Stochastic modulation of the Montgomery’s rings to generate the self-imaging effect with revival features

The synthesis of optical fields that follows a stochastic process and whose statistical mean values generate the self-imaging-revivals effect is analyzed. A sufficient condition for optical fields to exhibit the self-imaging effect occurs when the frequency representation is located on the Montgomery’s rings. The study is performed by implementing stationary random fluctuations on the Montgomery’s rings of additive and multiplicative types. The additive noise is of the stochastic radial walk type with zero mean. Multiplicative noise generates stochastic angular fluctuations in the rings and is implemented using the Karhunen–Loève theorem. The modal representation implicit in the theorem is obtained by interpreting the self-imaging planes as an optical cavity, assuring the statistical periodicity of the noise. A time consonance of the random fluctuations for each ring allows to determine the revivals period for the self-imaging optical fields. The model is corroborated by computer simulations.