Multi-target collaborative optimization design method for space gravitational wave telescope and space gravitational wave telescope

Abstract

The invention discloses a multi-target collaborative optimization design method for a space gravitational wave telescope and the space gravitational wave telescope, and solves the technical problem that an existing space gravitational wave telescope design method is difficult to consider wavefront quality, TTL noise suppression, backward stray light control and engineering installation and adjustment feasibility at the same time. The method is characterized in that TTL noise is used as a direct optimization target parallel to a wavefront error, and a space gravitational wave telescope with high robustness on angular jitter and platform micro-vibration is designed by using a minimum Prewitt gradient weighted joint optimization algorithm.

Description

Technical Field

[0001] This invention relates to space gravitational wave telescopes, and more specifically to a multi-objective collaborative optimization design method for space gravitational wave telescopes and a space gravitational wave telescope designed using this method. Background Technology

[0002] The optical performance requirements of space-based gravitational wave telescopes differ fundamentally from those of traditional astronomical telescopes. To ensure the accuracy of inter-satellite laser interferometry measurements, they not only require high wavefront quality to guarantee wavefront accuracy after propagation over extremely long distances, but also extremely high optical path stability and extremely low stray light levels. Among these, the TTL (tilt-to-length) noise introduced by the jitter and wavefront error coupling caused by the satellite platform housing the test mass block, as well as the non-uniformity of wavefront distortion distribution at the entrance pupil, are key factors limiting optical path stability.

[0003] Current design methods for space-based gravitational wave telescopes largely follow the direct optimization method for wavefront errors used in traditional telescopes. This method works by minimizing the residual wave aberrations of the optical system to approximate a single-curvature spherical wave, thereby reducing the variability of the wavefront in different directions within the line-of-sight jitter range and achieving the goal of suppressing TTL noise. However, this traditional method has the following inherent drawbacks:

[0004] 1) The high-order complex surface shape introduced to optimize wavefront error has greatly increased the difficulty of achieving high-precision machining and ultra-smooth surface machining. When the surface roughness is difficult to reach 5 Å or even 2.5 Å, the backscattering caused by its surface defects cannot be effectively suppressed. Therefore, there is a problem that it is difficult to meet the requirements of low TTL noise and low backscatter light distribution.

[0005] 2) The extremely high wavefront quality requirements make space gravitational wave telescopes extremely sensitive to assembly and adjustment tolerances. The design method based on complex surface combinations has many assembly and adjustment dimensions and small tolerances, which can easily exceed the existing process capabilities and make it difficult to achieve. Furthermore, the all-microcrystalline glass hydroxide catalytic bonding process used in the assembly and adjustment process is irreversible. Once cured, there is no room for subsequent adjustment and compensation. This places almost stringent requirements on the initial assembly and adjustment tolerances. Excessive assembly and adjustment errors will increase the risk of failure. Therefore, there is a problem of not being able to balance low TTL noise and high assembly and adjustment tolerance requirements.

[0006] 3) Traditional designs often require a difficult trade-off between complex freeform surfaces and ultra-smooth fabrication to suppress backscattering, making it difficult to simultaneously meet the stringent background noise requirements for scientific measurements. To avoid high-order complex surface shapes and tolerance sensitivity, simple spherical or low-order aspherical designs are often used. This design approach sacrifices system compactness, resulting in a significant increase in the axial dimensions and overall volume of space gravitational wave telescopes. In space applications, this directly translates into more severe thermal control challenges and lower structural natural frequencies, which is detrimental to achieving ultra-high optical path stability. Summary of the Invention

[0007] The purpose of this invention is to solve the technical problems that existing space gravitational wave telescope design methods cannot simultaneously take into account wavefront quality, TTL noise suppression, backscatter control, and engineering assembly feasibility, and to provide a multi-objective collaborative optimization design method for space gravitational wave telescopes and a space gravitational wave telescope.

[0008] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0009] A multi-objective cooperative optimization design method for a space-based gravitational wave telescope, characterized by the following steps:

[0010] S1. Construct the initial structure of the space gravitational wave telescope and obtain the initial structural parameters. The initial structure includes a primary mirror, a secondary mirror, a third mirror, a fourth mirror, and an aperture stop. The laser signal from the far-field transmitter is incident on the primary mirror, and after being imaged at the intermediate image plane by the primary mirror and the secondary mirror in sequence, it is reflected by the third mirror and the fourth mirror in sequence and then emitted in parallel to the aperture stop.

[0011] The structural parameters include: the primary mirror's reflecting surface type, vertex radius of curvature, quadratic surface coefficient, and its distance from the secondary mirror; the secondary mirror's reflecting surface type, vertex radius of curvature, quadratic surface coefficient, and its distance from the intermediate image plane; the intermediate image plane's tilt angle and its distance from the third mirror; the third mirror's reflecting surface type, tilt angle, tilt type, and its distance from the fourth mirror; and the fourth mirror's reflecting surface type, tilt angle, tilt type, and its distance from the aperture stop.

[0012] S2. The minimum Prewitt gradient weighted joint optimization algorithm is used to determine the magnitude and spatial distribution characteristics of TTL noise in the initial structure within the full aperture and full field of view;

[0013] S3. Based on the magnitude and spatial distribution characteristics of TTL noise, construct an error control function based on multi-objective cooperation;

[0014] S4. Using the error control function as the evaluation function, input the initial structural parameters into the optical design software and the error control function into the macro program for optical parameter optimization. Use the macro program to drive the optical design software to perform iterative optimization calculations. Adjust the initial structural parameters during the iteration process until the value of the error control function meets the preset target value, then terminate the calculation to obtain the optimized structural parameters.

[0015] S5. Based on the optimized structural parameters, analyze whether the tolerances of the initial structure meet the preset tolerances. If not, adjust the weighting factor of the error control function and return to step S4. If yes, proceed to step S6.

