Local frequency estimation for the fringe pattern with a spatial carrier: principle and applications

Area of Science:

• Optics
• Image Processing
• Metrology

Background:

• Fringe pattern analysis is crucial for various metrology applications.
• Traditional methods face challenges with detuning errors and boundary accuracy.
• Spatial carriers are often used in fringe analysis for phase retrieval.

Purpose of the Study:

• To present a local frequency estimation approach for fringe patterns with spatial carriers.
• To introduce applications of this approach in fringe pattern analysis.
• To improve phase accuracy at aperture boundaries in Fourier-transform methods.

Main Methods:

• A local frequency estimation method is developed, utilizing pixel neighborhoods.
• A 2D spatial carrier phase-shifting algorithm is derived to avoid detuning errors.
• A novel aperture extrapolation method is introduced to enhance boundary phase accuracy.

Main Results:

• The local frequency estimation effectively determines 2D spatial frequencies per pixel.
• The derived algorithm successfully handles stronger phase deformations and avoids detuning errors.
• The aperture extrapolation method significantly improves phase accuracies at aperture boundaries.

Conclusions:

• The proposed local frequency estimation approach enhances fringe pattern analysis.
• The developed methods offer improved accuracy and robustness in phase retrieval.
• This work contributes to more precise fringe analysis techniques.