Free-form surface-based entrance pupil coaxial space gravitational wave detection telescope and its design method

Abstract

The present invention provides a free-form surface-based coaxial space gravitational wave detection telescope with an entrance and exit pupil, and a design method thereof, to address the technical problems that existing off-axis five-transistor space gravitational wave detection telescopes with coaxial entrance and exit pupils cannot simultaneously achieve low TTL coupling noise and low backward stray light distribution, or that the introduction of more free-form surfaces into the coaxial space gravitational wave detection telescope with an entrance and exit pupil increases the system size and error sources, and increases the difficulty of assembly and adjustment. The free-form surface-based coaxial space gravitational wave detection telescope of the present invention, based on the coaxial entrance and exit pupil design, sets four mirrors as free-form surface reflectors, and the incident angles of the third and fourth mirrors are the same, thereby achieving low far-field wavefront distortion while reducing TTL coupling noise and ensuring high wavefront quality. At the same time, considering the impact of free-form surface processing technology on system performance, the incident angles of the third and fourth mirrors are uniformly designed, which can effectively reduce backward stray light.

Description

Technical Field

[0001] The present invention relates to a space gravitational wave detection telescope, and in particular to an entrance-exit coaxial space gravitational wave detection telescope based on a free-form surface and a design method thereof. Background Art

[0002] Compared to traditional ground-based gravitational wave detection telescopes, space-based gravitational wave detection telescopes have longer baselines and lower background noise, enabling them to detect gravitational wave signals at lower frequencies. Currently, mainstream space-based gravitational wave detection telescopes use ultra-long baseline laser interferometry to extract characteristic signals. For example, the LISA program uses three satellites to form an equilateral triangle with sides as long as 2.5 million kilometers. Laser beams travel back and forth between the satellites to form an interferometric optical path. When gravitational waves pass through, spacetime distortion slightly alters the optical path length (approximately picometers), causing a phase difference in the laser interferometer signal. This weak signal is amplified by the ultra-long baseline accumulation effect, ultimately extracting the characteristic signal caused by the gravitational waves from the ambient signal.

[0003] As a key component of space-based gravitational wave detection technology, space-based gravitational wave telescopes simultaneously collect weak, picowatt-level laser signals transmitted from satellite base stations millions of kilometers away, and transmit watt-level laser signals from local base stations to satellite base stations millions of kilometers away. This enables the integrated transmission and reception of gravitational wave detection laser signals, establishing a stable, million-kilometer-wide, bidirectional detection link between the two base stations. Therefore, space-based gravitational wave telescopes require an extremely high signal-to-noise ratio, specifically requiring extremely low far-field wavefront distortion, extremely low TTL (TTL) coupling noise, and extremely low backward stray light.

[0004] like Figure 1 As shown, the existing off-axis four-mirror space gravitational wave detection telescope with non-coaxial entrance and exit pupils includes a system aperture 01, a primary mirror 02, a secondary mirror 03, a triple mirror 04, a quadruple mirror 05 and a system exit pupil 06, wherein the primary mirror 02 is a parabolic reflector, the secondary mirror 03 is a hyperbolic reflector, and the triple mirror 04 and the quadruple mirror 05 are both spherical reflectors. However, since the entrance and exit pupils are not coaxial, this solution introduces additional TTL coupling noise to the entire system. Although the industry currently adopts a solution with coaxial entrance and exit pupils to effectively reduce TTL coupling noise, it uses an off-axis five-mirror structure to achieve this. As shown Figure 2 、 Figure 3As shown in the figure, off-axis penta-transistor space-based gravitational wave detection telescopes with coaxial entrance and exit pupils include two typical structures: an "S"-type off-axis penta-transistor structure with coaxial entrance and exit pupils and a "δ"-type off-axis penta-transistor structure with coaxial entrance and exit pupils. These structures, respectively, include a coaxial aperture 001, a primary reflector 002, a secondary reflector 003, a triple reflector 004, a quadruple reflector 005, a quintuple reflector 006, and a coaxial exit pupil 007. The difference between the two structures lies in the orientation of the quadruple reflector 005 and the location of the quintuple reflector 006. However, neither of these structures can simultaneously achieve low TTL coupling noise and low backscattered light distribution, resulting in a failure to further improve the overall detection performance of the system. Summary of the Invention

[0005] The purpose of the present invention is to solve the technical problems that the existing off-axis five-transmission space gravitational wave detection telescope with coaxial entrance and exit pupils cannot simultaneously take into account low TTL coupling noise and low backward stray light distribution, resulting in the inability to further improve the overall detection performance of the system, or the introduction of more free-form surfaces in the space gravitational wave detection telescope with coaxial entrance and exit pupils greatly increases the system size and error sources, and the difficulty of assembly and adjustment is also greatly increased. The present invention provides a space gravitational wave detection telescope with coaxial entrance and exit pupils based on free-form surfaces and a design method thereof.

