CN115980996B - Design method of space gravitational wave telescope - Google Patents
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Abstract
The invention discloses a design method of a space gravitational wave telescope, relates to the technical field of optical design and optical communication, and solves the problems that the existing gravitational wave telescope does not consider the function of laser signal emission in the design process, cannot meet the optimal design index requirement when being used for emitting laser signals, cannot meet the use requirement and the like. When the telescope is used as a gravitational wave telescope for receiving plane waves, the final evaluation standard is the size of TTL coupling noise. When the telescope is used for emitting Gaussian beams, the divergence angle of the emitted signal beams is ensured to be as small as possible, and the beam waist position of the emitted signal beams is positioned at a certain position between the emitting end and the receiving end, so that the highest energy density and the highest energy of the signals received by the receiving end can be ensured.
Description
Technical Field
The invention relates to the technical field of optical design and optical communication, in particular to a design method of a space gravitational wave telescope.
Background
Since space gravitational wave detection has not yet been formally put into use in China and internationally, all techniques are in an exploration stage, so that mature techniques cannot be referred to. At present, the main stream method for realizing the detection of the space gravitational wave is to adopt a gravitational wave detector of a space laser interferometer to detect the gravitational wave. The gravitational wave detectors of the pair of the space laser interferometers are millions of kilometers apart, when gravitational waves pass through, the optical path between the test masses in the gravitational wave detectors of the two space laser interferometers is changed, and therefore the magnitude of the gravitational waves can be inverted by the change of the optical path, and the space laser interferometers comprise space gravitational wave telescopes and the like.
Because the laser interference method is adopted, the related fields comprise the optical design field and the optical communication technical field. When a telescope is used as the receiving end, the received beam comes from the outside of millions of people and can be considered as a flat-top beam with evenly distributed energy. So when the space gravitational wave telescope is used as the receiving end, its function is equivalent to a conventional optical telescope. When the gravitational wave telescope is used as the transmitting end, the gravitational wave telescope acts as a laser beam expander. In summary, the gravitational wave telescope has the functions of both a transmitting telescope and a receiving telescope, which is very different from the traditional optical telescope. When the gravitational wave telescope transmits laser signals outwards, the transmitting caliber must be large, and the beam waist is positioned on the emergent light path, so that the opposite end can receive the laser signals with enough energy on the distance of millions kilometers, and the traditional laser transmitting device cannot consider.
The existing optical communication technology adopts a point list graph and an evaluation method of surrounding circle energy to determine whether the design index of the optical system meets the requirement.
When the conventional optical telescope is used for imaging, only the advantages and disadvantages of the image quality are considered in the design process, and the Nyquist frequency evaluation or the point list evaluation is generally selected for the evaluation method. When an existing optical telescope is used as a laser emission telescope, only the size of its divergence angle is generally considered. According to the different divergence angles which can be realized by the laser emitting end, the emitting calibers with different sizes are selected. When the gravitational wave is detected, the far-end optical signal is received and the local laser signal is transmitted by adopting the same telescope, so that the space gravitational wave telescope is designed, and the space gravitational wave telescope is considered to be used as a receiving device of the laser signal and a transmitting device of the laser signal. Namely, the designed space gravitational wave telescope not only needs to meet the function of the telescope as a signal receiving telescope, but also meets the requirement of the telescope as a laser signal transmitting device under the condition of the same structural parameter. Meanwhile, as a signal receiving device, the evaluation method is not limited to a point column diagram and a nyquist frequency method, TTL coupling noise and wave aberration are used as standards for evaluating the performance of a receiving-end telescope, the concept and related content of the TTL coupling noise are disclosed in literature 'jittering optical path coupling noise and diffraction (Tilt-to length coupling and diffraction aspects in satellite interferometry),Sonke Schuster,2017,Von der QUEST-Leibniz-Forschungsschule der GottfriedWhihelm Leibniz UniversitazurErlangung des grades,2017 years in inter-satellite interferometry', and an external stray light diaphragm is required to be considered to be eliminated. However, the existing gravitational wave telescope only considers the design of the laser signal receiving end, and does not consider the function of the gravitational wave telescope for transmitting laser signals, so that when the gravitational wave telescope is used for transmitting laser signals, the gravitational wave telescope does not necessarily reach the optimal design index requirement, and therefore, the gravitational wave telescope cannot meet the use requirement.
