TY - CHAP
T1 - Fourier Data Processing in Optics
AU - Zalevsky, Zeev
AU - Mendlovic, David
AU - Shabtay, Gal
AU - Levy, Uriel
N1 - Publisher Copyright:
© 2016 by Taylor & Francis Group, LLC.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85168439257&partnerID=8YFLogxK
U2 - 10.1081/E-EOE2-120009528
DO - 10.1081/E-EOE2-120009528
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AN - SCOPUS:85168439257
SN - 9781439851012
SP - 784
EP - 798
BT - Encyclopedia of Optical and Photonic Engineering Second Edition
PB - CRC Press
ER -