[0006] The technical concept of the present invention is as follows: In order to realize the extremely high signal-to-noise ratio required for a space gravitational wave detection telescope, that is, extremely low far-field wavefront distortion, extremely low TTL coupling noise and extremely low backward stray light, the present invention first adopts the idea of coaxial entrance and exit pupils to reduce TTL coupling noise; secondly, because the introduction of more free-form surfaces will greatly increase the system size and error sources, and greatly increase the difficulty of assembly and adjustment, the present invention only uses Zernike polynomials to optimize the free-form surfaces of four of the mirrors to introduce optimization degrees of freedom, thereby achieving lower far-field wavefront distortion. However, due to the limitations of free-form surface processing technology, the roughness of the surface of the four mirrors is relatively high, and higher roughness will increase the distribution of backward stray light. Therefore, the present invention creatively combines the influence of the incident angle in the reflective light path on the stray light distribution, and divides the 180° turning angle of the overall light path evenly on the three mirrors and the four mirrors. Each reflector is responsible for a 90° turn of the light path, that is, the incident angles of the three mirrors and the four mirrors are set to 45° respectively. This can effectively reduce backward stray light and meet the signal-to-noise ratio requirements of the space gravitational wave detection telescope.

[0007] In order to achieve the above objectives, the technical solutions provided by the present invention are as follows:

[0008] A free-form surface-based entrance and exit pupil coaxial space gravitational wave detection telescope, comprising an aperture stop, a primary mirror, a secondary mirror, a third mirror, a fourth mirror and an exit pupil;

[0009] The primary mirror is a parabolic reflector, the secondary mirror is a hyperbolic reflector, the third mirror is an ellipsoidal reflector, and the fourth mirror is a free-form reflector;

[0010] The aperture stop and the primary mirror are sequentially located on the incident light path of the far-field parallel laser, and the primary mirror and the secondary mirror form a Cassegrain structure;

[0011] The three mirrors are located on the laser light path reflected by the secondary mirror, the four mirrors are located on the laser light path reflected by the three mirrors, and the exit pupil is located on the laser light path reflected by the four mirrors; the three mirrors, the four mirrors, and the exit pupil are all located on the side of the primary mirror away from the aperture stop, and the four mirrors and the exit pupil are located on the central optical axis of the aperture stop;

[0012] The incident angles of the three mirrors and the four mirrors are the same, both recorded as , Determined by the following formula:

[0013]

[0014] In the above formula, is the off-axis distance of the primary mirror, is the length of the entire space gravitational wave telescope optical system, is the distance between the four mirrors and the exit pupil, The distance between the primary mirror and the secondary mirror, is the distance between the secondary mirror and the tertiary mirror; for The upper boundary value of for The lower boundary value of ;

[0015] The primary mirror, secondary mirror, third mirror and fourth mirror do not interfere with each other.

[0016] Furthermore, the incident angles of the three mirrors and the four mirrors are The angle is 45°, which allows the optical axis to pass through two 90° turns and achieve coaxial design of entrance and exit pupils, greatly reducing backward stray light.

[0017] Furthermore, the four mirrors use Zernike polynomials to perform free-form surface optimization.

[0018] Furthermore, the central optical axes of the aperture stop, primary mirror, secondary mirror, third mirror, fourth mirror and exit pupil are located in the same vertical plane, which can avoid introducing additional off-axis aberrations and meet the requirements of miniaturization of the optical system.

[0019] In addition, the present invention also provides a design method for the above-mentioned free-form surface-based entrance and exit coaxial space gravitational wave detection telescope, comprising the following steps:

[0020] Step 1: Determine the distance between the primary and secondary mirrors based on the entrance pupil diameter and geometric dimensions of the space-based gravitational wave detection telescope to be designed, and then construct a Cassegrain structure with the primary and secondary mirrors coaxial. Plan the primary image plane position of the space-based gravitational wave detection telescope to be designed, and de-axis the aperture based on the primary image plane position. After de-axising the aperture, optimize the variable parameters of the Cassegrain structure to ensure that the image of the Cassegrain structure is located at the primary image plane and optimize the image quality to near the diffraction limit.

[0021] Step 2: Place the third mirror on the path of the laser light reflected by the secondary mirror, so that it is located behind the primary image plane and the reflecting surface is set toward the primary mirror, so that the laser light reflected by the third mirror is emitted toward the side of the primary mirror away from the aperture stop; Place the fourth mirror on the path of the laser light reflected by the third mirror, so that the fourth mirror and the exit pupil are located on the central optical axis of the aperture stop;

[0022] Step 3: Select the four-mirror type as the Zernike Fringe (Zernike fringe) sagittal height. Based on the incident wavelength λ, entrance pupil diameter, field of view angle, focal length, and compression ratio of the space-based gravitational wave detection telescope to be designed, the variable parameters of the optical system after adding three or four mirrors are optimized using wave aberration as the evaluation index.

