Techniques for arbitrary sampling in two-dimensional Fourier transforms

Area of Science:

• Optics and Photonics
• Computational Imaging
• Signal Processing

Background:

• Accurate computation of optical propagation is crucial for imaging and phase retrieval.
• Traditional methods like the padded fast Fourier transform (FFT) have limitations in speed and sampling flexibility.
• Exploring alternative computational approaches is essential for advancing optical techniques.

Purpose of the Study:

• To evaluate the performance of matrix triple product (MTP) and chirp z-transform (CZT) for 2D optical propagation.
• To compare MTP and CZT against the conventional padded 2D FFT.
• To identify optimal computational strategies for phase-retrieval algorithms.

Main Methods:

• Theoretical analysis of MTP and CZT algorithms for optical propagation.
• Empirical benchmarking of MTP, CZT, and padded 2D FFT run times.
• Performance evaluation across various sampling regimes relevant to phase retrieval.

Main Results:

• MTP and CZT demonstrate computational performance comparable to or exceeding the padded 2D FFT.
• Both MTP and CZT offer enhanced flexibility in controlling sampling parameters.
• The chirp z-transform (CZT) shows particular promise as a versatile alternative to the 2D FFT.

Conclusions:

• MTP and CZT are effective and efficient methods for 2D optical propagation computations.
• For phase-retrieval applications, CZT presents a robust and flexible general-purpose alternative to the padded 2D FFT.
• These findings can guide the selection of computational tools for advanced optical imaging and analysis.