Unwrapping of interferometric phase-fringe maps by the discrete cosine transform

Area of Science:

• Optics and Photonics
• Image Processing
• Metrology

Background:

• Interferometric techniques produce phase data with 2π cyclic discontinuities (phase wraps).
• Phase unwrapping is critical for accurate data interpretation in fields like electronic speckle pattern interferometry (ESPI).

Purpose of the Study:

• To investigate and apply an iterative least-squares phase unwrapping technique based on the discrete cosine transform (DCT).
• To assess the algorithm's performance on ESPI data using standard computer hardware.

Main Methods:

• Implementation of the Ghiglia and Romero iterative least-squares unwrapping algorithm.
• Application of the algorithm to phase data obtained from electronic speckle pattern interferometry.
• Utilizing discrete cosine transform for efficient minimization.

Main Results:

• Successful removal of phase wraps from ESPI data.
• Demonstrated robustness against noise and ability to handle phase inconsistencies.
• Algorithm proved fast and easy to implement on modest personal computer hardware.
• Local errors did not propagate, ensuring data integrity.

Conclusions:

• The iterative least-squares DCT-based phase unwrapping method is effective for ESPI.
• This technique offers a practical solution for accurate interferometric data analysis.
• The algorithm's speed, robustness, and ease of implementation make it suitable for widespread use.