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Recursive algorithm for phase retrieval in the fractional fourier transform domain.

W X Cong, N X Chen, B Y Gu

|February 28, 2008

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This study introduces a new recursive algorithm for phase retrieval using the discrete fractional Fourier transform (dFrFT). The method simplifies computations and successfully recovers phase information from two intensity measurements without an initial phase estimate.

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Area of Science:

Digital Signal Processing
Image Reconstruction
Fourier Optics

Background:

Phase retrieval is crucial for reconstructing signals and images.
Conventional iterative algorithms often require initial phase estimates and complex computations.
The fractional Fourier transform (FrFT) offers a powerful tool for signal analysis in a transformed domain.

Purpose of the Study:

To introduce and validate a novel recursive algorithm for phase retrieval.
To implement phase retrieval in the discrete fractional Fourier transform (dFrFT) domain.
To simplify computational complexity and eliminate the need for initial phase estimates in phase retrieval.

Main Methods:

Discussion of the discrete fractional Fourier transform (dFrFT) and its properties.
Proposal of a recursive algorithm for phase retrieval using two intensity measurements in the dFrFT domain.
Utilizing simulation results to verify the algorithm's performance.

Main Results:

The proposed recursive algorithm simplifies computational manipulations.
The algorithm successfully retrieves phase information without requiring an initial phase estimate.
Simulation results demonstrate the effectiveness of the approach in recovering phase from two intensities.

Conclusions:

The developed recursive algorithm offers an efficient method for phase retrieval in the dFrFT domain.
This approach provides a significant advantage over conventional iterative methods by reducing computational load and initial condition requirements.
The method is validated through simulations, showing successful phase recovery.