Modeling and decoupling phase-shift-induced wavefront distortion in high NA spherical Fizeau interferometry via...

Area of Science:

• Optical metrology
• Interferometry
• Wavefront sensing

Background:

• High numerical-aperture (NA) Fizeau interferometry faces challenges with axial mechanical phase shifting.
• Spatially nonuniform phase shifts cause wavefront distortion (defocus, spherical aberrations) and violate conventional phase-shifting interferometry (PSI) assumptions.
• Multiple reflections in Fizeau cavities introduce harmonic artifacts, degrading measurement accuracy.

Purpose of the Study:

• To develop a novel algorithm, aberration-related iterative algorithm (ARIA), to address systematic errors in Fizeau interferometry.
• To accurately reconstruct surface figures by mitigating phase-shift errors and harmonic artifacts.
• To enable high-precision optical measurements without requiring hardware modifications.

Main Methods:

• Developed ARIA, integrating a physical model of the phase-shift field parameterized by Zernike polynomials.
• Employed a two-level iterative framework decoupling surface figure and harmonic components using extended linear least-squares.
• Utilized a reciprocal phase-shifting scheme for validation with forward and reverse datasets.

Main Results:

• ARIA reduced reconstructed RMS error from 17.93 nm to 4.20 nm (forward) and 3.98 nm (reverse).
• Residual RMS values were approximately 1.00 nm and 1.25 nm relative to a reciprocal-average reference.
• Demonstrated effective suppression of phase-shift-induced distortion and harmonic artifacts.

Conclusions:

• ARIA significantly enhances measurement precision in high-NA Fizeau interferometry.
• The algorithm successfully corrects for systematic wavefront distortions and harmonic noise.
• ARIA offers a robust, software-based solution for high-accuracy optical metrology.