Disclosure of Invention
The invention provides a design method of a space gravitational wave telescope, which aims to solve the problems that the existing gravitational wave telescope does not consider the function of laser signal emission in the design process, cannot meet the optimal design index requirement when being used for emitting laser signals, cannot meet the use requirement and the like.
A design method of a space gravitational wave telescope designs the telescope into a structure of an off-axis four-inverse telescope; the structure consists of an aperture diaphragm, a parabolic reflector, a hyperboloid reflector, a first spherical reflector and a second spherical reflector, wherein parallel rays at infinity enter a space gravitational wave telescope through the aperture diaphragm, are subjected to primary imaging at a primary imaging surface after passing through the parabolic reflector, and finally exit to an exit pupil position through the spherical reflector and the spherical reflector; the specific design method is realized by the following steps:
Designing a telescope receiving end light path, wherein the receiving end light path comprises an aperture diaphragm, a parabolic reflector and a hyperboloid reflector;
Determining the distance from the aperture diaphragm to the parabolic reflector and the distance from the hyperboloid reflector to the primary image surface according to the envelope size of the optical system, determining the reflection of light rays at infinity through the aperture diaphragm, the parabolic reflector and the hyperboloid reflector, reaching the primary image surface, and finally completing the design of a receiving end light path of the optical system according to the size of the diameter of the entrance pupil, the field of view and the design wavelength;
step two, designing an inverted rear-end optical path, wherein the rear-end optical path comprises a first spherical reflector, a second spherical reflector and an exit pupil position;
Determining the designed image height of the inverted rear-end light path according to the image height of the primary image plane of the receiving-end light path designed in the step one;
determining the size of the entrance pupil diameter of the inverted rear-end light path according to the size of the exit pupil diameter required by design; determining the size of the angle of view of the inverted rear-end light path according to the required angle magnification and the angle of view; finally, the design of an inverted rear-end light path is completed;
Combining the telescope receiving end light path designed in the step one and the inverted rear end light path designed in the step two, and optimizing by taking wave aberration as an index, wherein the requirement of the optimizing index is less than or equal to lambda/30, so as to obtain the primary design of the space gravitation telescope;
step four, taking the light path of the receiving end of the space gravitational wave telescope preliminarily designed in the step three as a transmitting device, optimally designing variable parameters in an optical system, taking a Gaussian beam as a light source, and placing the beam waist of the Gaussian beam at an exit pupil position; performing ray tracing on the emitting device, checking the beam waist position, the diameter of an exit pupil and the size of a divergence angle, ensuring that the diameter of the exit pupil is equal to the diameter of the aperture diaphragm 1, and realizing further optimization of an optical path;
Step five, taking the receiving end light path as a signal receiving device, and returning to the step four if the space gravitational wave telescope meets the technical index requirement that the wave aberration is less than or equal to lambda/30 and the technical index requirement cannot be met; if the technical index requirements can be met, executing the step six;
step six, checking whether the space gravitational wave telescope meets the requirement of TTL coupling noise, if the TTL coupling noise is less than or equal to 25 pm/mu rad, considering that the TTL coupling noise index requirement is met, and executing step seven; if the TTL coupling noise requirement cannot be met, returning to the step one;
And seventhly, carrying out tolerance analysis on the space gravitational wave telescope, namely: and (3) distributing processing and adjustment errors of each optical element of the space gravitational wave telescope, analyzing and simulating whether the yield of the space gravitational wave telescope meets the requirement under the actual condition, and finally designing the space gravitational wave telescope.
