Tilt-shift determination and compensation in phase-shifting interferometry

A method combining spatial and time-domain processing is proposed to extract the phase from spatial carrier interferograms with tilt-shift errors. The proposed method determines the piston values and tilt-shift errors based on the Fourier transform method and then compensates for it by least-squares fitting. Therefore, phase-retrieval errors introduced by uncalibrated fluctuations (including tilt-shift errors) in the phase increments can be alleviated without the necessity of extensive iterative calculations. Simulated results and experiments demonstrate the effectiveness of the proposed method. Compared to other techniques, the proposed method extracts the phase distribution accurately without edge artifacts and waviness caused by tilt-shift errors. The ability to perform both spatial and time-domain processing in a single instrument provides the flexibility for precision metrology applications in both dynamic environments.