Coherence volume of an optical wave field with broad frequency and angular spectra

We consider the sizes of a region in a three-dimensional space in which an optical wave field excites mutually coherent perturbations. We discuss the conditions under which the length of this region along the direction of propagation of the wave field and, correspondingly, its volume are determined either by the width of the frequency spectrum of the field or by the width of its angular spectrum, or by the parameters of these spectra simultaneously. We obtain expressions for estimating extremely small values of the coherence volume of the fields with a broad frequency spectrum and an extremely broad angular spectrum. Using the notion of instantaneous speckle-modulation of the wave field, we give a physical interpretation to the occurrence of a limited coherence volume of the field. The length of the spatiotemporal coherence region in which mutually coherent perturbations occur at different times is determined. The coherence volume of a wave field that illuminates an object in high-resolution microscopy with frequency broadband light is considered. The conditions for the dominant influence of the angular or frequency spectra on the longitudinal length of the coherence region are given, and the conditions for the influence of the frequency spectrum width on the transverse coherence of the wave field are examined. We show that, when using fields with broad and ultrabroad spectra in high-resolution microscopy, this influence should be taken into account.