Fourier Data Processing in Optics

This entry provides an overview of the developments in the field of optical Fourier data processing. The discussion begins with definitions and the properties of the Fourier transform and also its relevancy to optics in “Fourier Optics,” and then, in “The Wigner Representation,” by defining the Wigner representation—its mathematical definition and its properties. The subject of optical correlation and pattern recognition is discussed starting with the conventional match filters and then the circular, the Mellin, and the logarithmic harmonics decomposition, and then, the section presents the joint transform correlator and the Wavelet transform. Various techniques for statistical processing are presented, and common performance measurements, such as signal-to-noise ratio, peak-to-correlation efficiency, and Horner efficiency are discussed. The fractional Fourier transform is mentioned, including its mathematical definitions, its relation to fractional correlation, and its applications in engineering science.