Theory and application of robust linear phase-shift algorithm for phase-shift deflectometry method

Area of Science:

• Optical metrology
• Signal processing

Background:

• N-step Discrete Fourier Transform (N-DFT) algorithms are widely used for phase-shift analysis.
• These algorithms face challenges with Gamma distortion and phase detuning, limiting measurement accuracy.
• Simultaneous suppression of multiple error sources remains a key challenge in optical metrology.

Purpose of the Study:

• To analyze the error propagation characteristics of N-step DFT algorithms.
• To design a novel algorithm capable of simultaneously suppressing Gamma distortion and phase detuning.
• To evaluate the performance of the new algorithm against existing methods through simulations and experiments.

Main Methods:

• Theoretical analysis based on polynomial theory to study error propagation in N-DFT.
• Design and implementation of a Robust Linear Phase-Shift (RLPS) algorithm.
• Performance evaluation using the Manuel Servin method, spectral response analysis, and detuning robustness tests.
• Physical experiments using inclined plane and concave mirrors to validate algorithm performance.

Main Results:

• N-DFT algorithms cannot simultaneously suppress Gamma distortion and phase detuning.
• The RLPS algorithm demonstrates simultaneous suppression of both error types.
• RLPS exhibits superior stability and accuracy over N-DFT and exponential algorithms, particularly in gradient measurement, peak-to-valley (PV), and root-mean-square (RMS) error reduction.
• Physical experiments confirm RLPS improves measurement stability and accuracy under detuning and without Gamma calibration.

Conclusions:

• The RLPS algorithm provides a significant advancement in optical metrology by overcoming the limitations of N-DFT.
• RLPS offers enhanced stability and accuracy, crucial for precise optical surface measurements.
• The developed algorithm is robust to detuning and Gamma distortion, simplifying measurement procedures.