# A wavelength diversity technique for smoothing of speckle

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## Abstract

Theoretical and experimental results are given for the wavelength dependence of speckle, thus establishing a method for the reduction of speckle noise in holographic microscopy with the use of multitoned illumination and a panchromatic viewing system. A model is presented for a partially diffuse phase type of object and the statistical behavior of t he speckle produced in the image of this object is studied. A calculation is made for the spectral autocorrelation function which gives a wavelength spacing required to decouple the speckle patterns produced by two tones, this spacing being found to be inversely proportional to the standard deviation of the heights of the scatterers on the object. A criteria is defined for the degradation of an image due to speckle and the resultant improvement is found to depend on the square root of the number of independent tones used. The wavelength dependence of speckle is verified in a series of experiments where we illuminate the object by both laser and bandlimited light. We first demonstrate the averaging of speckle in the image of a pap smear when we use four tones of an argon laser (5145, 4965, 4880 and 4765 Å). We then show that the image of a rough object is speckly even for bandwidths up to 5Å; and then we demonstrate the smoothing of speckle when both a scotch tape diffuser and a section of an optic nerve is illuminated by six equally spaced bandlimited tones scanning 1,500Å. Thus, in this study, we demonstrate the feasibility of eliminating objective speckle in holographic microscopy using a multimonochromatic source and also provide a theoretical basis for studying the properties of rough surfaces by studying the wavelength diversity of the speckle produced by them.

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