loading
Documents

Research.Publish.Connect.

Paper

Authors: Tomohiro Aoyagi ; Kouichi Ohtsubo and Nobuo Aoyagi

Affiliation: Faculty of Information Sciences and Arts, Toyo University, 2100 Kujirai, Saitama, Japan

ISBN: 978-989-758-364-3

Keyword(s): Fresnel Transform, Dual Orthogonal Property, Eigenvalue Problem, Jacobi Method, Hermitian Matrix.

Abstract: The fundamental formula in an optical system is Rayleigh diffraction integral. In practice, we deal with Fresnel diffraction integral as approximate diffraction formula. By optical instruments, an optical wave is subject to a band limited. To reveal the band-limited effect in Fresnel transform plane, we seek the function that its total power in finite Fresnel transform plane is maximized, 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. Moreover, we also prove that the eigenfunctions corresponding to distinct eigenvalues have dual orthogonal property. By discretizing the kernel and integral calculus range, the eigenvalue problems of the integral equation depend on a one of the Hermit ian matrix in finite dimensional vector space. We use the Jacobi method to compute all eigenvalues and eigenvectors of the matrix. We consider the application of the eigenvectors to the problem of approximating a function and showed the validity of the eigenvectors in computer simulation. (More)

PDF ImageFull Text

Download
CC BY-NC-ND 4.0

Sign In Guest: Register as new SciTePress user now for free.

Sign In SciTePress user: please login.

PDF ImageMy Papers

You are not signed in, therefore limits apply to your IP address 35.173.234.237

In the current month:
Recent papers: 100 available of 100 total
2+ years older papers: 200 available of 200 total

Paper citation in several formats:
Aoyagi, T.; Ohtsubo, K. and Aoyagi, N. (2019). Band-limited Orthogonal Functional Systems for Optical Fresnel Transform.In Proceedings of the 7th International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS, ISBN 978-989-758-364-3, pages 147-153. DOI: 10.5220/0007367001470153

@conference{photoptics19,
author={Tomohiro Aoyagi. and Kouichi Ohtsubo. and Nobuo Aoyagi.},
title={Band-limited Orthogonal Functional Systems for Optical Fresnel Transform},
booktitle={Proceedings of the 7th International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,},
year={2019},
pages={147-153},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0007367001470153},
isbn={978-989-758-364-3},
}

TY - CONF

JO - Proceedings of the 7th International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,
TI - Band-limited Orthogonal Functional Systems for Optical Fresnel Transform
SN - 978-989-758-364-3
AU - Aoyagi, T.
AU - Ohtsubo, K.
AU - Aoyagi, N.
PY - 2019
SP - 147
EP - 153
DO - 10.5220/0007367001470153

Login or register to post comments.

Comments on this Paper: Be the first to review this paper.