Some developments on fractional Fourier optics

Daomu Zhao; Shaomin Wang

doi:10.1117/12.471424

20 September 2002 Some developments on fractional Fourier optics

Daomu Zhao, Shaomin Wang

Proceedings Volume 4927, Optical Design and Testing; (2002) https://doi.org/10.1117/12.471424
Event: Photonics Asia, 2002, Shanghai, China

Abstract

Some developments on fractional Fourier optics are reported in this paper. First, a thick lens can be regarded as a fractional Fourier transformer. Second, relations between the Collins formulae and the fractional Fourier transform or fractional Hankel transform are bridged, we show that the Collins formulae in spatial domain or in spatial-frequency domain can be described by the fractional Fourier transform or fractional Hankel transform. Third, connections between the multi-element resonators and the scaled fractional Fourier transforms are established, it is shown that there exists twice scaled fractional Fourier transform for beams in completing one round trip, the beam oscillation in resonator can be viewed as a process of consecutive implementing scaled fractional Fourier transform. Finally, some extensions of the fractional Fourier transforms to misaligned optical systems are simply reviewed.

Citation Download Citation

Daomu Zhao and Shaomin Wang "Some developments on fractional Fourier optics", Proc. SPIE 4927, Optical Design and Testing, (20 September 2002); https://doi.org/10.1117/12.471424

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