The invention has the beneficial effects that:
The space gravitational wave telescope provided by the invention has the function of receiving plane wave beams and the function of emitting Gaussian beams. When the telescope is used as a gravitational wave telescope for receiving plane waves, the final evaluation standard is the size of TTL coupling noise. When the telescope is used for emitting Gaussian beams, the divergence angle of the emitted signal beams is ensured to be as small as possible, and the beam waist position of the emitted signal beams is positioned at a certain position between the emitting end and the receiving end, so that the highest energy density and the highest energy of the signals received by the receiving end can be ensured.
In the invention, when designing the space gravitational wave telescope, the TTL coupling noise is the second largest noise source for space gravitational wave detection according to the practical problem faced by space gravitational wave detection. The telescope is also a main part for generating TTL coupling noise, and the space gravitational wave telescope meeting the use requirement is designed according to the telescope. Second, conventional optical telescopes only consider designing unilateral reception, and do not need to be considered as a laser emitting device. In order to meet the use requirement, the telescope must integrate the signal receiving function of the traditional imaging telescope and the transmitting function of the traditional laser signal transmitting device. The invention completely meets the related requirements and the use requirements of space gravitational wave detection.
Aiming at the designed space laser interference gravitational wave telescope, TTL coupling noise is required to be used as a standard for evaluating whether the telescope is qualified or not. And comparing the size of TTL coupling noise specified in the technical index requirements with the size of TTL coupling noise of the calculated newly designed space gravitational wave telescope to determine whether the designed optical system meets the technical index requirements.
Drawings
FIG. 1 is a diagram of the optical path of a space gravitational wave telescope in the form of an off-axis four-reflection structure in the design method of the space gravitational wave telescope according to the present invention;
FIG. 2 is a schematic diagram of primary imaging of a primary mirror of a space gravitational wave;
FIG. 3 is a schematic diagram of a spatial gravitational wave inversion three-four mirror and intermediate image plane design;
FIG. 4 is a schematic diagram of the structure of the transmitting end of the space gravitational wave off-axis four-reflector;
Fig. 5 is a flowchart of a design method of a space gravitational wave telescope according to the present invention.
In the figure: 1. the aperture diaphragm, 2, the parabolic reflector, 3, hyperboloid reflector, 4, the primary image surface department, 5, the first spherical reflector, 6, the second spherical reflector, 7, exit pupil position.
Detailed Description
The present embodiment will be described with reference to fig. 1 to 5, which illustrate a method for designing a space gravitational wave telescope, in which the space gravitational wave telescope employs a space gravitational wave telescope in the form of an off-axis four-back structure as shown in fig. 1. The gravitational wave telescope uses a parabolic reflector 2 as a large-caliber primary mirror, and has the main function of receiving laser signals reflected by a far-end telescope as much as possible. The hyperboloid reflector 3 is used as a secondary mirror and is matched with the parabolic reflector 2, so that the received parallel signal beam can be well focused, and the focal point size is a diffuse spot similar to an ideal image point. At the focal plane where this focal point is located, an extinction diaphragm is provided, at position 4 in fig. 1 (the extinction diaphragm is present but not shown). The stray light eliminating diaphragm can eliminate the influence of other useless interference signals outside the designed view field. The light ray at the primary image surface 4 continues to propagate forwards, and after being reflected by the first spherical reflecting mirror 5 and the second spherical reflecting mirror 6, the light ray exits in a parallel beam, and the actual exit pupil position of the system is at 7, so that the space gravitational wave telescope is convenient to be connected with other subsequent systems.
As shown in fig. 1, the spatial gravitational wave telescope is composed of an aperture diaphragm 1, a parabolic mirror 2, a hyperboloid mirror 3, a primary image surface 4, a first spherical mirror 5 and a second spherical mirror 6, and 7 is a final real exit pupil position. The parallel light rays at infinity are incident into the space gravitational wave telescope, and finally exit as parallel light rays after one imaging.
