On-Machine Calibration Method for In Situ Stereo Deflectometry System

Deflectometry is a promising method for the <italic>in situ</italic> measurement of specular surfaces. However, the accuracy of this method largely depends on the geometrical calibration, which suffers from a low convergence rate and local minima during the optimization. Off-machine calibration results in a change in geometry parameters due to the repeated disassembly of the measurement system and change of ambient temperature, which largely affects the measurement accuracy. This article presents a flexible on-machine calibration method with fewer intermediate parameters to accelerate the optimization for the <italic>in situ</italic> stereo deflectometry system. An inclined mirror with a fixed angle was mounted on the spindle of an ultraprecision machine tool and used as a reference plane reflecting the fringe displayed on the display screen. The reflected fringe captured by the cameras was encoded by an inclined mirror moving along the <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula>-axis and the <inline-formula> <tex-math notation="LaTeX">$Z$ </tex-math></inline-formula>-axis of the machine tool. The preknowledge of the movement distance of the ultraprecision machine tool along the <inline-formula> <tex-math notation="LaTeX">$Z$ </tex-math></inline-formula>-axis and rotation angle of the spindle with a nanoscale accuracy was used to largely reduce the number of intermediate variables involved in the optimization, thus improving the convergence speed of the global optimization method and calibration reliability. The experiment results show that this calibration method has higher calibration accuracy, measurement accuracy, and reliability compared to the conventional off-machine calibration method.