[0016] S6. Based on the optimized structural parameters, analyze whether the stray light of the initial structure meets the preset index. If not, adjust the weight factor of the error control function and return to step S4. If yes, use the optimized structural parameters as the design parameters of the space gravitational wave telescope to complete the design of the space gravitational wave telescope.

[0017] Furthermore, step S2 is detailed as follows:

[0018] S2.1. Divide the entire field of view of the initial structure into m×n field of view grids, and set the coordinates of the sampling points of the current field of view grid. Initialize to , ,in, , ;

[0019] S2.2 Calculate the full aperture optical path distribution matrix of the predefined central field of view;

[0020] S2.3 Calculate the optical path length of the current field of view grid at the exit pupil position;

[0021] S2.4 Based on the optical path length of the current field of view grid at the exit pupil position, calculate the optical path length of the initial structure at different apertures at the exit pupil position in sequence to obtain the full aperture optical path distribution matrix of the initial structure at the exit pupil position under the current field of view grid.

[0022] S2.5 Calculate the deviation matrix between the full aperture optical path distribution matrix of the current field of view grid and the full aperture optical path distribution matrix of the center field of view;

[0023] S2.6. Based on the deviation matrix, calculate the magnitude and spatial distribution characteristics of the TTL noise at the sampling point location of the current field of view grid.

[0024] S2.7, Order ,judge Whether it is true or not, if so, then according to , Redetermine the current field of view grid and return to step S2.3; otherwise, proceed to step S2.8.

[0025] S2.8, Order ,judge Whether it is true or not, if so, then according to , Re-determine the current field of view grid and return to step S2.3. If not, obtain the magnitude and spatial distribution characteristics of TTL noise at the sampling point locations of m×n field of view grids and proceed to step S2.9.

[0026] S2.9. Based on the magnitude and spatial distribution characteristics of TTL noise at the sampling points of m×n field-of-view grids, determine the magnitude and spatial distribution characteristics of TTL noise of the initial structure in the full aperture and full field of view.

[0027] Furthermore, in step S3, the constructed error control function based on multi-objective cooperation is as follows:

[0028]

[0029] In the formula, For error control function, This represents the wavefront error at the exit pupil position of the space gravitational wave telescope. for Weighting factors; To determine the magnitude and spatial distribution characteristics of TTL noise within the full aperture at the exit pupil position of the effective field of view, for Weighting factors; Errors caused by ensuring structural parameters for Weighting factors; Indicates full field of view Coordinates of sampling points in the inner field of view grid , Represents the coordinates of the sampling point The area of ​​the micro-element.

[0030] Furthermore, in step S1, when constructing the initial structure of the space gravitational wave telescope, a mathematical relationship model between the tilt angle of the third reflecting mirror and the tilt angle of the fourth reflecting mirror is established through geometric optics analysis:

[0031]

[0032] In the formula, Let be the parallelism error between the incident ray at the entrance pupil position and the exit ray at the exit pupil position of the space gravitational wave telescope, and its value satisfies... , The tilt angle of the intermediate image plane. The tilt angle of the third reflecting mirror. The tilt angle of the fourth reflecting mirror;

[0033] In step S1, when constructing the initial structure of the space gravitational wave telescope, the following conditions should be met when setting the tilt angles of the third and fourth reflecting mirrors:

[0034] .

[0035] Furthermore, in step S1, the initial structure of the space gravitational wave telescope is constructed using a mirror splicing strategy.

[0036] Meanwhile, the present invention also provides a space gravitational wave telescope, which is special in that it is obtained by adopting the above-mentioned multi-objective collaborative optimization design method of space gravitational wave telescope, including a primary mirror, a secondary mirror, a third mirror, a fourth mirror and an aperture stop. The laser signal from the far-field transmitting end is incident on the primary mirror, and after being imaged at the intermediate image plane by the primary mirror and the secondary mirror in sequence, it is reflected by the third mirror and the fourth mirror in sequence and then emitted in parallel to the aperture stop.

[0037] Furthermore, the primary mirror has a quadric surface with a vertex radius of curvature ranging from -1298.56±20mm and a quadric surface coefficient ranging from -1±0.22, and its distance from the secondary mirror ranges from -625.78±12mm; the secondary mirror has a hyperboloid surface with a vertex radius of curvature ranging from -49.105±5mm and a quadric surface coefficient ranging from -1.187±0.22, and its distance from the intermediate image plane ranges from 547.87±10mm; the intermediate image plane has a distance from the third mirror ranging from 251±10mm and a tilt angle ranging from -0.75±0.45°; the third mirror has a second-order freeform surface with a distance from the fourth mirror ranging from -92.48±12mm; and the fourth mirror has a planar surface with a distance from the aperture stop ranging from 270±9mm.

[0038] Furthermore, the tilt angle of the third reflecting mirror satisfies The tilt type is eccentric bending;

[0039] The tilt angle of the fourth reflecting mirror satisfies The tilt type is eccentric bending.

[0040] Furthermore, the primary mirror has a quadric surface with a vertex radius of curvature of -1298.56 mm and a quadric surface coefficient of -1, and its distance from the secondary mirror is -625.78 mm; the secondary mirror has a hyperboloid surface with a vertex radius of curvature of -49.105 mm and a quadric surface coefficient of -1.187, and its distance from the intermediate image plane is 547.87 mm; the intermediate image plane has a tilt angle of -0.75°, and its distance from the third mirror is 251 mm; the third mirror has a second-order freeform surface with a tilt angle of 12.5° and an eccentric curvature, and its distance from the fourth mirror is -92.48 mm; the fourth mirror has a planar surface with a tilt angle of -12.125° and an eccentric curvature, and its distance from the aperture stop is 270 mm.

