Design Of Ultra-high Precision And Ultra-stable Off-axis Four-reflective Optical System

Gravitational waves are an important prediction of Einstein’s theory of general relativity.General relativity predicts that the movement of massive objects causes a distortion of spacetime,creating ripples that propagate at the speed of light,which are called gravitational waves.Gravitational wave detection is one of the cutting-edge areas of modern physics.Its purpose is not only to directly test Einstein’s theory but also to help us understand the structure and evolution of the universe.The discovery of gravitational waves has opened a new era in the study of gravitational wave astronomy,and is a new window for human observation of the universe.Space-based gravitational wave detectors can detect low-frequency gravitational wave signals ranging from 0.1 m Hz to 1 Hz,providing complementary coverage to ground-based gravitational wave detectors and achieving wider bandwidth coverage of gravitational wave detection.The space-based gravitational wave detection utilizes the Doppler frequency shift generated by the relative motion of spacecrafts.It measures the periodic changes of sub-nanometer distance between the space-borne test masses using differential laser interferometry,and computes the gravitational wave signal.The measurement baseline can reach millions of kilometers,significantly improving the sensitivity to gravitational strain,and capable of detecting low-frequency gravitational wave signals in the m Hz frequency band.The telescope on board is the critical payload of space-based gravitational wave detection satellite and the core component of the laser system.Its performance and stability have a direct impact on the detection capabilities and mission success of gravitational wave detection.In contrast to traditional telescopes,gravitational wave experiments cannot ignore the impact of optical wavefront tilt on gravitational wave detection accuracy.Low-order aberrations can also introduce considerable displacement measurement noise.As a long baseline interferometer,the emitted light beam is a Gaussian beam,and the curvature error caused by diffraction directly affects the far-field energy distribution,resulting in inter-star misalignment error.To achieve the detection of gravitational wave signals in the frequency range of 1 m Hz to 0.1 Hz with an interferometer arm length ranging from several hundred thousand to several million kilometers,the measurement accuracy of sub-picometer level requires the telescope to have ultra-high optical wavefront quality,ultra-high optical path stability,ultra-high stray light suppression capability,and ultra-stable thermo-mechanical adaptability.In response to the requirements of space-based gravitational wave detection,this article designs an ultra-high precision and ultra-stable off-axis four-reflective nonfocusing optical system.As the receiver and transmitter of the detection laser beam,the telescope optical system uses an off-axis four-reflective optical system.The primary mirror M1 and secondary mirror M2 form a first image plane,which is then further reflected by the tertiary mirror M3 and the quaternary mirror M4 to form a non-focusing optical path.A stop is placed at the first image plane to effectively suppress stray light and enhance measurement accuracy.The telescope optical components are made of ultra-low coefficient of thermal expansion microcrystalline glass to effectively improve the thermo-mechanical stability of the entire system.Since the interferometer arm length is on the order of millions of kilometers,to ensure strong signal reception,the optical system should have a large aperture and high magnification.The designed optical system in this article has an entrance pupil of 300 mm,an exit pupil size of 5mm,and a magnification of 60 x.The system has two fields of view: a capture field of view of 200 μrad and a scientific field of view of 20 μrad.The capture field of view is required for mutual capture of orbiting satellites,and the scientific field of view is the working field of the telescope.Considering the pointing stability of orbiting satellites,the scientific field of view can better accomplish the gravitational wave measurement mission.Based on the basic parameters of the optical system,a coaxial four-reflective system is first designed.On the basis of the coaxial system,an off-axis structure is obtained by aperture off-axis method.The distance between the mirrors and the position of the exit pupil are controlled well in the system optimization process to match with the interferometer behind.The angle misalignment measurement of the laser differential interferometry system is coupled with the interference measurement result,producing Tilt-To-Length(TTL)noise,which is the second largest noise source in gravitational wave detection.In addition,if the optical path consistency in the scientific field of view is poor,the non-symmetric wavefront error of the telescope will also cause TTL noise when a slight displacement of the optical axis occurs between the transmitting and receiving telescopes.Therefore,the wavefront error and TTL noise in the scientific field of view are important indicators for evaluating the optical system.In the design process,the aperture stop is set at the exit pupil position to reduce the dispersion and separation of the main ray at the aperture,reduce the changes in the optical path length(OPL)with the field of view,and limit stray light entering the backend of the system.The strict control of the parallelism between the outgoing main ray of M4 and the optical axis reduces the coupled TTL error.By optimizing the tilt angle of the first image plane and matching the number of freeform surface terms of M3,the system has better TTL error and wavefront RMS comprehensive optical performance indicators.After optimization,a reasonable optical system structure has been obtained.In the scientific field of view(±20 μrad),the Tilt-To-Length(TTL)noise of the telescope jitter optical path coupling is less than 0.06 pm/nrad,and the RMS wavefront aberration at each edge(±20 μrad in X and Y directions)is less than 0.002λ.The imaging quality in the alignment field of view(±200 μrad)reaches the diffraction limit.Finally,tolerance analysis and thermal analysis are conducted on the system,and the tolerance allocation and analysis results can meet the requirements of design,manufacturing,and assembly.The temperature influence analysis results show that although the thermal expansion caused by a uniform temperature field changes the optical spacing,the changes in the optical path difference in different fields of view are very small,i.e.δTTL is small,and TTL is mainly affected by changes in the surface shape caused by temperature gradients.In conclusion,the design of the space-based telescope optical system has been analyzed and refined based on design requirements,design principles,constraints,and technical indicators,and has undergone multiple iterations of optimization.Performance,tolerance,and temperature influence analyses have also been conducted.The design results can meet the technical indicators and functional requirements of the space-based telescope for gravitational wave detection.