active optics system for wavefront correction. This addresses the impact of rapidly changing atmospheric turbulence on wavefront distortion correction introduced by the telescope itself.

[0063] As an optional embodiment, the method for wavefront correction based on time-series wavefront data after filtering out dynamic aberrations includes the following steps:

[0064] Based on the time-series wavefront data after filtering out dynamic aberrations, the quasi-static field wavefront of the telescope mosaic field of view is reconstructed using a wavefront reconstruction algorithm. N calibration points are selected based on the distribution of the mosaic sub-mirrors, and the corresponding mosaic sub-mirror for each calibration point is determined. N is greater than or equal to 2, typically taking values ​​of 4, 6, or 8. The calibration points are selected using a uniform distribution.

[0065] For each selected calibration point, the wavefront aberration of each calibration point is extracted from the reconstructed field wavefront, and the wavefront feature value of each calibration point is calculated to represent the wavefront situation of the corresponding stitched sub-mirror. The feature value characterizes the contribution of the pose error of the corresponding stitched sub-mirror to the wavefront aberration.

[0066] The formula for calculating the wavefront eigenvalue S at each calibration point is:

[0067] ;

[0068] or, ;

[0069] or, ;

[0070] in, Indicates light intensity. Let M represent the integral variable in the xy plane of the spliced ​​sub-mirror, and M represent the area of ​​the aperture stop region. This represents the coordinates of the calibration point. Any one of the three calculation formulas can be chosen to calculate the corresponding function value, which serves as the wavefront characteristic value for each calibration point.

[0071] Based on the wavefront eigenvalues ​​of each calibration point, the pose of the corresponding mosaic sub-mirrors at each calibration point is sequentially adjusted to achieve wavefront correction. After wavefront correction for each mosaic sub-mirror, the wavefront data of the telescope is measured again. By comparing the changes in the wavefront eigenvalues ​​of the telescope before and after adjustment for each calibration point, the mapping relationship between the pose adjustment amount of each mosaic sub-mirror and the change in the telescope's wavefront eigenvalues ​​is determined. A sensitivity matrix is ​​constructed from the changes in the wavefront eigenvalues ​​of each mosaic sub-mirror at each calibration point. The sensitivity matrix is ​​then used to calculate the pose adjustment amounts required for other mosaic sub-mirrors. Wavefront correction is then performed on all mosaic sub-mirrors, thereby achieving phase and confocal alignment of the entire mosaic telescope's primary mirror and improving the overall imaging quality of the telescope system.

[0072] In summary, the above description is merely a preferred embodiment of this specification and is not intended to limit the scope of protection of this specification. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this specification should be included within the scope of protection of this specification.

[0073] The systems, apparatuses, modules, or units described in one or more of the above embodiments may be implemented by a computer chip or entity, or by a product having a certain function. A typical implementation device is a computer. Specifically, a computer may be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smartphone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or any combination of these devices.

[0074] It should also be noted that 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 limitation, 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.

[0075] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments.

Claims

1. A method for wavefront correction of a sky survey telescope based on time-series filtering, characterized in that, include: S1: Obtain the time-series wavefront data of the telescope through the wavefront curvature sensing method; S2: Decompose the time-series wavefront data in the spatial domain using Zernike polynomials, and construct a time-series coefficient sequence in the time domain using the coefficients of each term of the Zernike polynomials; S3: Perform frequency domain analysis on the time-series coefficient sequence of each term of the Zernike polynomial and calculate the power spectrum of the time-series coefficient sequence of each term; S4: Based on the preset atmospheric turbulence characteristic frequency threshold, analyze the power spectrum of each time series coefficient sequence, identify the part of the power spectrum that is higher than the atmospheric turbulence characteristic frequency threshold as dynamic aberration caused by atmospheric turbulence, and identify the part that is lower than the atmospheric turbulence characteristic frequency threshold as static aberration of the telescope itself. S5: Filter out dynamic aberrations and perform wavefront correction based on the time-series wavefront data after filtering out dynamic aberrations.

2. The method for wavefront correction of a sky survey telescope based on time-series filtering according to claim 1, characterized in that, S1: Acquiring time-series wavefront data of the telescope through a wavefront curvature sensing method, including: Real-time acquisition of sequenced star images of the target observed by the telescope; Based on each frame of the star image sequence, the wavefront phase corresponding to each frame of the star image across the full aperture of the telescope is restored by wavefront curvature sensing method. The wavefront phases corresponding to each frame of star image are sorted in the time domain to form time-series wavefront data.

3. The method for wavefront correction of a sky survey telescope based on time-series filtering according to claim 2, characterized in that, The formula for calculating the wavefront phase for each frame of star image is: ； in, For wavefront curvature, For wavefront phase meter, This represents the pre-focal light intensity distribution. This represents the light intensity distribution after focusing. Total light intensity This is the defocusing amount.

4. The method for wavefront correction of a sky survey telescope based on time-series filtering according to claim 1, characterized in that, In step S3, the power spectrum of each term's time-series coefficient sequence is calculated by performing frequency domain analysis on the time-series coefficient sequence of each term using the Fast Fourier Transform.

5. The method for wavefront correction of a sky survey telescope based on time-series filtering according to claim 1, characterized in that, The atmospheric turbulence characteristic frequency threshold is the Greenwood frequency.

6. The method for wavefront correction of a sky survey telescope based on time-series filtering according to claim 5, characterized in that, The Greenwood frequency The formula for calculation is: ； in, These are empirical parameters. The average wind speed during the telescope observation process. This is the atmospheric coherence length.

7. The method for wavefront correction of a sky survey telescope based on time-series filtering according to claim 1, characterized in that, In step S5, the power spectrum after dynamic aberrations are filtered out is inversely transformed to reconstruct the time-series wavefront data after dynamic aberrations are filtered out.

8. The method for wavefront correction of a sky survey telescope based on time-series filtering according to claim 1, characterized in that, The telescope is a modular telescope, and its mirror surface consists of multiple modular sub-mirrors.

9. The method for wavefront correction of a sky survey telescope based on time-series filtering according to claim 8, characterized in that, The wavefront correction based on the time-series wavefront data after filtering out dynamic aberrations includes: The field wavefront of the telescope is reconstructed based on the time-series wavefront data after filtering out dynamic aberrations, and N calibration points are selected on the field wavefront, and the corresponding splicing sub-mirrors for each calibration point are determined. Calculate the wavefront eigenvalues ​​for each calibration point; Based on the wavefront eigenvalues ​​of each calibration point, wavefront correction is performed sequentially on the corresponding stitched sub-mirrors, and the change in wavefront eigenvalues ​​after wavefront correction is obtained for each stitched sub-mirror. A sensitivity matrix is ​​constructed by measuring the change in wavefront eigenvalues ​​corresponding to each calibration point, and wavefront correction is performed on all spliced ​​sub-mirrors based on the sensitivity matrix.

10. The method for wavefront correction of a sky survey telescope based on time-series filtering according to claim 9, characterized in that, The formula for calculating the wavefront eigenvalue S at each calibration point is: ； or, ; or, ; in, Indicates light intensity. Let M represent the integral variable in the xy plane of the spliced ​​sub-mirror, and M represent the area of ​​the aperture stop region. Indicates the coordinates of the calibration point.

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