[0023] Step 4: Perform wavefront aberration analysis, TTL coupling noise analysis, and backward stray light analysis on the optical system optimized in step 3. If the results of each analysis meet the corresponding requirements, the variable parameter optimization of the optical system is completed and step 5 is executed. If any analysis result does not meet the corresponding requirements, the incident angle of the three mirrors and the off-axis amount of the four mirrors are adjusted, and the variable parameters of the current optical system are optimized again until the results of each analysis meet the corresponding requirements.

[0024] Step 5: Perform tolerance analysis on the optical system and allocate the mirror processing tolerances and installation tolerances for the primary mirror, secondary mirror, third mirror, and fourth mirror. Then, use the Monte Carlo method to simulate and analyze the mirror processing tolerances and installation tolerances for the primary mirror, secondary mirror, third mirror, and fourth mirror to ensure that the overall optical system meets the qualification rate requirements and complete the design of the free-form surface-based entrance and exit coaxial space gravitational wave detection telescope.

[0025] Furthermore, in step 4, the result of the wavefront aberration analysis must satisfy the following conditions: the wavefront aberration is better than λ / 80;

[0026] The results of the TTL coupled noise analysis must meet the following requirements: TTL coupled noise is less than 25 pm / μrad;

[0027] The results of the backward stray light analysis must meet the following requirements: the backward stray light energy suppression ratio reaches 10 -10 Magnitude.

[0028] Furthermore, in step 1, the variable parameters of the Cassegrain structure include the curvature radius of the primary mirror, the curvature radius of the secondary mirror, and the conic coefficient of the secondary mirror;

[0029] In step 3, the variable parameters of the optical system after adding three mirrors and four mirrors include the curvature radius of the primary mirror, the curvature radius of the secondary mirror, the cone coefficient of the secondary mirror, the curvature radius of the third mirror, the cone coefficient of the third mirror, the curvature radius of the fourth mirror, the cone coefficient of the fourth mirror and the Zernike polynomial aspheric coefficient of the four mirror.

[0030] The beneficial effects of the present invention compared to the prior art are as follows:

[0031] 1. The free-form surface-based entrance-and-exit coaxial space gravitational wave detection telescope provided by the present invention, on the basis of the entrance-and-exit coaxial design, sets the four mirrors as free-form surface reflectors, and the incident angles of the third and fourth mirrors are the same, thereby achieving lower far-field wavefront distortion (low wave aberration) on the basis of reducing TTL coupling noise and ensuring high wavefront quality; at the same time, considering the impact of free-form surface processing technology on system performance, the incident angles of the third and fourth mirrors are designed in a unified manner, which can effectively reduce backward stray light.

[0032] 2. The present invention sets the incident angle of the three-mirror and the four-mirror to 45°, so that the optical axis can achieve two 90° turns and the entrance and exit pupils are coaxial, which greatly reduces the backward stray light. Under the premise of meeting the signal-to-noise ratio requirements of the space gravitational wave detection telescope, the subsequent supporting mechanical structure is light in weight, and the overall structure is compact and more stable, effectively improving the detection performance and reliability of the entire system.

[0033] 3. The present invention introduces the design of a free-form surface on the basis of coaxial entrance and exit pupils, and uses Zernike polynomials to optimize the free-form surface, thereby achieving the purpose of correcting aberrations, improving system imaging quality, and making the structure compact. While ensuring high wavefront quality, the TTL coupling noise caused by wave aberrations can be further reduced, so that the optical path stability, backward stray light distribution and system assembly and processing feasibility of the space gravitational wave detection telescope are taken into account. Compared with the existing off-axis five-transmission space gravitational wave detection telescope with coaxial entrance and exit pupils, the present invention has the advantages of lower assembly difficulty and smaller errors introduced in the later processing links.

[0034] 4. The design method of the free-form surface-based entrance-and-exit coaxial space gravitational wave detection telescope provided by the present invention is based on the Cassegrain structure with coaxial primary and secondary mirrors. At the same time, the four mirror surfaces are selected as the Zernike Fringe (Zernike fringe) sagittal height. Wave aberration is used as an evaluation index and the geometric constraint of entrance-and-exit coaxiality is adopted to optimize the optical system. The optimization variables are relatively few, the method is simple and practical, and good wave aberration can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a schematic diagram of the structure of an existing off-axis quadruple-transmission space gravitational wave detection telescope with different entrance and exit pupil axes;

[0036] Figure 1 The reference numerals are: 01 - system aperture, 02 - primary mirror, 03 - secondary mirror, 04 - triple mirror, 05 - quadruple mirror, 06 - system exit pupil.

