Analysis of some two dimensional functions using two dimensional Fourier transforms: Image reconstruction and physical significance

Abstract

The Fourier transform can be thought of being the decomposition of the image into two dimensional spatial sinusoidal frequency components. Two dimensional Gaussian, Rectangular (Rect) and Circular (Circ) functions were created using two dimensional Fourier series and transform approximations. The Fourier domain or frequency domain represents a point of a particular frequency contained in the spatial domain image. Here the spectrum of two dimensional basic signals (including images) is analyzed from the point of view of diffraction patterns.