Abstract

Following the Volterra theorem, every nonlinear operator can be implemented with a sum of integrals applied over the input. The second-order Volterra operator that describes many useful systems can be related to a single integral that is a projection of an operation called the triple correlation. This operation may be easily implemented optically and thus be incorporated into fast real-time nonlinear control systems. We present a theoretical investigation of the relation existing between the Volterra operators and the triple correlation as well as an experimental demonstration that validates the theory.

© 2001 Optical Society of America

Optoelectronic implementation of the triple correlation

David Mendlovic, Adolf W. Lohmann, David Mas, and Gal Shabtay
Opt. Lett. 22(13) 1018-1020 (1997)

Fractional triple correlation and its applications

David Mendlovic, David Mas, Adolf W. Lohmann, Zeev Zalevsky, and Gal Shabtay
J. Opt. Soc. Am. A 15(6) 1658-1661 (1998)

Parallel fractional correlation: an optical implementation

Sergio Granieri, Myrian Tebaldi, and Walter D. Furlan
Appl. Opt. 40(35) 6439-6444 (2001)

Interaction of first- and second-order direction in motion-defined motion

Johannes M. Zanker and Nicholas R. Burns
J. Opt. Soc. Am. A 18(9) 2321-2330 (2001)

Generality of matched filtering and minimum Euclidean distance projection for optical pattern recognition

Richard D. Juday
J. Opt. Soc. Am. A 18(8) 1882-1896 (2001)