Optical holography and computational intelligence: algebraic foundations

Alexander V. Pavlov

doi:10.1117/12.403629

13 October 2000 Optical holography and computational intelligence: algebraic foundations

Alexander V. Pavlov

Proceedings Volume 4120, Applications and Science of Neural Networks, Fuzzy Systems, and Evolutionary Computation III; (2000) https://doi.org/10.1117/12.403629
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

Our main interest is to formulate algebraic description of both Geometrical and Fourier-approximations of Optics. We use triangular- norms based approach to formulate algebraic descriptions for both geometrical and Fourier-approximations of optics. To take into consideration real nonlinearity of recording media the measure theory is used. Unlimited plane wave as an universal set is considered. For geometrical optics an algebraic model as designed. Logical operators, parameterized by recording media operators, are defined. To extend dynamical range of negative recording media from linear to over-exposure one, non-additive measure is defined. Algebraic properties of the model in dependence on the approximating function choosing are discussed. Theoretical conclusions are illustrated by experimental measuring and numerical simulation for two-layered optical system. For Fourier- approximation Fourier-duality is used to design semi-ring by DeMorgan's law using, 4-f Fourier-holography setup constructs sequence of model's elements, corresponding to Peano's axioms. Convolution is an abstract addition and correlation is an abstract subtraction in the model Fuzzy- valued measure is defined and fuzzy-value logic is designed. Theoretical conclusions are confirmed by experimental demonstration of logical inference Generalized Modus Ponens realization.

Citation Download Citation

Alexander V. Pavlov "Optical holography and computational intelligence: algebraic foundations", Proc. SPIE 4120, Applications and Science of Neural Networks, Fuzzy Systems, and Evolutionary Computation III, (13 October 2000); https://doi.org/10.1117/12.403629

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available