[0037] Figure 2 This is a schematic diagram of the structure of an existing "S"-shaped off-axis five-trans space gravitational wave detection telescope with coaxial entrance and exit pupils;

[0038] Figure 3 This is a schematic diagram of the structure of an existing "δ" type off-axis five-trans space gravitational wave detection telescope with coaxial entrance and exit pupils;

[0039] Figure 2 、 Figure 3 The reference numerals are: 001 - coaxial aperture, 002 - primary reflector, 003 - secondary reflector, 004 - triple reflector, 005 - quadruple reflector, 006 - penta reflector, 007 - coaxial exit pupil.

[0040] Figure 4 This is a schematic structural diagram of an embodiment of an entrance / exit coaxial space gravitational wave detection telescope based on a free-form surface according to the present invention;

[0041] Figure 4 The reference numerals are: 1-aperture stop; 2-primary mirror; 3-secondary mirror; 4-third mirror; 5-fourth mirror; 6-exit pupil. DETAILED DESCRIPTION

[0042] In order to make the advantages and features of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] A free-form surface-based coaxial space gravitational wave detection telescope with entrance and exit pupils, such as Figure 4 As shown, the space-based gravitational wave detection telescope is an off-axis quadruple mirror structure, specifically including an aperture stop 1, a primary mirror 2, a secondary mirror 3, a third mirror 4, a fourth mirror 5, and an exit pupil 6. To avoid introducing additional off-axis aberrations and meet the requirements of optical system miniaturization, the central optical axes of the entire optical system in this embodiment are all located in the same vertical plane.

[0044] The primary mirror 2 is a parabolic reflector, the secondary mirror 3 is a hyperbolic reflector, the aperture stop 1 and primary mirror 2 are sequentially located in the incident optical path of the far-field parallel laser, and the secondary mirror 3 is located in the laser optical path after reflection from the primary mirror 2, so that the primary mirror 2 and secondary mirror 3 form a Cassegrain structure. The third mirror 4, the fourth mirror 5, and the exit pupil 6 are all placed on the side of the primary mirror 2 away from the aperture stop 1, that is, the third mirror 4, the fourth mirror 5, and the exit pupil 6 are all located on the non-reflective side of the primary mirror 2.

[0045] The third mirror 4 is an ellipsoidal reflector located in the path of the laser light after reflection by the secondary mirror 3. To make the overall optical system compact and achieve a coaxial structure of the entrance and exit pupils, the reflective surface of the third mirror 4 is set toward the direction of the primary mirror 2, so that the laser light reflected by the third mirror 4 is emitted toward the side of the primary mirror 2 away from the aperture stop 1. The fourth mirror 5 is a free-form surface reflector located in the path of the laser light after reflection by the third mirror 4. The fourth mirror 5 and the exit pupil 6 are both placed on the central optical axis of the aperture stop, thus achieving a coaxial design of the entrance and exit pupils based on the free-form surface.

[0046] In order to reduce the system's backward stray light distribution, since the off-axis amount of the three mirrors 4 is 10 -4 mm level, it can be approximately considered that the optical axis after reflection by the secondary mirror 3 is parallel to the entrance pupil optical axis, so the optical path turning angle of the third mirror 4 and the fourth mirror 5 is Same (the turning angle of the three mirrors 4 That is, the angle between the optical axis after reflection by the secondary mirror 3 and the optical axis after reflection by the third mirror 4, and the turning angle of the optical path of the fourth mirror 5 That is, the angle between the optical axis after reflection by the third mirror 4 and the optical axis after reflection by the fourth mirror 5). Correspondingly, the incident angles of the two are Similarly, the main functions of the three mirrors 4 and the four mirrors 5 are to collimate the light and give the light path a displacement in the direction perpendicular to the entrance pupil axis. The incident angles of the three mirrors 4 and the four mirrors 5 are Determined by the following formula:

[0047] (1)

[0048] In the above formula, is the off-axis amount of the primary mirror 2, is the length of the entire space gravitational wave telescope optical system, is the distance between the four mirrors 5 and the exit pupil 6, is the distance between the primary mirror 2 and the secondary mirror 3, is the distance between the secondary mirror 3 and the tertiary mirror 4, for The upper boundary value of for The lower boundary value of .

