We discuss the tilt-to-length (TTL) coupling noise caused by interference between a flat-top beam and a Gaussian beam. Several physical models are presented to research the effects of non-diffracted and diffracted beams on TTL noise. A special case that can remove TTL coupling noise is discovered and is verified via both theoretical analysis and numerical simulations. The proposed case could provide desirable suggestions for the construction of high-precision interferometers such as the Laser Interferometer Space Antenna (LISA), Taiji program, or other interferometry systems.

Space-based gravitational wave detection programs, such as the Laser Interferometer Space Antenna (LISA) or Taiji program, obtain gravitational wave signals by measuring the change in the distance between three satellites by laser. The telescope is an important part of the measurement system, and its function is to transmit and receive laser signals. Due to changes in the space environment, the telescope will inevitably introduce additional dynamic aberrations, which will bring optical path errors to the inversion of gravitational wave signals. Taking LISA as an example, to achieve pm-level measurement accuracy at the detection frequency of 0.1 mHz–1 Hz, the stability requirements of the telescope are less than 1 pm/Hz^1/2. This paper theoretically deduces the aberration types that affect the telescope’s stability and conducts simulation analysis according to the actual phase demodulation method, which verifies the theory’s correctness. In addition, using this theory, it can be concluded that under the condition that the total size of the telescope aberration is determined to be stable, reducing the ratio of rotationally symmetric aberrations such as “spherical aberration” and “defocusing” among common aberrations can significantly improve the stability of the telescope. The conclusion guides the optical system design of LISA or Taiji.

Large-aperture space telescopes have played an important role in space gravitational wave detection missions. Overcoming the influence of the space environment on interstellar laser distance measurement and realistic high-concentration laser distance measurement is one of the topics that LISA and Taiji are working hard on. It includes solar temperature, spatial stress relief, pointing shake and tilt, etc. However, when considering the impact of vibration on the telescope, both LISA and Taiji only consider the resonance impact of vibration on structural parts, which greatly ignores the impact of high-frequency micro-vibration on space ranging. This paper first considers space gravitational wave detection. Then, we establish the heterodyne interference model and demodulation algorithm of the optical phase-locked loop, and then introduce the vibration component for theoretical analysis. The results show that, although the resonance effect of low-frequency vibration on the system structure is avoided in space gravitational wave detection, the influence of high-frequency micro-vibration on heterodyne interference cannot be ignored. At the same time, we quantitatively analyze the influence efficiency of amplitude and frequency; in the premise of small amplitudes, the influence of vibration frequency is related to the frequency of the heterodyne signal, which has important guiding significance in engineering.

Surface imperfections or contamination on an optical smooth surface is usually inevitable and causes scattering. The directional information of the scattered ray can be related to the spatial frequency through the grating equation. On the other hand, the layout of the optical system determines whether a scattered ray will finally reach the detector according to the positions and directions of the scattered rays. Therefore, the scattering propagation in an optical system is usually band-limited and the effective optical range differs for different systems. In this paper, a method based on ray tracing is described that can statistically determine the optical scattering and the band of roughness. The results can be an essential reference for optical surface polishing and contamination control.

In many optical engineering applications, a spherical cap shaped optical element is widely used such as concave or convex mirrors in reflective optics. Such an element can also tilt around the vertex which corresponds to an off-axis optical design. The optical backscattering of such an optical element sometimes could be important. For example, in the space-based gravitational wave detection, the backscattering of such an element could be superimposed with the local oscillator and limits the sensitivity of the spacecraft. The scattered contributions depend on the scattering property of the mirror surfaces and the geometrical arrangement including the radius of curvature, the tilt and the interval between the scattering source and detector plane. Based on random estimation method, this paper starts from the radiometry, combines these variables and calculates the theoretical amount of back scattered light for both diffuse and superpolished surfaces. The results are compared with analytical and ray tracing solution. The conclusions can be used to further improve the optical design of the telescope or extended to other cases where the backscattered light should be controlled.

In order to meet the requirements of standardized design of star sensor lens, a Computer Aided Design (CAD) system based on parametric modeling was established for star sensor lens to shorten the product design cycle and improve the technological quality and reliability of lens design. At first, the structural design parameters and their interactions of a star sensor lens designed by alignment turning process were confirmed. Then, the parametric modeling of the optical system was carried out on the lens' design. By calculating the technology indicators of the lens in real time, the designer could adjust the lens design reasonably. The multi-segment parametric modeling for rotation body based on dimension chain was carried out for the lens structure. The installation, location, structure and size of lens components were automatically designed and graphically presented, rather than manually and repetitively designed. By combining the global design of assembly drawing with the design of lens components and giving real-time feedback of lens weight and other information, the designer could design the spatial layout reasonably and evaluate the design result, so as to quickly iterate over the lens design. The application results show that the time for designing the assembly drawing of a 9-in-1 star sensor lens is reduced from original similar to 15h to similar to 3h, thereby greatly improving the design efficiency. This system can ensure the design technology and reliability, meet the standardized design requirements of star sensor lens, and provide ideas for the parametric modeling of other precision instruments.