The parabolic mirror 2 and the hyperboloid mirror 3 are used together to converge the light rays at infinity almost to an ideal image point. The stray light eliminating diaphragm is set up to eliminate stray light beyond ideal image point, and the position is shown as 4 in fig. 1. The light rays at the primary image plane (position 4 in fig. 1) are reflected by the first spherical reflecting mirror 5 and the second spherical reflecting mirror 6, and finally exit in parallel beams, and the exit pupil position is shown as 7 in fig. 1. The specific design process is as follows:
The first step: according to the envelope size of the optical system, the distance from the aperture diaphragm 1 to the parabolic mirror 2 and the distance from the hyperboloid mirror 3 to the primary image surface 4 can be determined, so that the light rays at infinity are determined to reach the primary image surface 4 after being reflected by the aperture diaphragm 1, the parabolic mirror 2 and the hyperboloid mirror 3, and the light rays are the light paths of the first half optical system. The design of the first half optical system can be determined according to the size of the entrance pupil diameter, the field of view, the design wavelength, and the like, as shown in fig. 2.
And a second step of: determining the design image height of the inverted second half optical system according to the image height at the primary image plane; determining the size of the entrance pupil diameter of the inverted second half optical system according to the size of the exit pupil diameter 7 required in fig. 1; determining the magnitude of the angle of view of the inverted second half optical system according to the required angle magnification and angle of view in fig. 1; the design of the inverted second half optical system can be finally completed as shown in fig. 3.
And a third step of: combining the front half part of the space gravitational wave telescope designed in the first step with the rear half part of the space gravitational wave telescope designed in the second step, and optimizing by taking wave aberration as an index, wherein the requirement of the optimization index is less than or equal to lambda/30, and lambda is the wavelength; and obtaining the preliminary design result of the space gravitational wave telescope, as shown in figure 1.
Fourth step: the receiving end of the designed space gravitational wave telescope is used as a transmitting device, and the corresponding light path diagram is shown in fig. 4. The variable parameters of the optical system (the radius of curvature of the optical element in the optical system, the conic coefficient, the interval between elements, etc.) are optimally designed, and the beam waist of the gaussian beam is set at the exit pupil position 7 in fig. 4 with the gaussian beam as the light source. The laser emitting device performs ray tracing to check the beam waist position, the exit pupil diameter and the divergence angle. The diameter of the exit pupil is ensured to be equal to the diameter of 1 in fig. 1, so that when the telescope is used for emitting laser signals, the divergence angle of the emitted signal beam is ensured to be minimum, and the energy of the received laser signals is ensured to be maximum.
Fifth step: after the optimization design in the fourth step, the space gravitational wave telescope is re-checked to be used as a signal receiving device, and whether the space gravitational wave telescope can continuously meet the technical index requirement that the wave front difference is less than or equal to lambda/30. If the technical index requirement cannot be met, repeating the fourth step, and if the index requirement cannot be met after multiple attempts, repeating the first, second, third, fourth and fifth steps.
Sixth step: and calculating the designed space gravitational wave telescope to check whether the space gravitational wave telescope meets the requirements of TTL coupling noise, and if the TTL coupling noise is smaller than or equal to 25 pm/mu rad, considering that the space gravitational wave telescope meets the requirements of TTL coupling noise indexes. If the TTL coupling noise requirement cannot be met, returning to the step one.
