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
(000.3870) General : Mathematics
(070.4340) Fourier optics and signal processing : Nonlinear optical signal processing
(070.4550) Fourier optics and signal processing : Correlators
(120.4820) Instrumentation, measurement, and metrology : Optical systems
(200.4560) Optics in computing : Optical data processing
Zeev Zalevsky, Eran Gur, and David Mendlovic, "Optical implementation of second-order nonlinear Volterra operators with use of triple correlation," J. Opt. Soc. Am. A 18, 164-169 (2001)