A simple optical system for interpreting coherence theory
  A new theoretical technique for understanding, analyzing and developing optical systems is presented. The approach is statistical in nature, where information about an object under investigation is discovered, by examining deviations from a known reference statistical distribution. A Fourier optics framework and a scalar description of the propagation of monochromatic light is initially assumed. An object (belonging to a known class of objects) is illuminated with a speckle field and the intensity of the resulting scattered optical field is detected at a series of spatial locations by point square law detectors. A new speckle field is generated (with a new diffuser) and the object is again illuminated and the intensities are again measured and noted. By making a large number of these statistical measurements - an ensemble averaging process (which in general can be a temporal or a spatial averaging process) - it is possible to determine the statistical relationship between the intensities detected in different locations with a known statistical certainty. It is shown how this physical property of the optical system can be used to identify different classes of objects (discrete objects or objects that vary continuously as a function of several physical parameters) with a specific statistical certainty. The derived statistical relationship is a fourth order statistical process and is related to the mutual intensity of scattered light. A connection between the integration time of the intensity detectors and temporal coherence and hence temporal bandwidth of a quasi-monochromatic light source is discussed. We extend these results to multiple wavelengths and polarizations of light. We briefly discuss how the results may be extended to non-paraxial optical systems. 
Damien P. Kelly
physics.optics