Fast Fourier transform based direct integration algorithm for the linear canonical transform

Dayong Wang; Changgeng Liu; Yunxin Wang; Jie Zhao

doi:10.1117/12.884980

9 April 2011 Fast Fourier transform based direct integration algorithm for the linear canonical transform

Dayong Wang, Changgeng Liu, Yunxin Wang, Jie Zhao

Proceedings Volume 7822, Laser Optics 2010; 78220I (2011) https://doi.org/10.1117/12.884980
Event: Laser Optics 2010, 2010, St. Petersburg, Russian Federation

Abstract

The linear canonical transform(LCT) is a parameterized linear integral transform, which is the general case of many well-known transforms such as the Fourier transform(FT), the fractional Fourier transform(FRT) and the Fresnel transform(FST). These integral transforms are of great importance in wave propagation problems because they are the solutions of the wave equation under a variety of circumstances. In optics, the LCT can be used to model paraxial free space propagation and other quadratic phase systems such as lens and graded-index media. A number of algorithms have been presented to fast compute the LCT. When they are used to compute the LCT, the sampling period in the transform domain is dependent on that in the signal domain. This drawback limits their applicability in some cases such as color digital holography. In this paper, a Fast-Fourier-Transform-based Direct Integration algorithm(FFT-DI) for the LCT is presented. The FFT-DI is a fast computational method of the Direct Integration(DI) for the LCT. It removes the dependency of the sampling period in the transform domain on that in the signal domain. Simulations and experimental results are presented to validate this idea.

Citation Download Citation

Dayong Wang, Changgeng Liu, Yunxin Wang, and Jie Zhao "Fast Fourier transform based direct integration algorithm for the linear canonical transform", Proc. SPIE 7822, Laser Optics 2010, 78220I (9 April 2011); https://doi.org/10.1117/12.884980

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available