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A theory is described to relate the statistical properties of the fields backscattered from rough surfaces to those of speckle in synthetic hetic aperture rdar (SAR) images. The expressions are derived for the autocorrelation and cross-correlation functions of speckle intensity in both single-look and multilook images of stationary random rough surfaces in terms of the SAR system parameters and the autocorrelation function of backscatter radar cross-section fluctuations. It is shown that if the correlation scale of cross-section fluctuations is comparable with or greater than the SAR resolution, the correlation functions of speckle intensity depend on those of the cross-section fluctuations. This property, therefore, may be applied to image classification. Comparison on of the theory with computer simulation shows good agreement.