[0049] In the design task of this embodiment, the length of the entire space gravitational wave telescope optical system is The minimum distance between the four mirrors 5 and the exit pupil 6 is 100mm. The exit pupil 6 directly faces the interface of the subsequent optical interference platform, that is, the exit pupil 6 is located 100mm behind the reflected light path of the four mirrors 5. Considering the aperture of the main mirror 2 and to ensure that the subsequent light path does not have a central obstruction, the off-axis distance of the main mirror 2 in this embodiment is 800mm. Designed to be 200mm; the distance between primary mirror 2 and secondary mirror 3 =600mm. Since the entrance-exit pupil ratio is 100×, the focal length ratio between the front group composed of primary mirror 2 and secondary mirror 3 and the rear group composed of third mirror 4 and fourth mirror 5 is also 100×. Based on the known distance between the position of the primary real image and the secondary mirror 3, plus the proportionally reduced distance of the rear group, the distance between the secondary mirror 3 and the third mirror 4 is obtained. , at this time, the position of the three mirrors 4 can be determined; after determining the position of the three mirrors 4, the incident angle can be calculated by formula (1) Range 53°> >38°, the position of the fourth mirror 5 is determined according to the intersection of the laser light path after reflection from the third mirror 4 and the entrance pupil optical axis.

[0050] Due to the limitations of free-form surface processing technology, the surface roughness of the quad mirror 5 is relatively high, which will increase the distribution of backward stray light. While changing the light propagation path, it also affects the distribution of stray light, mainly in the following two aspects:

[0051] Geometric shielding effect: large light path turning angle It can make the scattered light at the edge of the primary mirror 2 more difficult to be reflected to the focal plane by the secondary mirror 3, thereby reducing stray light.

[0052] Scattering direction deviation: The scattered light on the surface of the four mirrors 5 may originally propagate along the mirror symmetry direction, but the off-axis design makes the scattered light deviate to the turning angle of the optical path side.

[0053] The scattering caused by the roughness of the free-form surface obeys the distribution of the bidirectional reflectance distribution function (BRDF). In the off-axis design, the light path turning angle Changed the incident angle of the quad mirror 5 and scattering angle Relationship:

[0054] (2)

[0055] In formula (2), is the actual reflection direction of the four mirrors 5, , Surface roughness parameter of the four mirrors 5. Larger optical path turning angle (i.e. smaller angle of incidence ) will cause the stray light distribution to shift to a larger angle, away from the sensitive area of the exit pupil plane. But for the system as a whole, a larger optical path turning angle The result is a longer optical axis dimension, and the larger the dimension, the greater the positioning error will inevitably be introduced in the later stage of assembly and adjustment. Therefore, the present invention numerically simulates the BRDF scattering model of the four mirrors 5 after inputting the spectral power density PSD of the surface topography of the measured surface roughness test sample. When the incident angle of the four mirrors 5 is When the angle approaches 45°, the stray light component caused by the surface roughness of the four mirrors 5 tends to a minimum, which can effectively reduce the processing requirements for the surface roughness of the reflector. Therefore, after comprehensively considering the backward stray light energy suppression effect and the overall size and installation error of the system, the incident angle of the four mirrors 5 is set to Iterative optimization for 45°, that is, the optical path turning angle The incident angles of the third mirror 4 and the fourth mirror 5 are the same, also 45°. After being reflected by the third mirror 4 and the fourth mirror 5, the laser light path as a whole realizes a 180° turn, which is equivalent to the 180° turning angle of the entire light path being evenly divided between the third mirror 4 and the fourth mirror 5, with each reflector taking on a 90° turn.

[0056] Since the far-field parallel laser is non-parallel after being reflected by the primary mirror 2, the secondary mirror 3 and the third mirror 4, the rear group composed of the third mirror 4 and the fourth mirror 5 is designed to treat the first real image formed by the front group composed of the primary mirror 2 and the secondary mirror 3 as a real object, and perform secondary imaging, and finally present parallel light with high wavefront quality at the exit pupil 6.

[0057] The receiving optical path of the free-form surface-based entrance and exit coaxial space gravitational wave detection telescope of the present invention is as follows: the far-field parallel laser emitted by the reference at a distance of millions of kilometers is incident on the reflecting surface of the primary mirror 2 through the aperture stop 1, reflected by the primary mirror 2 and then reflected by the secondary mirror 3, and then reflected by the third mirror 4 and the fourth mirror 5 in sequence, and finally emitted as a parallel light beam at the exit pupil 6 position, and connected to the subsequent optical interference platform.

[0058] The specific design parameters of the primary mirror 2, secondary mirror 3, and tertiary mirror 4 in this embodiment are shown in Table 1:

[0059] Table 1 Optical system parameters

[0060]

[0061] The specific design parameters of the four mirrors 5 are shown in Table 2:

[0062] Table 2 Zernike polynomial aspheric coefficients

[0063]

[0064] In this embodiment, the four mirrors 5 use Zernike polynomials to perform free-form surface optimization (aspheric surface optimization). The Zernike polynomial aspheric surface coefficients use eight high-order coefficients, namely G3, G4, G5, G8, G9, G11, G12, and G17. This increases the degree of freedom in the design of the space gravitational wave detection telescope, and can effectively improve its imaging quality while meeting the system size requirements, so that the system wavefront quality meets the actual detection accuracy requirements.

