Orthogonal functional system for finite Fresnel transform

Tomohiro Aoyagi; Kouichi Ohtsubo M.D.; Nobuo Aoyagi

doi:10.1117/12.2316999

24 April 2018 Orthogonal functional system for finite Fresnel transform

Tomohiro Aoyagi, Kouichi Ohtsubo M.D., Nobuo Aoyagi

Proceedings Volume 10711, Biomedical Imaging and Sensing Conference; 107112A (2018) https://doi.org/10.1117/12.2316999
Event: SPIE Structured Light, 2018, Yokohama, Japan

Abstract

The Fresnel transform has been studied mathematically and revealed the topological properties in Hilbert space. Main aim is to reveal the property of band-limited function. We seek the function that its total power is maximized in finite Fresnel transform plane, on condition that an input signal is zero outside the bounded region. This problem is a variational one with an accessory condition. This leads to the eigenvalue problems of Fredholm integral equation of the first kind. The kernel of the integral equation is Hermitian conjugate and positive definite. Therefore, eigenvalues are real non-negative numbers. We prove that the eigenfunctions corresponding to distinct eigenvalues are orthogonal.

Citation Download Citation

Tomohiro Aoyagi, Kouichi Ohtsubo M.D., and Nobuo Aoyagi "Orthogonal functional system for finite Fresnel transform", Proc. SPIE 10711, Biomedical Imaging and Sensing Conference, 107112A (24 April 2018); https://doi.org/10.1117/12.2316999

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