The development trend of onboard electro-optical systems towards multifunctionality, high performance, and light weight poses higher demands on the development of optical systems. Reflective optical systems are widely employed in various types of onboard electro-optical devices due to their broad bandwidth and compact working characteristics, and they face challenges such as obscuration of secondary mirrors, limited field of view, and low optimization degrees in traditional coaxial reflective systems. Off-axis three-mirror reflective optical systems with freeform surfaces can address these issues. However, the development and maturity of freeform surface design and manufacturing techniques pose challenges to freeform surface shape measurement and system alignment. In previous studies, computer-generated holograms (CGHs) are adopted for single mirror shape measurement, but there is limited publicly available information on multi-mirror shape measurement with CGHs and their joint baseline design.

We propose a method for CGH joint baseline design of multi-mirror shape measurement to enable independent high-precision positioning of each mirror during alignment. The core idea is to combine detection and design to ensure high-precision shape measurement and achieve high-precision positioning and stabilization of multiple mirrors. The specific process of the joint baseline design for multi-mirror CGHs is as follows (Fig. 1). 1) The input parameters for the mirror shape are set, including posture parameters and surface parameters. 2) The initial point for CGH posture optimization is calculated based on the parameters. Additionally, CGH posture parameters (tilt and distance from the measured surface) are optimized to ensure the integrity and moderate size of the holographic areas for primary mirror and third mirror. 3) Additional holographic areas are designed based on posture parameters, including rough alignment areas, angular alignment areas, and interference order marking areas. The angular alignment area utilizes a reflective grating design with the shining angle set as the incident angle of the interferometer's light rays. 4) The manufacturability of the designed fringe patterns is examined. If the patterns meet the processing requirements, the joint baseline design is considered complete to proceed to system alignment. Otherwise, the first step should be returned and the design parameters should be readjusted until the fringe patterns meet the processing requirements. The alignment process using multi-mirror joint baseline design CGH is as follows (Fig. 3). 1) The two-mirror posture optimization CGH design is finished based on the system parameters. 2) The CGH alignment baseline is set, the interferometer is aligned with the main mirror alignment area, and the alignment of the interferometer and the main mirror is fixed. 3) The primary mirror is aligned. The interferometer posture is adjusted based on the alignment area of the main mirror interferometer. The misalignment is reflected by the sensitivity matrix of the detection optical path. According to the sensitivity matrix theory, under small misalignment, Zernike polynomial coefficients are linearly related to the misalignment. The main mirror should be fine-tuned based on interferometric fringe Zernike coefficients. 4) The third mirror is aligned. The interferometer posture is adjusted based on the alignment area of the three-mirror interferometer and the third mirror are fine-tuned based on the interferometric fringe Zernike coefficients. Meanwhile, the posture and stabilization of primary mirror and third mirror are completed. 5) The system alignment baseline is established by the interferometer, and a theodolite is employed to align the system baseline and the reticle at the exit pupil. 6) The secondary mirror is aligned. A collimated laser is adopted to position the tilt and pitch of the secondary mirror. 7) The secondary mirror is fine-tuned to achieve the desired image quality at the zero field of view. 8) The angles of the interferometer and the collimated mirror are adjusted to the off-axis field of view, and the imaging quality at the off-axis field of view is measured. If it meets the design requirements, system alignment is ended. Otherwise, the zero field of view should be returned and the wavefront error adjustment should be continued until the off-axis field of view also meets the design requirements.

The CGH design is limited by the following factors, including minimum stripe width greater than 1.5μm, single holographic area diameter smaller than 80mm, and complete CGH diameter smaller than 160mm. The designed CGH (Fig. 5) with minimum stripe width 1.78μm meets the manufacturing process and design requirements. The fabrication error analysis can simplify the model to a linear grating model (Fig. 7). The main fabrication errors (Table 2) contain substrate shape error, stripe width error, etching depth error, and stripe duty cycle error. Among them, the substrate shape error has the most significant influence on CGH imaging. However, the substrate's manufacturing accuracy is smaller than λ/100 and does not affect subsequent preparation of etched stripes. The other errors cause wavefront error changes within the tolerance range and have a minimal effect on CGH positioning accuracy. In production, it is essential to first suppress substrate shape errors and then pay attention to stripe width errors, further improving the precision of CGH shape measurement. Transmission wavefront measurement (Fig. 8) is performed on the fabricated CGH product. The comprehensive wavefront error in the measured CGH is less than λ/80, which meets the requirements for shape measurement accuracy. In the experiment (Table 3), the main mirror is aligned first, and the RMS of the single mirror shape is 0.022λ. Then, the three mirrors are aligned and the RMS of the single mirror shape is 0.032λ, which satisfies the design requirement that the RMS of the single mirror alignment shape should be less than 0.050λ. Finally, the secondary mirror is aligned. In the full-field imaging quality test (Table 6), the field angle adjustment is realized via theodolite positioning and optical system rotation. The RMS wavefront aberration in the near-infrared wavelength range is less than 0.093λ, and in the long-wave infrared wavelength range, it is less than 0.126λ. The RMS wavefront aberration at the central field of view is 0.079λ, which meets the design requirements for imaging quality.

This method has excellent application prospects. Meanwhile, it is applied to separate structure alignment in this study and has application significance in the off-axis three-mirror integrated structures. High-precision positioning using CGH can calibrate the common baseline machining errors. This method can be widely adopted in the alignment of freeform off-axis systems and the design of optical systems with freeform surfaces.