[0065] At the same time, the present invention also proposes a design method for the above-mentioned free-form surface-based entrance and exit coaxial space gravitational wave detection telescope, which specifically includes the following steps:

[0066] Step 1: Design of the large-aperture optical path at the front end of the space gravitational wave detection telescope.

[0067] According to the optical transmission efficiency requirements of the space gravitational wave detection telescope to be designed, the entrance pupil diameter in this embodiment is determined to be 300mm, and the overall geometric size requirements are further determined. After clarifying the requirements, according to the entrance pupil diameter and overall geometric size requirements of the space gravitational wave detection telescope to be designed, the distance from the aperture stop 1 to the primary mirror 2 is set to 600nm, and then the distance from the primary mirror 2 to the secondary mirror 3 is determined, and the primary mirror 2 and the secondary mirror 3 are built into a coaxial Cassegrain structure. Then, according to the system size requirements, the position of the primary image plane of the space gravitational wave detection telescope to be designed is determined, and the aperture is de-axised according to the position of the primary image plane. After the aperture is de-axis, the curvature radius of the primary mirror 2, the curvature radius of the secondary mirror 3, and the cone coefficient of the secondary mirror 3 are used as optimization items for variable parameter optimization to ensure that the off-axis Cassegrain structure is imaged at the primary image plane, and the imaging quality of the Cassegrain structure is optimized to approach the diffraction limit.

[0068] Step 2: Design of the optical path for the back-end image transfer of the space gravitational wave detection telescope.

[0069] Place the triple mirror 4 in the path of the laser light reflected by the secondary mirror 3, with the triple mirror 4 positioned behind the primary image plane and its reflective surface facing the primary mirror 2. This allows the laser light reflected by the triple mirror 4 to exit the primary mirror 2 on the side away from the aperture stop 1. Then, place the quad mirror 5 in the path of the laser light reflected by the triple mirror 4, with the quad mirror 5 and the exit pupil 6 positioned on the central optical axis of the aperture stop, thereby achieving a coaxial structural design for the entrance and exit pupils. To reduce the distribution of backward stray light in the system, the 180° turning angle of the overall optical path is evenly divided between the triple mirror 4 and the quad mirror 5, with the triple mirror 4 and the quad mirror 5 each taking a 90° turn. Furthermore, an incident angle of 45° effectively reduces the processing requirements for the mirror surface roughness. The optical path is perpendicular to the central optical axis of the aperture stop and is positioned at a 45° angle to the incident light axis after reflection by the secondary mirror 3. Furthermore, the optical path is positioned at a 45° angle to the incident light axis after reflection by the third mirror 4. Taking into account the distribution of backward stray light and the requirements of a compact optical system, a solution for distributing the optical path turning angles is developed. The overall 180° turning angle of the optical path is evenly divided between the third mirror 4 and the fourth mirror 5, with each mirror responsible for a 90° turning of the optical path. This results in parallel laser light reflected by the fourth mirror 5, which then exits in the direction of the central optical axis of the aperture stop 1. At this point, the third mirror 4 and the fourth mirror 5 simultaneously perform the functions of laser collimation and optical path turning.

[0070] Step 3: Introduce a free-form surface mirror to optimize the system optical path.

[0071] The surface shape of the quad mirror 5 is selected as the Zernike Fringe height, and the 17th-order Zernike polynomial aspheric coefficient variables are introduced to increase the degree of freedom of optimization of the system. Based on the operating wavelength, entrance pupil diameter, field of view angle, and magnification requirements of the space-based gravitational wave detection telescope to be designed, the curvature radius of the primary mirror 2, the curvature radius of the secondary mirror 3, the conic coefficient of the secondary mirror 3, the curvature radius of the third mirror 4, the conic coefficient of the third mirror 4, the curvature radius of the fourth mirror 5, the conic coefficient of the fourth mirror 5, and the Zernike polynomial aspheric coefficient of the fourth mirror 5 are optimized with wavefront aberration as the primary evaluation metric. The evaluation metric for wavefront aberration is required to be better than λ / 80.

[0072] Step 4: Perform wavefront aberration analysis, TTL coupling noise analysis, and backward stray light analysis.

[0073] The overall optical system optimized in step 3 is subjected to wavefront aberration analysis, TTL coupling noise analysis, and backward stray light analysis to meet the requirements of high wavefront quality, high optical path stability, and high backward stray light energy suppression ratio for the telescope optical system. Specifically, the wavefront aberration is better than λ / 80, the TTL coupling noise is less than 25pm / μrad, and the backward stray light energy suppression ratio must reach 10 -10 Magnitude.

