Implementing non-scalar diffraction in Fourier optics via the Braunbek method

Diffraction, Fourier Optics and Imaging

Nonuniform sampled scalar diffraction calculation using nonuniform fast Fourier transform.

Scalar diffraction calculations, such as the angular spectrum method (ASM) and Fresnel diffraction, are widely used in the research fields of optics, x rays, electron beams, and ultrasonics. It is possible to accelerate the calculation using fast Fourier transform (FFT); unfortunately, acceleration of the calculation of nonuniform sampled planes is limited due to the property of the FFT that im...

Non - vanishing of scalar products of Fourier -

Optics beyond the diffraction limit

In this lecture, we introduce the basic concepts of near-field optics using two different points of view: the plane-wave angular spectrum and the electric-dipole radiation. The first approach leads naturally to the diffraction limit and to the concepts of evanescent waves and near field. The second approach shows that the basic laws of electromagnetic radiation also lead to the classical resolu...

Implementing non-stationary filtering in time and in Fourier domain

Non-stationary filtering of seismic data can be accomplished in time or in Fourier domain by the theory of non-stationary convolution (Margrave, 1998). Here I show the results of implementing this theory for time-variant filtering of seismic data with an arbitrary number of filters and for forward and inverse NMO correction in the frequency domain. In the first case I show that the filters may ...