Instantaneous speckle structures in a partially coherent optical wave field with broad frequency and angular spectra

We consider the hypothesis of instantaneous volume speckle structures in a partially coherent optical wave field of frequency-broadband radiation from an extended light source. We discuss the spatiotemporal correlation properties of instantaneous speckle structures and the relation of these properties with the spatiotemporal coherent properties of the wave field. We show that the instantaneous speckle structures determine spatial fluctuations of the wave field and its spatial coherent properties. Using numerical calculations of the field of wave perturbations in the near-field diffraction region of the extended light source, we obtain images of instantaneous speckle structures in the longitudinal cross section of the wave field and investigate the correlation properties of the spatial distribution of the instantaneous intensity of the wave field in the direction of its propagation as functions of the width of the frequency spectrum and the width of the angular spectrum of the field. We show that the longitudinal length of instantaneous speckles can be determined either by the width of the frequency spectrum of the field, or the width of its angular spectrum, or, jointly, by the width of the frequency spectrum and the width of the angular spectrum of the field. We find conditions under which instantaneous speckle structures propagate, experiencing decorrelation changes during their propagation, to a distance that is determined by the width of the angular spectrum of the field.