Coherence conditions define the volume of a mode and the number of modes in a radiation field. The number of spatial modes or independent channels is equal to the maximum number of pixels in a plane. The field amplitudes of thermal sources fluctuate randomly, and the superposition of different modes produces a fluctuating interference pattern (speckle) in space and time. A stationary interference pattern or a standing wave can, even for such a source, be obtained in the focal plane of a lens. The observation of interference patterns in other planes requires observation times shorter than the coherence time. Under these conditions one can observe only the photon shot noise and not the interference fringes with presently available x-ray sources.
Propagation in space conserves the number of modes or the information content of a radiation field. A recording of the field on a two-dimensional surface contains sufficient information to reconstruct a two-dimensional object with high fidelity. Reconstruction of a three-dimensional scene requires a large number of two-dimensional recordings. Imaging with lenses or mirrors with incoherent illumination adds the contributions from many different coherent illuminations and allows reconstruction of each plane in a three-dimensional scene with high fidelity by a simple change of focus.
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