Axiomatic System Theory And Optical Images

Giovanni Crosta

doi:10.1117/12.958384

18 June 1980 Axiomatic System Theory And Optical Images

Giovanni Crosta

Proceedings Volume 0212, Optics and Photonics Applied to Three-Dimensional Imagery; (1980) https://doi.org/10.1117/12.958384
Event: Optics, Photonics, and Iconics Engineering Meeting, 1979, Strasbourg, France

Abstract

Several practical problems which arise in optics are related to achieving a desired three-dimensional signal distribution inside a bounded spatial domain. If we deal with harmonic time dependence, we find an example in integrated circuit microfabrication; if time dependence is arbitrary, we may think of pulse compression in dispersive media. To all of these problems there is a unifying approach based on axiomatic system theory. This theory is well-known to rely on the state space formulation. The way in which the in put acts on the state is quantified by the "controllability" concept. Similarly "observability" relates output data to the state. Strictly related to this approach is the "opt-imal control problem", where the task is to find an input which minimizes a functional consisting of two addenda: a physical term comparing the obtained output with the desired one by some quadratic criterion, and an economical term related to the cost of a given input. These concepts are widely used in signal processing, control theory, etc. Their application to optical problems requires them to be extended to distributed parameter systems. For the cases discussed in the text controllability results will be given and optimal control problems will be stated.

Citation Download Citation

Giovanni Crosta "Axiomatic System Theory And Optical Images", Proc. SPIE 0212, Optics and Photonics Applied to Three-Dimensional Imagery, (18 June 1980); https://doi.org/10.1117/12.958384

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