[0041] Meanwhile, the present invention also provides a receiver for a long-distance laser communication system. Its special feature is that it is obtained by adopting the multi-target collaborative optimization design method of the above-mentioned space gravitational wave telescope, including a primary mirror, a secondary mirror, a third mirror, a fourth mirror, and an aperture stop. The laser signal from the far-field transmitter is incident on the primary mirror, and after being imaged at the intermediate image plane by the primary mirror and the secondary mirror in sequence, it is reflected by the third mirror and the fourth mirror in sequence and then emitted in parallel to the aperture stop.

[0042] Compared with the prior art, the present invention has the following beneficial technical effects:

[0043] 1. This invention provides a multi-objective collaborative optimization design method for space gravitational wave telescopes. It employs a minimum Prewitt gradient weighted joint optimization algorithm to precisely control the magnitude and spatial distribution characteristics of TTL noise in the entire aperture and field of view of the space gravitational wave telescope. This method achieves a fundamental shift from passively suppressing wavefront aberrations to indirectly reduce noise, to actively suppressing noise by directly controlling the wavefront distortion distribution using gradient weighting. It can customize the design and constraint of TTL noise performance of space gravitational wave telescopes for different mission requirements, balancing the contradiction between noise suppression and surface simplification.

[0044] 2. This invention discloses a multi-objective collaborative optimization design method for a space gravitational wave telescope. The constructed error control function based on multi-objective collaboration incorporates TTL noise as an independent optimization objective, integrating it alongside wavefront error, structural and manufacturing tolerances into the optimization process. Through macro-program iteration, the optimal solution is achieved, balancing low TTL noise, low backscattered light distribution requirements, and high assembly tolerance requirements.

[0045] 3. This invention provides a multi-objective collaborative optimization design method for a space gravitational wave telescope. Through geometric optics analysis, the tilt angle relationship model of the third and fourth reflecting mirrors is determined. This allows the design process to select only the tilt angle of one mirror, and simultaneously ensure the spatial separation of the primary and secondary mirrors in the vertical axis direction (Y-axis) and the parallelism of the outgoing and incoming optical axes by adjusting the tilt of the image plane. This greatly simplifies the evaluation function and promotes the rapid optimization and convergence of structural parameters.

[0046] 4. The present invention provides a space gravitational wave telescope that, while meeting the TTL noise index (1 pm / nrad) and wavefront requirements, significantly simplifies the optical structure and greatly reduces the number and order of surface shapes: the number of required high-order complex surface shapes is reduced from three off-axis high-order aspherical surfaces with 10th-order terms to only one second-order freeform surface, and the fourth reflecting mirror is simplified to a plane, reducing the challenge of ultra-high surface finish processing. This makes it easier to obtain the mirror surface quality required to meet the ultra-low stray light index under existing processing capabilities, and effectively controls the backscattered light level from the source.

[0047] 5. The present invention provides a space gravitational wave telescope whose simplified surface shape directly leads to a significant relaxation of tolerances. Specifically, the curvature radius tolerance of the primary mirror is relaxed from 5 μm to 1 mm; the eccentricity tolerance of the primary mirror is relaxed from 0.5 μm to 10 μm; the tilt tolerance of the secondary mirror is relaxed from 5.4″ to 20″; and the tilt tolerance of the third and fourth mirrors is relaxed from 0.6′ to 10′, which greatly reduces the assembly and adjustment risks of the all-microcrystalline glass bonding structure. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating an embodiment of the multi-objective collaborative optimization design method for a space gravitational wave telescope according to the present invention.

[0049] Figure 2 This is a schematic diagram of the structure of an embodiment of the space gravitational wave telescope of the present invention;

[0050] Figure 3 This is a mathematical model diagram showing the tilt angles of the third and fourth reflecting mirrors in step S1 of an embodiment of the multi-objective collaborative optimization design method for a space gravitational wave telescope of the present invention.

[0051] Figure 4 This is a flowchart illustrating the minimum Prewitt gradient weighted joint optimization algorithm in step S2 of an embodiment of the multi-objective collaborative optimization design method for a space gravitational wave telescope of the present invention.

[0052] Figure 5 This is a full-field TTL noise distribution diagram along the Y-axis of an embodiment of the multi-objective collaborative optimization design method for a space gravitational wave telescope of the present invention.

[0053] Figure 6 This is a distribution diagram of the TTL noise gradient variation values ​​along the Y-axis in the full field of view of an embodiment of the multi-objective collaborative optimization design method for a space gravitational wave telescope of the present invention.

[0054] The annotations in the attached figures are explained as follows:

[0055] 1-Primary mirror, 2-Secondary mirror, 3-Intermediate image plane, 4-Third reflecting mirror, 5-Fourth reflecting mirror, 6-Aperture stop. Detailed Implementation

[0056] To make the objectives, advantages, and features of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Those skilled in the art should understand that these embodiments are merely used to explain the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0057] This embodiment provides a multi-objective collaborative optimization design method for a space gravitational wave telescope, realizing the design of a space gravitational wave telescope with low TTL noise and relaxed tolerances, which has high engineering feasibility under the current manufacturing technology level. Its core lies in constructing a comprehensive evaluation function that simultaneously considers wavefront error, TTL noise, and structural parameter assurance. Wavefront error is analyzed using methods such as inter-satellite full-link transmission simulation to identify optical aberrations sensitive to TTL noise. Other aberrations are not overly constrained; a wavefront error sufficient to meet the acquisition requirements of traditional telescopes is sufficient. The TTL noise optimization process employs a minimum Prewitt gradient weighted joint optimization algorithm. By directly constraining the TTL noise within a reasonable range across the entire field of view and controlling the derivative of the TTL noise, noise abrupt changes within the effective field of view are avoided, ultimately obtaining an optical structure that achieves the best balance between performance and feasibility.

