The fundamental formula in an optical system is Rayleigh diffraction integral. In practice, we deal with Fresnel diffraction integral as approximate diffraction formula. Fresnel transforms and inverse Fresnel transforms have been formulated systematically and defined as a bounded additive, a unitary operator in Hilbert space. To investigate 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 of Hermitian conjugate and positive definite. Moreover, we prove that the eigenfunctions corresponding to distinct eigenvalues have dual orthogonal property. By discretizing the kernel and integral range to seek the approximate solutions, the eigenvalue problems of the integral equation can depend on a one of the Hermitian matrix in finite-dimensional complex value 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 problems of the approximating any functions. We show the validity and limitation of the eigenvectors in computer simulations.