Frequency-variable illumination has been used previously to provide high resolution imaging in one dimension. The paper extends the results on this imaging by frequency scanning to derive the expression for a two-dimensional image. This is the Fourier transformation, with respect to the angle and frequency of illumination, of the electric field detected in the far-field region of the object. The case is considered of a rough object and it is shown that for roughness finer than the resolution of the imaging system, the image has a granular appearance corresponding to the classical speckle effect. Large scale phase perturbations lead to the elevation displacement effect.
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