[0058] like Figure 1 As shown in the figure, this embodiment presents a multi-objective cooperative optimization design method for a space gravitational wave telescope, which includes the following steps:

[0059] S1. Construct the initial structure of the space gravitational wave telescope and obtain the initial structural parameters. See [link to documentation]. Figure 2 The optical structure of this space gravitational wave telescope is an off-axis three-mirror system plus a plane mirror, including a primary mirror 1, a secondary mirror 2, a third mirror 4, a fourth mirror 5, and an aperture stop 6. After the laser signal from the far-field transmitter is transmitted over an ultra-long distance, it first enters the primary mirror 1, and is then imaged at the intermediate image plane 3 by the primary mirror 1 and the secondary mirror 2 in sequence. After being reflected by the third mirror 4 and the fourth mirror 5 in sequence, it is emitted in parallel to the aperture stop 6. Each mirror is bonded to the substrate of the space gravitational wave telescope using a hydroxide bonding process.

[0060] The structural parameters include: the type of the reflecting surface of the primary mirror 1, the vertex radius of curvature, the quadratic surface coefficient, and its distance from the secondary mirror 2; the type of the reflecting surface of the secondary mirror 2, the vertex radius of curvature, the quadratic surface coefficient, and its distance from the intermediate image plane 3; the tilt angle of the intermediate image plane 3 and its distance from the third reflecting mirror 4; the type of the reflecting surface of the third reflecting mirror 4, the tilt angle, the tilt type, and its distance from the fourth reflecting mirror 5; and the type of the reflecting surface of the fourth reflecting mirror 5, the tilt angle, the tilt type, and its distance from the aperture stop 6.

[0061] Furthermore, through geometric optics analysis, a mathematical model was established to show the relationship between the tilt angle of the third mirror 4 and the tilt angle of the fourth mirror 5. This reduced the coupling error between the space gravitational wave telescope and the back-end optical measurement module, and improved the ease of assembly and adjustment.

[0062]

[0063] In the formula, The parallelism error between the incident ray at the entrance pupil and the exit ray at the exit pupil of the space gravitational wave telescope, whose value satisfies... , The tilt angle of the intermediate image plane 3. The tilt angle of the third reflecting mirror 4. The tilt angle of the fourth reflecting mirror 5 is as follows: Figure 3 As shown, XOY is the coordinate system of the intermediate image plane 3, X'O'Y' is the coordinate system of the third mirror 4, and X"O"Y" is the coordinate system of the fourth mirror 5. Once the tilt angle of either the third mirror 4 or the fourth mirror 5 is initially selected, the angle of the other mirror can be adjusted by measuring the tilt angle of the intermediate image plane 3 once to compensate for the tilt angle. This ensures the parallelism of the exit and incident optical axes of the space gravitational wave telescope, guarantees the perpendicularity of the exit pupil position to the support plate, and reduces the difficulty of assembly, adjustment, and testing.

[0064] By employing the tilted asymmetric structure of the third and fourth mirrors 4 and 5—that is, a differentiated tilt angle design—the remaining aberrations of the primary mirror 1 and secondary mirror 2 are compensated for by higher-order asymmetric sensitive aberrations caused by the off-aperture optical structure. Furthermore, the tilt angles of the third and fourth mirrors 4 and 5 must meet at least the following angle range to ensure the overall performance of the space gravitational wave telescope. -10 The level of stray light suppression.

[0065] The tilt angles of the third reflecting mirror 4 and the fourth reflecting mirror 5 satisfy the following conditions:

[0066] .

[0067] In step S1, the process of constructing the initial structure of the space gravitational wave telescope using a mirror stitching strategy is as follows:

[0068] S1.1 Based on the aperture, field of view, and center obstruction ratio of the secondary mirror 2 relative to the primary mirror 1 of the space gravitational wave telescope, calculate and design a reasonable front sub-optical system, denoted as the first module, which includes the primary mirror 1 and the secondary mirror 2. Adopt a coaxial offset aperture design strategy, and focus on controlling the aberration along the axis in the design to minimize it, while allowing a small amount of transverse aberration to be retained.

[0069] S1.2. Based on the relative aperture of the first module and the angular magnification Γ of the space gravitational wave telescope, determine the field of view Fov2 = Γ × Fov1 of the second module, where Fov1 is the field of view of the first module. Using this as input, conduct the optical design of the second module. The second module consists of a third reflecting mirror 4 and a fourth reflecting mirror 5. A reverse optical path design strategy is adopted. During the design process, light originates from the intermediate image plane 3, is first reflected by the fourth reflecting mirror 5, and then reflected by the third reflecting mirror 4. The design must satisfy the following correspondence:

[0070] a1. The image plane size of the second module is the same as that of the first module;

[0071] a2. At the same position on the image plane, the angle between the light rays of the first module and the optical axis is equal in magnitude but opposite in direction to the angle between the light rays of the second module and the optical axis.

[0072] a3. The absolute value of the distance between the exit pupil position of the second module and the image plane is equal to that of the distance between the exit pupil position of the first module and the image plane, but with opposite signs.

[0073] S1.3. The second module is mirrored and reversed along the Y-axis, and then spliced ​​with the first module at the image plane, ensuring that the exit pupil positions of the two modules coincide, thus obtaining the initial structure of the space gravitational wave telescope.

[0074] S2. The minimum Prewitt gradient weighted joint optimization algorithm is used to determine the magnitude and spatial distribution characteristics of TTL noise in the initial structure across the entire aperture and field of view; such as Figure 4 As shown, the specific process is as follows:

[0075] S2.1. Divide the entire field of view of the initial structure into m×n field of view grids, and set the coordinates of the sampling points of the current field of view grid. Initialize to , ,in, , ;

[0076] S2.2 Calculate the full aperture optical path distribution matrix of the predefined central field of view;

[0077] S2.3 Calculate the optical path length of the current field of view grid at the exit pupil position;

[0078] S2.4 Based on the optical path length of the current field of view grid at the exit pupil position, calculate the optical path length of the initial structure at different apertures at the exit pupil position in sequence to obtain the full aperture optical path distribution matrix of the initial structure at the exit pupil position under the current field of view grid.

