Introduction to Fourier Optics

Aperture effect
When the incident wave goes through an aperture, the observed field is the combination. If a distant object is viewed through a small circular aperture that is placed close to the eye, there is an apparent "shadowing" of the center of the viewed image, while the inner perimeter of the aperture is bright.

What is Fourier Optics?(quoted from http://www.fourieroptics.org.uk/ )
Fourier optics describes the propagation of light using Fourier analysis. It can be used to describe Fresnel and Fraunhofer diffraction. The Fraunhofer diffraction pattern is the Fourier transform of the diffracting object.
Fresnel diffraction describes the diffracted light field a large distance away from the object compared to the wavelength of light, but not so large the curvature of the wavefront can be neglected. Fraunhofer diffraction describes the diffracted light field a large distance away from the object such that the curvature of the wavefront can be neglected.
Possible uses are:
• Describing image formation
• Modelling the aberrations of an optical system
• Studying the performance of a lens
• Modelling diffraction patterns and light propagation
• Optical signal processing
• Optical computing