Measure for Approximation of Fourier Optics

The technique of Fourier holography is considered from the point of view of the construction of an algebraic model. It is shown that the technique yields a construction of a semigroup of fuzzy subsets with convolution as addition and correlation as subtraction. It is proved that in an approximation to linearity of the Fourier transformation, the Sugeno -measure, which takes fuzzy values, is an appropriate tool for Fourier optics.