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Direct Linear Transformation for the Measurement of In-Situ Peripheral Nerve Strain During Stretching

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Fast and accurate algorithm for the computation of complex linear canonical transforms.

Aykut Koç¹, Haldun M Ozaktas, Lambertus Hesselink

¹Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA. aykutkoc@stanford.edu

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|September 3, 2010

Summary

This summary is machine-generated.

A new algorithm efficiently computes complex linear canonical transforms (CLCTs), essential for modeling complex optical systems. This method accurately represents both lossy and lossless optical phenomena, including complex fractional Fourier transforms (CFRTs).

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Area of Science:

Optics and Photonics
Computational Science
Signal Processing

Background:

Complex linear canonical transforms (CLCTs) model input-output relationships in complex quadratic-phase systems.
Complex parameters enable representation of lossy paraxial optical systems like Gaussian apertures and graded-index media.
Lossless systems such as thin lenses and free space are also representable, along with arbitrary combinations.

Purpose of the Study:

To develop a fast and accurate numerical algorithm for computing CLCTs.
To enable the modeling of a wider range of paraxial optical systems, including lossy ones.
To provide an efficient method for computing complex-ordered fractional Fourier transforms (CFRTs) as a special case.

Main Methods:

The algorithm decomposes arbitrary CLCT matrices into real and complex chirp multiplications and Fourier transforms.
Output samples are computed from input samples in approximately N log N time complexity.
A space-bandwidth product tracking formalism is employed to ensure sufficient sampling for accurate reconstruction.

Main Results:

A computationally efficient and accurate algorithm for CLCTs has been successfully developed.
The algorithm effectively handles complex parameters, extending the applicability to lossy optical systems.
Complex-ordered fractional Fourier transforms (CFRTs) are computed accurately as a specific instance of the general algorithm.

Conclusions:

The developed algorithm offers a significant advancement in the numerical computation of CLCTs.
It provides a unified and efficient framework for analyzing diverse paraxial optical systems.
The method ensures information-theoretically sufficient sampling, leading to reliable transform reconstruction.