[0079] S2.5 Calculate the deviation matrix between the full aperture optical path distribution matrix of the current field of view grid and the full aperture optical path distribution matrix of the center field of view;

[0080] S2.6. Based on the deviation matrix, calculate the magnitude and spatial distribution characteristics of the TTL noise at the sampling point location of the current field of view grid.

[0081] S2.7, Order ,judge Whether it is true or not, if so, then according to , Redetermine the current field of view grid and return to step S2.3; otherwise, proceed to step S2.8.

[0082] S2.8, Order ,judge Whether it is true or not, if so, then according to , Re-determine the current field of view grid and return to step S2.3. If not, obtain the magnitude and spatial distribution characteristics of TTL noise at the sampling point locations of m×n field of view grids and proceed to step S2.9.

[0083] S2.9. Based on the magnitude and spatial distribution characteristics of TTL noise at the sampling points of m×n field-of-view grids, determine the magnitude and spatial distribution characteristics of TTL noise of the initial structure in the full aperture and full field of view.

[0084] The initial structure of the space gravitational wave telescope is optimized for directivity using the minimum Prewitt gradient weighted joint optimization algorithm. While meeting noise requirements and wavefront error, the simplest surface design of the space gravitational wave telescope is achieved, effectively alleviating the contradiction between complex surface shape and high stray light suppression.

[0085] S3. Based on the magnitude and spatial distribution characteristics of TTL noise, construct an error control function based on multi-objective cooperation:

[0086]

[0087] In the formula, For error control function, This represents the wavefront error at the exit pupil position of the space gravitational wave telescope. for Weighting factors; To determine the magnitude and spatial distribution characteristics of TTL noise within the full aperture at the exit pupil position of the effective field of view, for Weighting factors; Errors caused by ensuring structural parameters for Weighting factors; Indicates full field of view Coordinates of sampling points in the inner field of view grid , Represents the coordinates of the sampling point The area of ​​the micro-element.

[0088] S4. Using the error control function as the evaluation function, input the initial structural parameters into the optical design software, and input the preset constraint values ​​and error control function into the macro program used for optical parameter optimization; use the macro program to drive the optical design software to perform iterative optimization calculations, continuously adjusting the initial structural parameters during the iteration process until the value of the error control function meets the preset target value, at which point the calculation terminates, and the optimized structural parameters are obtained; the iterative optimization process is as follows:

[0089] b1. First, increase the weighting factor. The focus is on suppressing aberrations that are sensitive to TTL noise, constraining them to less than λ / 5, where λ is the wavelength, in order to accelerate optimization convergence.

[0090] b2. Introduce the following two terms of the error control function:

[0091] i. Reduce the weighting factor A to decrease the dependence of TTL noise control on the absolute value of wavefront error;

[0092] ii. Increase the weighting factor B to strengthen the constraint on the consistency of wavefront errors in each field of view, realize the direct constraint control of TTL noise, thereby reducing the overall requirement of high-precision wavefront for space gravitational wave telescopes, simplifying the complexity and tolerance sensitivity of reflector surface shape, and improving engineering feasibility;

[0093] iii. By controlling the parallelism of the outgoing and incoming optical axes and structural parameters through the weighting factor C, this part adopts a variable reduction strategy, that is, based on the tilt angle of the primary image plane, the third mirror 4 and its Y-axis eccentricity, five variables are simultaneously constrained, including the parallelism of the outgoing and incoming optical axes, the tilt of the third mirror 4 and the fourth mirror 5, and the Y-axis eccentricity, thereby improving the optimization efficiency.

[0094] b3. In the final optimization stage, the values ​​of each weight factor must satisfy B > C > A.

[0095] S5. Based on the optimized structural parameters, analyze whether the tolerances of the initial structure meet the preset tolerances. If not, adjust the weighting factor of the error control function and return to step S4. If yes, proceed to step S6.

[0096] S6. Based on the optimized structural parameters, analyze whether the stray light of the initial structure meets the preset index. If not, adjust the weight factor of the error control function and return to step S4. If yes, use the optimized structural parameters as the design parameters of the space gravitational wave telescope to complete the design of the space gravitational wave telescope.

[0097] The analysis process for stray light is as follows:

[0098] c1. Calculate the bidirectional scattering distribution function value based on the direction cosine of the light rays on the surface of each mirror and the incident angle;

[0099] c2. Based on the bidirectional scattering distribution function value and the scattering angle of each mirror, calculate the scattering energy within the solid angle and initially set the achievable surface roughness of each mirror.

[0100] c3. Evaluate the stray light generated at the exit pupil position due to the surface roughness of each mirror.

[0101] c4. If the stray light does not meet the requirements, tighten the roughness requirements of the sensitive surface and recalculate the stray light; if tightening the roughness to less than 2 Å still does not meet the requirements, return to step S4 to re-optimize.

[0102] c5. If the cumulative value of stray light on each surface still exceeds the standard, return to step c2 to further tighten the surface roughness requirements; if the surface roughness of all surfaces is already below 2 Å and still cannot meet the requirements, return to step S4 to re-optimize.

[0103] This embodiment describes a space gravitational wave telescope, such as... Figure 2 As shown, the multi-target collaborative optimization design method of the space gravitational wave telescope is adopted, including a primary mirror 1, a secondary mirror 2, a third mirror 4, a fourth mirror 5, and an aperture stop 6. The laser signal from the far-field transmitter is incident on the primary mirror 1, and after being imaged at the intermediate image plane 3 by the primary mirror 1 and the secondary mirror 2 in sequence, it is reflected by the third mirror 4 and the fourth mirror 5 in sequence and then emitted in parallel to the aperture stop 6.

