Phase-shifting interferometry corrupted by white and non-white additive noise

Area of Science:

• Optical Metrology
• Signal Processing

Background:

• Phase Shifting Algorithms (PSAs) are standard for phase estimation in interferometry.
• Previous analyses of PSA performance primarily focused on white additive noise.

Purpose of the Study:

• To investigate and report on the performance of PSAs with non-white additive noise.
• To generalize existing white noise analysis for PSAs to non-white noise conditions.

Main Methods:

• Utilizing the Frequency Transfer Function (FTF) of a PSA.
• Generalizing noise analysis from white to non-white additive noise scenarios.
• Calculating the ensemble average and variance of estimated phase for noisy interferograms.

Main Results:

• The study provides a generalized method to estimate phase variance in PSAs under non-white additive noise.
• For additive white noise, a novel relationship between PSA noise robustness, its FTF spectrum, and coefficients is established using Parseval's theorem.
• Phase variance is determined in both spectral and coefficient spaces for white noise conditions.

Conclusions:

• The FTF provides a powerful tool for analyzing PSA performance with various noise types.
• The findings offer new insights into the noise robustness of PSAs, particularly under non-white noise.
• This work extends the theoretical understanding of PSA behavior in practical, noisy optical metrology applications.