Carrier squeezing interferometry with π/4 phase shift: phase extraction in the presence of multi-beam interference

Area of Science:

• Optical Engineering
• Metrology

Background:

• Multi-beam interference complicates Fizeau interferometer measurements of high-reflectivity surfaces.
• Accurate phase extraction is crucial for precise surface testing.

Purpose of the Study:

• To develop an algorithm for extracting phase information from multi-beam interferograms in Fizeau interferometry.
• To improve phase retrieval precision for high-reflectivity surfaces.

Main Methods:

• Fourier series expansion was used to estimate multi-beam interference intensity up to the sixth harmonic.
• Carrier squeezing interferometry with a π/4 phase shift was employed for phase extraction.
• Conditions for a linear carrier were derived to separate phase-shift errors and phase in the frequency domain.

Main Results:

• The proposed algorithm achieved phase retrieving precision better than PV 0.008λ and RMS 0.001λ.
• High performance was maintained even with a test surface reflection coefficient as high as 0.9.
• The algorithm demonstrated robustness against phase shift variations within π/4±π/20 and existing phase-shift errors.

Conclusions:

• The developed algorithm effectively addresses multi-beam interference in Fizeau interferometry.
• Experimental validation confirmed the algorithm's superior performance, particularly in the presence of phase-shift errors.
• This method offers enhanced precision for testing challenging high-reflectivity optical surfaces.