[0074] If the system analysis results cannot meet the three corresponding requirements at the same time, the incident angle of the third mirror 4 and the off-axis amount of the fourth mirror 5 shall be adjusted, and the curvature radius of the primary mirror 2, the curvature radius of the secondary mirror 3, the cone coefficient of the secondary mirror 3, the curvature radius of the third mirror 4, the cone coefficient of the third mirror 4, the curvature radius of the fourth mirror 5, the cone coefficient of the fourth mirror 5 and the Zernike polynomial aspheric coefficient of the fourth mirror 5 shall be re-optimized until all analysis results meet all corresponding index requirements at the same time.

[0075] Step 5: Perform tolerance analysis to provide guidance accuracy for mirror processing and assembly.

[0076] Perform tolerance analysis on the space-based gravitational wave detection telescope obtained after step 4. Based on the current capabilities of each optical processing link, rationally allocate mirror processing tolerances, such as surface roughness and surface accuracy requirements, for primary mirror 2, secondary mirror 3, third mirror 4, and fourth mirror 5. Also, rationally allocate adjustment tolerances for each assembly step. Monte Carlo analysis is then used to analyze the machining and adjustment tolerances of primary mirror 2, secondary mirror 3, third mirror 4, and fourth mirror 5. This ensures that the overall optical system tolerances meet the required yield rate for the space-based gravitational wave detection telescope, completing the design of the free-form surface-based coaxial space-based gravitational wave detection telescope with both entrance and exit pupils.

[0077] Taking the far-field parallel laser signal power of 1W as a reference example, the backward stray light energy suppression ratio of the existing off-axis four-transmission space gravitational wave detection telescope with non-coaxial entrance and exit pupils, two different structures of the existing off-axis five-transmission space gravitational wave detection telescope with coaxial entrance and exit pupils, and the free-form surface-based space gravitational wave detection telescope with coaxial entrance and exit pupils of the present invention were analyzed under the same test environment. The analysis results are shown in Table 3.

[0078] Table 3 Analysis of backward stray light energy suppression ratio of four optical structures

[0079]

[0080] As can be seen, the backward stray light energy suppression ratio of the free-form surface-based coaxial entrance and exit pupil structure of the present invention is significantly superior to two different structures of existing off-axis five-transposer space-based gravitational wave detection telescopes with coaxial entrance and exit pupils. Furthermore, the TTL coupling noise of the embodiment of the present invention is 3.07 pm / μrad, meeting the detection practicality requirement of 25 pm / μrad. The wavefront aberration within the captured field of view is λ / 126, meeting the far-field wavefront quality requirement of less than λ / 80, ensuring a high signal-to-noise ratio for the space-based gravitational wave detection telescope.

[0081] The above description is only used to illustrate the technical solution of the present invention, rather than to limit it. For ordinary professional and technical personnel in this field, the specific technical solutions recorded in the above embodiments can be modified, or some of the technical features therein can be replaced by equivalents. These modifications or replacements do not cause the essence of the corresponding technical solution to deviate from the scope of the technical solution protected by the present invention.

Claims

1. A free-form surface-based coaxial space telescope for gravitational wave detection with pupils and eyes, characterized by: It includes an aperture stop (1), a primary mirror (2), a secondary mirror (3), a third mirror (4), a fourth mirror (5), and an exit pupil (6); The primary mirror (2) is a parabolic reflector, the secondary mirror (3) is a hyperbolic reflector, the third mirror (4) is an ellipsoidal reflector, and the fourth mirror (5) is a free-form reflector; The aperture stop (1) and the primary mirror (2) are sequentially located on the far-field parallel laser incident light path, and the primary mirror (2) and the secondary mirror (3) form a Cassegrain structure; The three mirrors (4) are located on the laser light path reflected by the secondary mirror (3), the four mirrors (5) are located on the laser light path reflected by the three mirrors (4), and the exit pupil (6) is located on the laser light path reflected by the four mirrors (5); the three mirrors (4), the four mirrors (5) and the exit pupil (6) are all located on a side of the primary mirror (2) away from the aperture stop (1), and the four mirrors (5) and the exit pupil (6) are located on the central optical axis of the aperture stop (1); The incident angles of the three mirrors (4) and the four mirrors (5) are the same, both recorded as , Determined by the following formula: ； In the above formula, is the off-axis amount of the primary mirror (2), is the length of the entire space gravitational wave telescope optical system, is the distance between the four mirrors (5) and the exit pupil (6), is the distance between the primary mirror (2) and the secondary mirror (3), is the distance between the secondary mirror (3) and the tertiary mirror (4); for The upper boundary value of for The lower boundary value of ; The primary mirror (2), the secondary mirror (3), the third mirror (4) and the fourth mirror (5) do not interfere with each other.

