High-precision calibration method for shear ratio based on the shearing wavefront feature extraction of a phase plate

A new method based on the shearing wavefront feature extraction (SWFE) of a phase plate is proposed to accurately estimate the shear ratio of the system. The relationship between the shear ratio of a quadriwave lateral shearing interferometer based on a randomly encoded hybrid grating (REHG) and the measurement sensitivity, dynamic range, and wavefront retrieval accuracy is analyzed to provide a theoretical guidance for practical application. The simulation result of the SWFE method shows that the relative error of the shear ratio value is about 1.8×10^-3, within the acceptable range of the system. In the experiment, two fused quartz phase plates etched with step change edge grooves were introduced to calibrate the shear ratio of the REHG wavefront diagnosis system. Then, the etching depths of these two phase plates and the figure error of a spherical surface were characterized by the REHG. A comparison with a ZYGO GPI interferometer exhibits that the testing results by the REHG are highly precise, which further confirms the effectiveness of the SWFE method in the shear ratio calibration. This shear ratio calibration method is available for similar kind of shearing interferometric wavefront sensor.