Determination of interferometer phase distributions by use of wavelets

Area of Science:

• Optical metrology
• Wavelet analysis
• Image processing

Background:

• Interferometry is crucial for precise measurements.
• Extracting phase information from fringe patterns is essential.
• Traditional phase retrieval methods often face challenges like phase unwrapping.

Purpose of the Study:

• To introduce a new technique for direct phase gradient extraction.
• To overcome limitations of existing phase retrieval methods.
• To enable accurate 2-D phase distribution reconstruction from single images.

Main Methods:

• Utilizing the maximum modulus of the continuous wavelet transform (CWT) of fringe data.
• Tracking CWT maxima to determine phase gradients.
• Integrating gradients to obtain the phase distribution, minimizing errors.
• Comparing the new method with standard phase retrieval techniques.

Main Results:

• The technique successfully extracts phase gradients directly from 2-D fringe data.
• Phase distribution is obtained with high accuracy via integration.
• Phase unwrapping complications are effectively circumvented.
• Excellent agreement is demonstrated when compared to standard methods.
• The method can extract full 2-D phase distributions from a single image, similar to Fourier-transform methods.

Conclusions:

• The presented CWT-based technique offers a robust alternative for phase gradient extraction.
• It simplifies phase retrieval by avoiding phase unwrapping.
• The method's ability to use single images enhances its practical applicability in optical metrology.