2. The free-form surface-based entrance / exit coaxial space gravitational wave detection telescope according to claim 1, characterized in that: The incident angles of the three mirrors (4) and the four mirrors (5) are is 45°.

3. The free-form surface-based entrance / exit coaxial space gravitational wave detection telescope according to claim 1 or 2, characterized in that: The four mirrors (5) are optimized for free-form surfaces using Zernike polynomials.

4. The free-form surface-based entrance / exit coaxial space gravitational wave detection telescope according to claim 3, characterized in that: The central optical axes of the aperture stop (1), the primary mirror (2), the secondary mirror (3), the third mirror (4), the fourth mirror (5) and the exit pupil (6) are located in the same vertical plane.

5. A design method for a free-form surface-based entrance / exit coaxial space gravitational wave detection telescope according to any one of claims 1 to 4, characterized in that: The following steps are involved: Step 1: Determine the distance between the primary mirror (2) and the secondary mirror (3) according to the entrance pupil diameter and geometric dimensions of the space gravitational wave detection telescope to be designed, and then build a Cassegrain structure in which the primary and secondary mirrors are coaxial; propose the position of the primary image plane of the space gravitational wave detection telescope to be designed, and perform aperture off-axis according to the position of the primary image plane; optimize the variable parameters of the Cassegrain structure after the aperture is off-axis to ensure that the imaging of the Cassegrain structure is located at the primary image plane, and optimize the imaging quality to approach the diffraction limit; Step 2: placing the three mirrors (4) on the laser light path reflected by the secondary mirror (3), so that the three mirrors (4) are located behind the primary image plane, and the reflecting surface is set in the direction of the primary mirror (2), so that the laser reflected by the three mirrors (4) is emitted toward the side of the primary mirror (2) away from the aperture stop (1); placing the four mirrors (5) on the laser light path reflected by the three mirrors (4), and at the same time, making the four mirrors (5) and the exit pupil (6) located on the central optical axis of the aperture stop (1); Step 3, the surface shape of the four mirrors (5) is selected as the Zernike Fringe height, and the variable parameters of the optical system after adding the three mirrors (4) and the four mirrors (5) are optimized based on the incident wavelength λ, entrance pupil diameter, field angle, focal length and compression ratio of the space gravitational wave detection telescope to be designed, with wave aberration as the evaluation index; Step 4, performing wavefront aberration analysis, TTL coupling noise analysis, and backward stray light analysis on the optical system optimized in step 3; If all analysis results meet the corresponding requirements, the variable parameter optimization of the optical system is completed and step 5 is executed; if any analysis result does not meet the corresponding requirements, the incident angle of the three mirrors (4) and the off-axis amount of the four mirrors (5) are adjusted, and the variable parameters of the current optical system are re-optimized until all analysis results meet the corresponding requirements; Step 5, perform tolerance analysis on the optical system, allocate the mirror processing tolerance and installation tolerance of the primary mirror (2), secondary mirror (3), third mirror (4) and fourth mirror (5); then use the Monte Carlo method to simulate and analyze the mirror processing tolerance and installation tolerance of the primary mirror (2), secondary mirror (3), third mirror (4) and fourth mirror (5) to ensure that the overall optical system meets the qualification rate requirements and complete the design of the free-form surface-based entrance and exit coaxial space gravitational wave detection telescope.

6. The design method of the free-form surface-based entrance / exit coaxial space gravitational wave detection telescope according to claim 5, characterized in that: In step 4, the result of the wavefront aberration analysis must satisfy the following requirements: the wavefront aberration is better than λ / 80; The results of the TTL coupled noise analysis must meet the following requirements: TTL coupled noise is less than 25 pm / μrad; The results of the backward stray light analysis must meet the following requirements: the backward stray light energy suppression ratio reaches 10 -10 Magnitude.

7. The design method of the free-form surface-based entrance / exit coaxial space gravitational wave detection telescope according to claim 5 or 6, characterized in that: In step 1, the variable parameters of the Cassegrain structure include the curvature radius of the primary mirror (2), the curvature radius of the secondary mirror (3), and the conic coefficient of the secondary mirror (3); In step 3, the variable parameters of the optical system after adding the three mirrors (4) and the four mirrors (5) include the curvature radius of the primary mirror (2), the curvature radius of the secondary mirror (3), the cone coefficient of the secondary mirror (3), the curvature radius of the three mirrors (4), the cone coefficient of the three mirrors (4), the curvature radius of the four mirrors (5), the cone coefficient of the four mirrors (5) and the Zernike polynomial aspheric coefficient of the four mirrors (5).

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