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.

Date Published: 24 April 2018
PDF: 3 pages
Proc. SPIE 10711, Biomedical Imaging and Sensing Conference, 107112A (24 April 2018); doi: 10.1117/12.2316999

Published in SPIE Proceedings Vol. 10711:
Biomedical Imaging and Sensing Conference
Toyohiko Yatagai; Yoshihisa Aizu; Osamu Matoba; Yasuhiro Awatsuji; Yuan Luo, Editor(s)