Effect of thermal expansion on speckle correlation from surface scattering of a transparent dielectric slab

We study the variation in the back-scattered light from a slab of silicate glass on a change of the glass temperature. Coherent illumination scattered from a ground surface of the glass creates a speckle pattern resulting from the sum of two different scattering events: one originating from the backward scattering from the rough surface, and the second from the forward-scattered light, which is Fresnel reflected from the flat back surface of the slab and rescattered (in the forward direction) by the rough surface. Experimental and theoretical studies show that on heating the glasses, the correlation between the initial and the final speckle patterns oscillates as a function of temperature with a frequency proportional to the thermally induced changes in the optical path in the glass. A measurement of the thermal expansion coefficient α is obtained from the oscillations with 0.01% accuracy, provided that the change in refractive index with temperature is known. The observed slow decrease, in the amplitude of the temperature-induced oscillations is in agreement with the theoretical analysis of the effect of uniform thermal expansion of the scattering surface. The surface expansion also results in a damped, slow oscillation of the correlation due to the nonrandom motion of the expanding scatterers, which result in the partial rephasing of the scattered waves when the scatterers move a distance on the order of a wavelength. If the refractive index change with temperature is unknown, the decrease in the amplitude of oscillations can be used to determine α, the thermal expansion coefficient while the oscillations can be used to determine the refractive index change with temperature. The method presented is thus an alternative for measuring the thermal expansion coefficient and the change of index with temperature, and can be applied when dealing with strongly scattering surfaces, where one cannot use the normal fringe method. Different glass thicknesses and sample tilts with respect to the incident laser beam are shown to modify the correlation function.