The formation of instantaneous speckle-modulated interference images of thin transparent layers in an optical microscope under an illuminating quasi-monochromatic or frequency broadband wave field with wide angular spectra and coherent effects are considered. Instantaneous speckle-modulated interference images of the layer in the transverse and longitudinal sections of the total wave field reflected by the layer are obtained by numerical simulation of the spatial distributions of the complex amplitude of the wave fields reflected by the layer faces and their superposition. The results of computer simulation of instantaneous speckle-modulated and experimentally observed averaged interference images of the layer under quasi-monochromatic and frequency broadband illuminating layer field with different width of the angular spectrum are presented. The mutual correlation of instantaneous speckle fields reflected by the layer faces and the effects of the influence of the width of the angular and frequency spectra of the illuminating field on the contrast of experimentally observed interference images of the layer are studied numerically. On the basis of the instantaneous speckle-modulation of the wave field the physical mechanism of the influence of angular width and the width of the frequency spectra of the illuminating field on the mutual coherence of the interfering wave fields is investigated.
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