[0104] The primary mirror 1 has a quadric surface with a vertex radius of curvature ranging from -1298.56±20mm and a quadric surface coefficient ranging from -1±0.22. Its distance from the secondary mirror 2 is -625.78±12mm. The secondary mirror 2 has a hyperboloid surface with a vertex radius of curvature ranging from -49.105±5mm and a quadric surface coefficient ranging from -1.187±0.22. Its distance from the intermediate image plane 3 is 547.87±10mm. The intermediate image plane 3 is 251±10mm from the third mirror 4, with a tilt angle ranging from -0.75±0.45° and a basic tilt type. The third mirror 4 has a second-order freeform surface and a distance of -92.48±12mm from the fourth mirror 5. The fourth mirror 5 has a planar surface and a distance of 270±9mm from the aperture stop 6.

[0105] The tilt angle of the third reflecting mirror 4 satisfies The tilt type is eccentric bending; the tilt angle of the fourth reflecting mirror 5 satisfies... The tilt type is eccentric bending.

[0106] Telescope aperture: 300mm, exit pupil diameter: 5mm, optical transmission efficiency: >95%, scientific field of view: ±8 Working field of view: ±20 Field of view: ±200 Far-field wavefront mass root mean square (RMS): < λ / 30@1064nm, stray light / emitted laser power: < 10 -10 TTL noise range: ±3.31×10 -2 pm / nrad.

[0107] The specific structural parameters of the space gravitational wave telescope in this embodiment are shown in Table 1. The primary mirror 1 has a quadric surface with a vertex radius of curvature of -1298.56 mm and a quadric surface coefficient of -1. Its distance from the secondary mirror 2 is -625.78 mm. The secondary mirror 2 has a hyperboloid surface with a vertex radius of curvature of -49.105 mm and a quadric surface coefficient of -1.187. Its distance from the intermediate image plane 3 is 547.87 mm. The intermediate image plane 3 is 251 mm from the third mirror 4, with a tilt angle of -0.75° and a basic tilt type. The third mirror 4 has a second-order freeform surface with a striped Zernike surface. The polynomial is determined to be that the distance between the fourth mirror 5 and the fourth mirror 6 is -92.48 mm, the tilt angle is 12.5°, and the tilt type is eccentric curvature; the reflecting surface of the fourth mirror 5 is a plane, the distance between the fourth mirror 5 and the aperture stop 6 is 270 mm, the tilt angle is -12.125°, and the tilt type is eccentric curvature.

[0108] Table 1

[0109]

[0110] The surface shape data of the third reflecting mirror 4 are shown in Table 2, with a maximum radial order of R. 2 That is, the coefficient of the second-order azimuth-independent term is -0.0477, and the coefficient of the second-order angular modulation component cos(2t) is 0.0014.

[0111] Table 2

[0112]

[0113] Based on the direction cosines of the light rays from each mirror surface and the incident angle, the bidirectional scattering distribution function value is calculated, and the energy within the solid angle range is calculated based on the scattering angle. When the surface roughness of the third mirror 4 is 5 Å, the stray light value caused by the roughness inside the space gravitational wave telescope is 1.16 × 10⁻⁶. -11 The design results have relaxed requirements for surface shape.

[0114] The stray light calculation results within the field of view of each mirror are shown in Table 3. The incident angle of primary mirror 1 is 9.4053°, the roughness is 5 Å, and the BSDF is 3.57 × 10⁻⁶. -6 sr -1 The calculated value is 9.20 × 10 -13 The incident angle of secondary mirror 2 is 9.8127°, the roughness is 2.5 Å, and the BSDF is 8.04 × 10⁻⁶. -7 sr -1 The calculated value is 2.87 × 10 -13 The third reflecting mirror 4 has an incident angle of 12.4559°, a surface roughness of 5 Å, and a BSDF of 1.79 × 10⁻⁶. -6 sr -1 The calculated value is 8.11 × 10 -12 The fourth reflecting mirror 5 has an incident angle of 11.9717°, a surface roughness of 2.5 Å, and a BSDF of 4.92 × 10⁻⁶. -7 sr -1 The calculated value is 2.24 × 10 -12 .

[0115] Table 3

[0116]

[0117] As shown in Table 4, the aspheric coefficient tolerance range of primary mirror 1 is ±0.0004, and the allowable surface shape error is 13.3 nm (1 / 80λ@1064nm); the aspheric coefficient tolerance range of secondary mirror 2 is ±0.003, the allowable surface shape error is 10 nm (1 / 100 / λ@1064nm), and the tilt tolerance range is ±20″; the allowable surface shape error of third mirror 4 is 10 nm (1 / 100 / λ@1064nm), the eccentricity tolerance range is ±0.02 mm, and the tilt tolerance range is ±10′; the allowable surface shape error of fourth mirror 5 is 6 nm (1 / 105λ@1064nm), the eccentricity tolerance range is ±0.02 mm, and the tilt tolerance range is ±10′.

[0118] Table 4

[0119]

[0120] The surface accuracy of the fourth reflector 5 is to suppress backscattering. The third reflector 4 and the fourth reflector 5 are loosely assembled. The third reflector 4 is a second-order freeform surface with a Zernike coefficient tolerance of 1 / 1000. The fourth reflector 5, as a planar reflector, significantly reduces the assembly and adjustment difficulty of the back-end module. In this embodiment, the tilt of the third reflector 4 and the fourth reflector 5 has a minimal impact on system performance, and its tilt error tolerance reaches 0.28°.

[0121] like Figure 5 As shown, the horizontal axis represents the field of view along the Y-axis, and the vertical axis represents the TTL noise within ±20° of the field of view. Within the range, that is, the area between the two vertical dashed lines in the figure, the variation of TTL noise in the horizontal direction corresponding to the Y-axis field of view is... Magnitude.

[0122] like Figure 6 As shown, the horizontal axis represents the field of view along the Y-axis, and the vertical axis represents the TTL noise gradient value. At the edge of the field of view, -200... -150 The TTL noise changes most rapidly between ±20° of the field of view. The TTL noise gradient within the range, i.e., the region between the two vertical dashed lines in the figure, has a gradient of 10. -4 The magnitude of the change is relatively small, with a gradual trend and no significant abrupt changes.

