Simultaneous measurement of displacement, pitch, and yaw angles of a cavity output mirror based on phase measuring deflectometry.

Accurate and high dynamic range measurement of the three attitude variations (i.e., displacement, pitch, yaw angles) has been widely researched based on various approaches to meet different application requirements. However, none of the existing methods can detect these three attitude variations at the same time. This paper proposes a method based on a classical phase measuring deflectometry (PMD) system and a double iteration algorithm to simultaneously measure the three variations of the output mirror in a laser resonator. The relationship between the attitude variations and the lateral displacement parameters (LDP) of the imaged structural fringes is derived in the PMD system. Through the established relationship, the attitude variations could be calculated once the LDP are detected. Furthermore, a two-step measuring scheme combining the four-step shifting phase and the color-coded fringe is proposed to effectively detect the LDP. Finally, an experiment is conducted to verify the feasibility of the proposed method.