Canceling the momentum in a phase-shifting algorithm to eliminate spatially uniform errors.

Area of Science:

• Optical Metrology
• Interferometry
• Signal Processing

Background:

• Phase-shifting interferometry (PSI) is susceptible to phase modulation nonlinearity.
• Nonlinearity introduces both uniform and nonuniform phase errors in measurements.
• Existing algorithms primarily address spatially variable errors, leaving uniform errors uncorrected.

Purpose of the Study:

• To develop a method for eliminating uniform phase errors caused by nonlinearity in PSI.
• To propose a design approach for phase-shifting algorithms that cancels the momentum of data-sampling weights.

Main Methods:

• Utilized characteristic polynomials in the Z-transform domain to analyze algorithm properties.
• Proposed modifying an M-frame algorithm to an (M+2)-frame algorithm.
• Introduced a new algorithm symmetry to cancel the uniform error component.

Main Results:

• Demonstrated that uniform phase error is proportional to the inertial momentum of the algorithm's weights.
• Successfully designed a modified (M+2)-frame algorithm that eliminates uniform errors.
• The proposed method effectively cancels the momentum, thereby removing the uniform error.

Conclusions:

• The proposed Z-transform-based design approach effectively eliminates uniform phase errors in PSI.
• The modified (M+2)-frame algorithm offers improved phase measurement accuracy by addressing nonlinearity.
• This technique provides a pathway for developing more robust phase-shifting algorithms.