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Fresnel transform phase retrieval from magnitude.
Todd A Pitts1, James F Greenleaf
1Accent Optical Technologies, Albuquerque, NM 87124, USA. pitts.todd@ieee.org
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
|September 4, 2003
Summary
This study introduces a phase retrieval method using Fresnel transforms for 2D signals. The technique accurately reconstructs optical phase shifts from ultrasound fields, validated by experimental data.
Area of Science:
- Optics
- Signal Processing
- Acoustics
Background:
- Phase retrieval is crucial for reconstructing wave fields.
- Traditional methods face limitations with complex signals and specific domains.
- Fresnel transform offers advantages in preserving spatial information.
Purpose of the Study:
- To develop a generalized projection method for phase recovery of 2D signals.
- To establish the uniqueness of phase retrieval under specific constraints.
- To demonstrate a practical application in ultrasound beam measurement.
Main Methods:
- Utilizing magnitude information in both spatial and Fresnel transform domains.
- Developing an optimally relaxed iterative algorithm for reduced computation.
- Applying the method to reconstruct optical phase shifts from ultrasound-induced intensity distributions.
Main Results:
- Uniqueness of phase retrieval for complex signals with finite support and Fresnel transform magnitude was established.
- An optimized algorithm significantly reduced the number of iterations required.
- Experimental reconstruction of a 3D acoustic pressure field showed excellent agreement with hydrophone measurements.
Conclusions:
- The generalized projection method provides quantitative phase retrieval for optical fields affected by ultrasound.
- Fresnel transform-based phase retrieval is effective for applications like ultrasound beam measurement.
- The method successfully reconstructs complex optical wavefronts and acoustic fields.