# Design and Error Analysis of an Optical Measurement System for the Wavefront of Large-Aperture Segmented Mirror

## TL;DR

This paper presents a new optical measurement system for large segmented mirrors in space, designed to improve wavefront accuracy and adaptability to temperature changes.

## Contribution

A novel optical measurement system for large-aperture segmented mirrors with expanded measurement range and improved accuracy for in-orbit coarse calibration.

## Key findings

- The designed measurement camera achieves near-diffraction-limited imaging quality with a 100 mm focal length and 16° × 12° field of view.
- The system's wavefront fitting accuracy meets requirements with peak-to-valley values of 0.397 mm and root mean square of 0.073 mm.
- The system shows strong temperature adaptability with lens surface error better than 1/80λ under 4 °C temperature rise.

## Abstract

To better meet the wavefront measurement requirements for large-aperture segmented mirrors after in-orbit deployment, this paper designs a measurement system based on an optical camera and targets. This system utilizes photogrammetry principles to measure target positions, fit the wavefront of the segmented mirror, and form a closed-loop control with the calibration mechanism. Based on the wavefront measurement range and accuracy requirements during the coarse calibration phase of the segmented mirror, the optical system was first designed. The measurement camera features a 16° × 12° rectangular field of view with a 100 mm focal length, achieving near-diffraction-limited imaging quality. The structural fundamental frequency of the measurement camera exceeds 400 Hz. Under a 4 °C temperature rise environment, the surface error of the optical lens remains better than 1/80λ. Based on error theory, a quantitative analysis of error sources and their impact on target position measurement accuracy was conducted, yielding theoretical measurement errors of ±0.0853 mm in the Z-direction and ±0.1525 mm in the X-direction. Through focal length calibration and imaging tests of the prototype, the measurement camera achieved a modulation transfer function greater than 0.11 with excellent imaging quality. With a focal length of 101.356 mm and a measurement range exceeding ±4 mm, it meets design requirements. Finite element simulation and Monte Carlo methods analyzed wavefront fitting accuracy under different operating conditions, yielding peak-to-valley values of 0.397 mm and root mean square values of 0.073 mm. The wavefront measurement system designed in this paper meets the structural rigidity and temperature adaptability requirements for in-orbit measurement systems. The prototype’s field of view satisfies the wavefront measurement range requirements, the camera’s focal length meets design specifications with good imaging quality, and the wavefront measurement deviation meets the accuracy requirements for the coarse calibration phase. Compared to current wavefront measurement systems, the proposed system significantly expands the measurement range, offering a novel wavefront measurement method for coarse calibration of tiled mirrors.