In this embodiment, the designed space laser interference gravitational wave telescope needs to use TTL coupling noise as a criterion for evaluating whether it is acceptable. Wherein, for the calculation of TTL coupling noise: because the telescope receives Gaussian beams emitted by light sources beyond million kilometers, the receiving end can be considered to receive flat-top beams after the Gaussian beams are transmitted to the space gravitational wave receiving telescope at the local end. After passing through the space gravitational wave telescope, the flat-top beam exits from the exit pupil, and the wavefront exiting from the exit pupil interferes with the local Gaussian beam on the photoelectric detector. Ideally, this is the case. The optical axis of the local gaussian beam is considered to coincide with the center of the photodetector and is taken as the reference axis of the system. Ideally, the principal ray of the flat-top beam coincides with this axis. In practical situations, the principal ray of the flat-top beam has a certain angle with the reference axis, which introduces TTL coupling noise. The wave front expression of the flat-top beam is:
E＝Aexp[i(k·r-wt)] (1)
Wherein A is complex amplitude of the plane light wave, r is a position vector of any point on the plane wave, k is propagation direction of the plane wave, w is angular frequency of the plane wave, and t is time;
The wavefront expression of the local Gaussian beam is
Wherein w (z) is the beam waist width of the Gaussian beam, ρ represents the distance from the spatial position in the Gaussian beam to the central axis of the Gaussian beam, z is the distance the Gaussian beam moves along the propagation direction, R (z) is the radius of curvature of the image plane of the Gaussian beam,An additional phase shift relative to the geometric displacement for a gaussian beam at a spatial transmission distance z; and c is a constant term, i is an imaginary unit.
The complex conjugate of the flat-top beam and the Gaussian beam is obtained, and the interference signal on the photoelectric detector is integrated, so that the phase corresponding to the interference beam can be obtained, and then the size of TTL coupling noise is obtained.
And comparing the size of TTL coupling noise specified in the technical index requirements with the size of TTL coupling noise of the calculated newly designed space gravitational wave telescope to determine whether the designed optical system meets the technical index requirements.
Seventh step: and performing tolerance analysis on the space gravitational wave telescope. According to the prior art, the processing and adjustment errors of the optical elements of the space gravitational wave telescope are reasonably distributed, and whether the yield of the space gravitational wave telescope meets the requirements or not under the actual condition of analysis and simulation is carried out.
In this embodiment, the designed space gravitational wave telescope can compress the approximately parallel signal beam emitted from the opposite end, and finally, the parallel beam is emitted at the exit pupil of the receiving end space gravitational wave telescope, and then, the subsequent light path is connected by the pupil connection principle. When the local end is used as a signal transmitting end, the laser signal can be emitted at a smaller divergence angle, and the beam waist position is positioned in the advancing direction of the optical signal, so that the opposite end can receive the optical signal with stronger power density.
In the process of detecting gravitational wave by adopting an inter-satellite laser interferometry method, a new method for optimizing the performance of the gravitational wave telescope is designed. When the method designs the gravitational wave telescope, the gravitational wave telescope not only has the function of receiving laser signals, but also can be used for transmitting signals with optimal performance. And when the device is used as a receiving end, the index requirements of wavefront difference and TTL coupling noise are met.
The space gravitational wave telescope designed by the embodiment not only adopts the point column diagram and the surrounding circle energy to evaluate the index, but also uses the wavefront difference and TTL coupling noise to evaluate the index requirement for receiving signals, and uses the divergence angle of laser beams to evaluate the technical index quality when transmitting signals. Meanwhile, an stray light eliminating diaphragm is designed to reduce interference of stray light on laser signals.
