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.

Triangular cavities are increasingly used in cavity ring-down spectrometers (CRDS) to compensate for the existence of optical feedback and other disadvantages of straight cavities. However, at the same time, the difficulty of the cavity mounting alignment process is increased. Consequently, the fast and stable establishment of resonance between the optical source and the triangular ring-down cavity has been widely explored for CRDS-based applications. The Hermite-Gaussian theory has unique advantages for the description of the Gaussian resonant beams characteristics in triangular cavities, while the theory is of great importance for the alignment in high finesse triangular ring-down cavities. Along these lines, in this work, the eigenfrequency separation characteristics of the Hermite-Gaussian modes in the triangular cavity, in the meridional and sagittal planes, as well as the excitation and transmission characteristics of the first-order mode in the high finesse cavity were verified. A static alignment method was established for the high-finesse triangular ring-down cavity, and the transmission suppression of the Hermite-Gaussian modes by the high-finesse cavity was overcome in the experiment. Finally, by leveraging the advantageous features of the fundamental and the first-order mode that are complementary to each other, the tilt and axis shift errors of each specified plane with directional high accuracy can be aligned. The static alignment scheme of the triangular cavity based on the Hermite-Gaussian theory that was established here paves the way for the mounting alignment of the CRDS instrument before the ring-down experiment, whereas the system accuracy of CRDS is further improved.

In this paper, the wing tip jet is proposed to improve the aerodynamic performance of the three-dimensional ONERA M6 wing at high Reynolds numbers. The CFD method is used to perform numerical simulation with the SST k-ω two-equation model. To verify present numerical model, ONERA M6 wing at the attack angle(α) of 2° is selected and the simulation results are in good agreement with the experimental data. The flow around the airfoil at high Reynolds number is simulated at 0°-14° attack angle, and the critical attack angle is 11° without jet. Finally, the influence of the jet on the aerodynamic characteristics of the airfoil at different attack angle are studied and it is found that the lift coefficient and lift-drag ratio of the airfoil increase with jet.