[0123] In summary, the optical system of the space-based gravitational wave telescope has a scientific field of view of ±8... The TTL noise within the range reaches the order of 1 / 1000 pm / nrad, within ±20 The TTL noise level is controlled at 4.06‰ pm / nrad within the specified range. Furthermore, based on the aforementioned curves, the limiting working field of view that meets the TTL noise parameter specifications can be estimated to be within ±80°. The TTL noise design specifications are met within the specified range, providing a possibility for exploring ways to reduce platform stability from an optical design perspective.

[0124] The low TTL noise optical design method based on multi-objective collaborative optimization proposed in this application has technical value not only in the field of space gravitational wave detection. The core of this method lies in solving a universal technical problem: how to ensure the quality and stability of the laser wavefront in environments with angular jitter or platform micro-vibrations, thereby ensuring the reliability of interferometric measurements or communication links. Therefore, this scheme is also applicable to long-distance laser communication systems with extremely high requirements for data transmission quality and bandwidth, such as inter-satellite laser communication, deep space exploration communication, and ground-based free-space optical communication.

[0125] In high-speed laser communication, physical jitter causes rapid spot drift and wavefront distortion at the receiver, which not only reduces signal strength but also introduces high-order phase and amplitude noise, significantly increasing the bit error rate of the communication system and thus limiting its maximum achievable bandwidth. Traditional optical designs for communication terminals often focus on energy efficiency and aberration correction, without prioritizing the suppression of jitter-wavefront coupling noise as a core optimization objective.

[0126] By applying the technical solution proposed in this embodiment, TTL noise is taken as a direct optimization target alongside wavefront error. Using a minimum Prewitt gradient weighted joint optimization algorithm, a laser communication optical system with high robustness to diagonal jitter and platform micro-vibration can be designed. Specifically:

[0127] Improved communication signal-to-noise ratio: By precisely controlling the full aperture and full field of view TTL noise, this embodiment can effectively suppress parasitic phase noise and optical path fluctuations caused by platform vibration coupled wavefront aberrations. This directly enhances the stability of coherent detection at the receiver and significantly reduces the bit error rate of the communication system.

[0128] Unlocking communication bandwidth potential: The reduction in bit error rate and the improvement in phase stability enable communication systems to adopt more efficient modulation and demodulation formats under the same hardware conditions, thereby achieving higher throughput and link bandwidth at the same carrier frequency.

[0129] Enhanced system robustness and reliability: The simplified optical surface and relaxed system tolerances of this embodiment also apply to laser communication terminals. This means that communication terminals can achieve and maintain their top-notch communication performance with lower manufacturing costs, higher assembly and adjustment success rates, and stronger on-orbit environment adaptability.

[0130] Therefore, the scope of protection of this application should be understood to cover all laser transmission systems that employ low TTL noise optical design methods, and their application scenarios are explicitly including but not limited to space gravitational wave detection and long-distance laser communication.

Claims

1. A multi-objective cooperative optimization design method for a space gravitational wave telescope, characterized in that, Includes the following steps: S1. Construct the initial structure of the space gravitational wave telescope and obtain the initial structural parameters. The initial structure includes a primary mirror (1), a secondary mirror (2), a third mirror (4), a fourth mirror (5), and an aperture stop (6). The laser signal from the far-field transmitter is incident on the primary mirror (1), and after being imaged at the intermediate image plane (3) by the primary mirror (1) and the secondary mirror (2) in sequence, it is reflected by the third mirror (4) and the fourth mirror (5) in sequence and then emitted in parallel to the aperture stop (6). The structural parameters include: the type of the primary mirror (1), the vertex radius of curvature, the quadratic surface coefficient, and the distance between it and the secondary mirror (2); the type of the secondary mirror (2), the vertex radius of curvature, the quadratic surface coefficient, and the distance between it and the intermediate image plane (3); the tilt angle of the intermediate image plane (3) and the distance between it and the third mirror (4); the type of the primary mirror (4), the tilt angle, the tilt type, and the distance between it and the fourth mirror (5); the type of the secondary mirror (5), the tilt angle, the tilt type, and the distance between it and the aperture stop (6). S2. The minimum Prewitt gradient weighted joint optimization algorithm is used to determine the magnitude and spatial distribution characteristics of TTL noise in the initial structure within the full aperture and full field of view; S3. Based on the magnitude and spatial distribution characteristics of TTL noise, construct an error control function based on multi-objective cooperation; S4. Using the error control function as the evaluation function, input the initial structural parameters into the optical design software and the error control function into the macro program for optical parameter optimization. Use the macro program to drive the optical design software to perform iterative optimization calculations. Adjust the initial structural parameters during the iteration process until the value of the error control function meets the preset target value, then terminate the calculation to obtain the optimized structural parameters. S5. Based on the optimized structural parameters, analyze whether the tolerances of the initial structure meet the preset tolerances. If not, adjust the weighting factor of the error control function and return to step S4. If yes, proceed to step S6. S6. Based on the optimized structural parameters, analyze whether the stray light of the initial structure meets the preset index. If not, adjust the weight factor of the error control function and return to step S4. If yes, use the optimized structural parameters as the design parameters of the space gravitational wave telescope to complete the design of the space gravitational wave telescope.

2. The multi-objective cooperative optimization design method for a space gravitational wave telescope according to claim 1, characterized in that, Step S2 is as follows: S2.

1. Divide the entire field of view of the initial structure into m×n field of view grids, and set the coordinates of the sampling points of the current field of view grid. Initialize to , ,in, , ; S2.2 Calculate the full aperture optical path distribution matrix of the predefined central field of view; S2.3 Calculate the optical path length of the current field of view grid at the exit pupil position; S2.4 Based on the optical path length of the current field of view grid at the exit pupil position, calculate the optical path length of the initial structure at different apertures at the exit pupil position in sequence to obtain the full aperture optical path distribution matrix of the initial structure at the exit pupil position under the current field of view grid. S2.5 Calculate the deviation matrix between the full aperture optical path distribution matrix of the current field of view grid and the full aperture optical path distribution matrix of the center field of view; S2.

