Physical Optics Analysis of Differential Wavefront Interferometry and Phase Compensation for Dynamic Doppler Frequency Shifts

Xiangzhi Yu and Chen Wang

Hopeman 224

Physical Optics Analysis of Differential Wavefront Interferometry-Typically, measuring or calibrating the stage movement in three degrees of freedom (DOF) requires three different setups. However, we have developed a 3-DOF fiber-delivered heterodyne interferometer which uses a single beam to simultaneously measure target displacement and changes in pitch and yaw. This interferometer applies differential wavefront sensing where each DOF can be decoupled and measured from phase information of the quadrant photodiode. Analytical models and simulations are currently being developed and experiments will be performed to validate how the beam diameter, beam aberrations, detector size, and beam centroid mismatch affect DWS.

Phase Compensation for Dynamic Doppler Frequency Shifts-Positioning calibration under dynamic conditions is becoming increasingly of interest for high precision fields. Heterodyne interferometry is often used to calibrate a stage’s position because it has high dynamic range and direct traceability to the meter. When using heterodyne interferometry, filtering is routinely performed to process and determine the measured phase change, which is proportional to the displacement from one target location to another, however, it introduces a phase delay dependent on the detection frequency, which leads to displacement errors when target velocity is non-constant as is the case in dynamic calibrations. This presentation presents a phase delay compensation method by measuring instantaneous detection frequency and solving for the corresponding phase delay in an FPGA in real-time, can significantly decrease the displacement error that is up to hundreds of nanometers to ±3 nm in dynamic cases and it will still keep sub-nanometer resolution for quasi-static calibrations.