Claims (2)
1. A design method of a space gravitational wave telescope is characterized in that: the telescope is designed into a structure of an off-axis four-inverse telescope; the structure consists of an aperture diaphragm, a parabolic reflector, a hyperboloid reflector, a first spherical reflector and a second spherical reflector, wherein parallel rays at infinity enter a space gravitation wave telescope through the aperture diaphragm, are subjected to primary imaging at a primary image plane through the parabolic reflector, and finally exit to an exit pupil position through the first spherical reflector and the second spherical reflector; the specific design method is realized by the following steps:
Designing a telescope receiving end light path, wherein the receiving end light path comprises an aperture diaphragm, a parabolic reflector and a hyperboloid reflector;
Determining the distance from the aperture diaphragm to the parabolic reflector and the distance from the hyperboloid reflector to the primary image surface according to the envelope size of the optical system, determining the reflection of light rays at infinity through the aperture diaphragm, the parabolic reflector and the hyperboloid reflector, reaching the primary image surface, and finally completing the design of a receiving end light path of the optical system according to the size of the diameter of the entrance pupil, the field of view and the design wavelength;
step two, designing an inverted rear-end optical path, wherein the rear-end optical path comprises a first spherical reflector, a second spherical reflector and an exit pupil position;
Determining the designed image height of the inverted rear-end light path according to the image height of the primary image plane of the receiving-end light path designed in the step one;
determining the size of the entrance pupil diameter of the inverted rear-end light path according to the size of the exit pupil diameter required by design; determining the size of the angle of view of the inverted rear-end light path according to the required angle magnification and the angle of view; finally, the design of an inverted rear-end light path is completed;
Combining the telescope receiving end light path designed in the step one and the inverted rear end light path designed in the step two, and optimizing by taking wave aberration as an index, wherein the requirement of the optimizing index is less than or equal to lambda/30, so as to obtain the primary design of the space gravitation telescope;
step four, taking the light path of the receiving end of the space gravitational wave telescope preliminarily designed in the step three as a transmitting device, optimally designing variable parameters in an optical system, taking a Gaussian beam as a light source, and placing the beam waist of the Gaussian beam at an exit pupil position; performing ray tracing on the emitting device, and checking the beam waist position, the diameter of an exit pupil and the size of a divergence angle, so as to ensure that the diameter of the exit pupil is equal to the diameter of an aperture diaphragm, and further optimizing an optical path;
Step five, taking the receiving end light path as a signal receiving device, and returning to the step four if the space gravitational wave telescope meets the technical index requirement that the wave aberration is less than or equal to lambda/30 and the technical index requirement cannot be met; if the technical index requirements can be met, executing the step six;
step six, checking whether the space gravitational wave telescope meets the requirement of TTL coupling noise, if the TTL coupling noise is less than or equal to 25 pm/mu rad, considering that the TTL coupling noise index requirement is met, and executing step seven; if the TTL coupling noise requirement cannot be met, returning to the step one;
And seventhly, carrying out tolerance analysis on the space gravitational wave telescope, namely: and (3) distributing processing and adjustment errors of each optical element of the space gravitational wave telescope, analyzing and simulating whether the yield of the space gravitational wave telescope meets the requirement under the actual condition, and finally designing the space gravitational wave telescope.
2. The method for designing a space gravitational wave telescope according to claim 1, wherein: the specific process of the step six is as follows:
The Gaussian beam becomes a flat-top beam after passing through a receiving end light path, and the flat-top beam exits from an exit pupil position; the wave front of the flat-top beam emitted from the exit pupil position interferes with the local Gaussian beam on the photoelectric detector; ideally, the optical axis of the local Gaussian beam coincides with the center of the photodetector and is used as the reference axis of the system; in practical cases, the principal ray of the flat-top beam has a certain included angle with the reference axis, so that TTL coupling noise is introduced; the wave front expression of the flat-top beam is as follows:
E＝Aexp[i(k·r-wt)]
Wherein A is complex amplitude of the planar light wave, r is a position vector of any point on the planar wave, k is propagation direction of the planar wave, w is angular frequency of the planar wave, t is time, and i is imaginary unit;
the wavefront expression of the local gaussian beam is:
wherein w (z) is the beam waist width of the Gaussian beam, ρ is the distance from the spatial position in the Gaussian beam to the central axis of the beam, z is the distance the Gaussian beam moves along the propagation direction, R (z) is the radius of curvature of the image plane such as the Gaussian beam, An additional phase shift, c constant term, generated relative to the geometric displacement for a gaussian beam at a spatial transmission distance z;
calculating complex conjugate of the flat-top beam and the Gaussian beam, integrating interference signals on the photoelectric detector to obtain phases corresponding to the interference beams, finally obtaining the size of TTL coupling noise, comparing the obtained size of TTL coupling noise with the size of TTL coupling noise specified in technical index requirements, and determining whether the TTL coupling noise in the designed optical system meets the technical index requirements.
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