24 April 2018 Orthogonal functional system for finite Fresnel transform
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Proceedings Volume 10711, Biomedical Imaging and Sensing Conference; 107112A (2018) https://doi.org/10.1117/12.2316999
Event: SPIE Structured Light, 2018, Yokohama, Japan
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.
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Tomohiro Aoyagi, Tomohiro Aoyagi, Kouichi Ohtsubo, Kouichi Ohtsubo, Nobuo Aoyagi, Nobuo Aoyagi, } "Orthogonal functional system for finite Fresnel transform", Proc. SPIE 10711, Biomedical Imaging and Sensing Conference, 107112A (24 April 2018); doi: 10.1117/12.2316999; https://doi.org/10.1117/12.2316999

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