Polynomial-exponent modeling and identification of the white-light scanning interferogram

Area of Science:

• Optics and Photonics
• Metrology
• Signal Processing

Background:

• White-light interferometry is vital for precise measurements but analyzing complex interferograms is challenging.
• Existing models may not fully capture variations in fringe and envelope patterns caused by light sources or dispersive media.

Purpose of the Study:

• To develop a robust polynomial-exponent model for white-light interferograms.
• To introduce a direct fast Fourier transform (FFT)-based algorithm for accurate interferogram analysis.
• To enable precise estimation of phase and dispersion parameters.

Main Methods:

• A polynomial-exponent model is formulated, incorporating differential equations and frequency-domain analysis.
• A two-step algorithm is proposed: 1) polynomial coefficient estimation, 2) amplitude and phase estimation.
• A method for calculating the dispersion parameter as a quadratic phase component is developed.

Main Results:

• The model accurately describes diverse envelope and fringe phase distributions.
• The algorithm successfully estimates fringe phase, even when unknown, at the envelope peak.
• Dispersion parameters are calculated with high accuracy, approaching the Cramér-Rao lower bound.

Conclusions:

• The proposed model and FFT-based algorithm offer a precise and efficient method for white-light interferogram analysis.
• This approach enhances the accuracy of optical metrology, particularly in the presence of dispersive effects.
• The technique provides a reliable framework for extracting higher-order interferogram parameters.