Pixelated mask spatial carrier phase shifting interferometry algorithms and associated errors

Area of Science:

• Optical Metrology
• Interferometry

Background:

• Phase calculation error is a primary limitation in temporal and spatial carrier phase shifting interferometry.
• This error stems from inaccuracies in the relative phase shift between sample points.
• In spatial carrier phase shifting interferometry, wavefront variations directly cause unavoidable phase shifting errors.

Purpose of the Study:

• To introduce and evaluate a novel pixelated spatial carrier phase shifting technique.
• To minimize phase shifting errors caused by wavefront variations in spatial carrier phase shifting interferometry.
• To derive a formula for phase calculation error and compare the new technique with existing methods.

Main Methods:

• Development of a pixelated spatial carrier phase shifting technique by 4D technologies.
• Grouping phase-shifted pixels around a single point in 2D to mitigate spatial wavefront variations.
• Derivation of a formula for phase calculation error in spatial carrier phase shifting interferometry.

Main Results:

• The pixelated technique effectively minimizes phase shift changes due to spatial variations in the test wavefront.
• A formula for phase calculation error in spatial carrier phase shifting interferometry was derived.
• The error associated with linear N-point averaging algorithms was analyzed and compared to the pixelated technique.

Conclusions:

• The pixelated spatial carrier phase shifting technique offers a significant improvement in reducing phase calculation errors.
• This method addresses the inherent limitations of spatial carrier phase shifting interferometry caused by wavefront distortions.
• The derived error formula provides a quantitative basis for evaluating and comparing phase shifting algorithms.