Comparative analysis on some spatial-domain filters for fringe pattern denoising.

Area of Science:

• Optics and Photonics
• Image Processing
• Metrology

Background:

• Fringe patterns from optical interferometry contain vital data on shape, deformation, and refractive index.
• Image noise significantly hinders the accurate demodulation and analysis of these fringe patterns.
• Effective denoising, particularly filtering along fringe orientation, is essential before data extraction.

Purpose of the Study:

• To analyze and compare four prominent fringe pattern denoising filters: coherence enhancing diffusion, spin filtering, second-order oriented partial-differential equations, and regularized quadratic cost function.
• To establish the theoretical relationships and equivalencies among these different filtering approaches.
• To validate theoretical findings with quantitative assessments on simulated fringe patterns.

Main Methods:

• Theoretical analysis of filter formulations to determine mathematical relationships.
• Implementation and application of coherence enhancing diffusion, spin filtering, second-order oriented partial-differential equations, and regularized quadratic cost function.
• Quantitative evaluation using simulated noisy fringe patterns to assess performance and validate equivalencies.

Main Results:

• Theoretical analysis demonstrates significant equivalencies among the four investigated fringe filtering methods.
• Quantitative results on simulated data confirm the theoretical findings, showing comparable performance.
• The study establishes that these distinct filters largely operate on similar principles for oriented fringe pattern enhancement.

Conclusions:

• The analyzed fringe denoising filters exhibit substantial theoretical and practical equivalence.
• This equivalence simplifies the choice of filter for researchers working with optical interferometric data.
• The findings contribute to more robust and efficient fringe pattern analysis in metrology and optical sensing.