Fourier Optics and Optical Signal Processing

Analytical and numerical analysis of linear optical systems

[+] Author Affiliations
Damien P. Kelly

University College Dublin, College of Engineering, Mathematical and Physical Sciences, School of Electrical, Electronic and Mechanical Engineering, Belfield, Dublin 4, Republic of Ireland

Bryan M. Hennelly

University College Dublin, College of Engineering, Mathematical and Physical Sciences, School of Electrical, Electronic and Mechanical Engineering, Belfield, Dublin 4, Republic of Ireland

William T. Rhodes

Florida Atlantic University, Imaging Technology Center, 777 Glades Road, Bldg. 43, Rm. 486, Boca Raton, Florida 33431, USA

John T. Sheridan

University College Dublin, College of Engineering, Mathematical, and Physical Sciences, School of Electrical, Electronic, and Mechanical Engineering, Belfield, Dublin 4, Republic of Ireland

Opt. Eng. 45(8), 088201 (September 05, 2006). doi:10.1117/1.2345070
History: Received October 19, 2005; Revised January 14, 2006; Accepted January 18, 2006; Published September 05, 2006
Text Size: A A A

The numerical calculation of the Fresnel transform (FST) presents significant challenges due to the high sampling rate associated with the chirp function in the kernel. The development of an efficient algorithm is further complicated by the fact that the output extent of the FST is dependent on the propagation distance. In this paper, we implement a recently proposed technique for efficiently calculating the FST in which we apply the Wigner distribution function and the space bandwidth product to identify suitable sampling rates. This method is shown to be suitable for all propagation distances. Our method can also be applied to describe the effect of a thin lens modeled as a chirp modulation transform (CMT). Combining our results for the FST and the CMT, we numerically calculate the light distribution at the output of both Cai-Wang and Lohmann Type-I optical fractional Fourier transform (OFRT) systems. Analytic solutions for the OFRT of rectangular window and circular apertures are presented. The analytical solutions are compared to experimental data and to numerical results for equivalent cases. Finally the numerical method is applied to examine the effect that apertured lenses, in the OFRT system, have on the output distribution.

Figures in this Article
© 2006 Society of Photo-Optical Instrumentation Engineers

Citation

Damien P. Kelly ; Bryan M. Hennelly ; William T. Rhodes and John T. Sheridan
"Analytical and numerical analysis of linear optical systems", Opt. Eng. 45(8), 088201 (September 05, 2006). ; http://dx.doi.org/10.1117/1.2345070


Tables

Access This Article
Sign in or Create a personal account to Buy this article ($20 for members, $25 for non-members).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging & repositioning the boxes below.

Related Book Chapters

Topic Collections

PubMed Articles
Advertisement
  • Don't have an account?
  • Subscribe to the SPIE Digital Library
  • Create a FREE account to sign up for Digital Library content alerts and gain access to institutional subscriptions remotely.
Access This Article
Sign in or Create a personal account to Buy this article ($20 for members, $25 for non-members).
Access This Proceeding
Sign in or Create a personal account to Buy this article ($15 for members, $18 for non-members).
Access This Chapter

Access to SPIE eBooks is limited to subscribing institutions and is not available as part of a personal subscription. Print or electronic versions of individual SPIE books may be purchased via SPIE.org.