6. Based on the deviation matrix, calculate the magnitude and spatial distribution characteristics of the TTL noise at the sampling point location of the current field of view grid. S2.7, Order ,judge Whether it is true or not, if so, then according to , Redetermine the current field of view grid and return to step S2.3; otherwise, proceed to step S2.

8. S2.8, Order ,judge Whether it is true or not, if so, then according to , Re-determine the current field of view grid and return to step S2.

3. If not, obtain the magnitude and spatial distribution characteristics of TTL noise at the sampling point locations of m×n field of view grids and proceed to step S2.

9. S2.

9. Based on the magnitude and spatial distribution characteristics of TTL noise at the sampling points of m×n field-of-view grids, determine the magnitude and spatial distribution characteristics of TTL noise of the initial structure in the full aperture and full field of view.

3. The multi-objective cooperative optimization design method for a space gravitational wave telescope according to claim 2, characterized in that: In step S3, the error control function based on multi-objective cooperation is constructed as follows: ； In the formula, For error control function, This represents the wavefront error at the exit pupil position of the space gravitational wave telescope. for Weighting factors; To determine the magnitude and spatial distribution characteristics of TTL noise within the full aperture at the exit pupil position of the effective field of view, for Weighting factors; Errors caused by ensuring structural parameters for Weighting factors; Indicates full field of view Coordinates of sampling points in the inner field of view grid , Represents the coordinates of the sampling point The area of ​​the micro-element.

4. The multi-objective cooperative optimization design method for a space gravitational wave telescope according to claim 3, characterized in that: In step S1, when constructing the initial structure of the space gravitational wave telescope, a mathematical relationship model between the tilt angle of the third mirror (4) and the tilt angle of the fourth mirror (5) is established through geometric optics analysis: ； In the formula, Let be the parallelism error between the incident ray at the entrance pupil position and the exit ray at the exit pupil position of the space gravitational wave telescope, and its value satisfies... , The tilt angle of the intermediate image plane (3) is... The tilt angle of the third reflecting mirror (4) is... The tilt angle of the fourth reflecting mirror (5); In step S1, when constructing the initial structure of the space gravitational wave telescope, the following conditions should be met when setting the tilt angles of the third reflecting mirror (4) and the fourth reflecting mirror (5): 。 5. The multi-objective cooperative optimization design method for a space gravitational wave telescope according to claim 4, characterized in that: In step S1, the initial structure of the space gravitational wave telescope is constructed using a mirror splicing strategy.

6. A space-based gravitational wave telescope, characterized in that: The space gravitational wave telescope is designed using the multi-target collaborative optimization design method described in any one of claims 1-5. It includes a primary mirror (1), a secondary mirror (2), a third mirror (4), a fourth mirror (5), and an aperture stop (6). The laser signal from the far-field transmitter is incident on the primary mirror (1), and after being imaged at the intermediate image plane (3) by the primary mirror (1) and the secondary mirror (2) in sequence, it is reflected by the third mirror (4) and the fourth mirror (5) in sequence and then emitted in parallel to the aperture stop (6).

7. The space gravitational wave telescope according to claim 6, characterized in that: The primary mirror (1) has a reflective surface of type quadratic curvature, with a vertex curvature radius ranging from -1298.56±20mm and a quadratic curvature coefficient ranging from -1±0.

22. The distance between the primary mirror (1) and the secondary mirror (2) ranges from -625.78±12mm. The secondary mirror (2) has a hyperboloid surface with a vertex curvature radius of -49.105±5mm and a quadratic surface coefficient of -1.187±0.

22. The distance between the secondary mirror (2) and the intermediate image plane (3) is 547.87±10mm. The distance between the intermediate image plane (3) and the third reflecting mirror (4) is 251±10mm, and the tilt angle is -0.75±0.45°. The third reflector (4) has a second-order freeform surface as its reflective surface, and the distance between it and the fourth reflector (5) is -92.48±12mm. The fourth reflecting mirror (5) has a planar reflective surface and a distance of 270±9mm between it and the aperture stop (6).

8. The space gravitational wave telescope according to claim 7, characterized in that: The tilt angle of the third reflecting mirror (4) satisfies The tilt type is eccentric bending; The tilt angle of the fourth reflecting mirror (5) satisfies The tilt type is eccentric bending.

9. The space gravitational wave telescope according to claim 8, characterized in that: The primary mirror (1) has a quadric surface with a vertex radius of curvature of -1298.56 mm and a quadric surface coefficient of -1. Its distance from the secondary mirror (2) is -625.78 mm. The secondary mirror (2) has a hyperboloid surface with a vertex radius of curvature of -49.105 mm and a quadric surface coefficient of -1.

187. Its distance from the intermediate image plane (3) is 547.87 mm. The tilt angle of the intermediate image plane (3) is - 0.75°, and its distance from the third mirror (4) is 251 mm; the third mirror (4) has a second-order freeform surface with a tilt angle of 12.5° and an eccentric bending tilt, and its distance from the fourth mirror (5) is -92.48 mm; the fourth mirror (5) has a flat surface with a tilt angle of -12.125° and an eccentric bending tilt, and its distance from the aperture stop (6) is 270 mm.

10. A receiver for a long-distance laser communication system, characterized in that: The space gravitational wave telescope is designed using the multi-target collaborative optimization design method described in any one of claims 1-5. It includes a primary mirror (1), a secondary mirror (2), a third mirror (4), a fourth mirror (5), and an aperture stop (6). The laser signal from the far-field transmitter is incident on the primary mirror (1), and after being imaged at the intermediate image plane (3) by the primary mirror (1) and the secondary mirror (2) in sequence, it is reflected by the third mirror (4) and the fourth mirror (5) in sequence and then emitted in parallel to the aperture stop (6).

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