Small-N Speckle: Phase-Contrast Approach

Abstract

The theory of image plane speckle is very well confirmed by experimental data, except the case in which a considerably small -N speckle (N<0.04) is produced by a deep phase screen.1 N is an effective number of scatterers that contribute to the complex amplitude of the scattered field. Here a new theoretical approach is proposed. It is assumed that for such a value of N there is a close relationship between the local value of parameters that characterize a phase screen at an arbitrary point and the value of intensity at the conjugate point of the image plane. Therefore the intensity fluctuation is considered similar to the phase-contrast effect and not the speckle phenomenon.A relation that expresses the intensity fluctuation in terms of first and second spatial derivatives of phase is calculated. This relation takes into account both the finite bandwidth of the imaging system and the displacement of the observation plane with respect to the image plane (defocusing). A formula for contrast versus N and defocusing is derived. Results obtained for a perfectly focused image of a gaussian screen are compared with the theory of Jakeman and McWhirter2 and with the experimental results of Levine and Dainty.1 This current research has shown that for a moderately rough screen (rms phase =211 rad) and N<0.012 the approach presented here is better confirmed by the experiment than the theory presented by Jakeman and McWhirter? It is found that the key parameter of the presented theory is a product of N and phase variance. The above conclusion can also be obtained from Jakeman and McWhirter's theory when approximations for N<<1 are performed.

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