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Theory of speckle intensity correlations over object position in a heavily scattering random medium

We present a general theory for optical imaging of moving objects obscured by heavily scattering random media. Measurements involve collecting a series of speckle intensity images as a function of the position of a moving object. A statistical average intensity correlation can be formed with the potential to provide access to microscopic and macroscopic information about the object. For macroscopic objects and translation distances that are both large relative to the wavelength, there is a clear method to invert measurements to form an image of the hidden object. Opportunities exist for super-resolution sensing and imaging, with far-subwavelength resolution. Importantly, there is no fundamental limit to the thickness of the background randomly scattering medium, other than the practical requirement of detecting an adequate number of photons and sufficient background scatter for developed Gaussian field statistics. The approach can be generalized to any wave type and frequency, under the assumption that there is adequate temporal coherence. Applications include deep tissue in vivo imaging and sensing in and through various forms of environmental clutter. The theory also provides another dimension for intensity interferometry and entangled state detection to the case with motion of the scatterer or emitter.