# American Institute of Mathematical Sciences

May  2016, 10(2): 409-432. doi: 10.3934/ipi.2016006

## Ghost imaging in the random paraxial regime

 1 Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris Diderot, 75205 Paris Cedex 13

Received  October 2014 Published  May 2016

In this paper we analyze a wave-based imaging modality called ghost imaging that can produce an image of an object illuminated by a partially coherent source. The image of the object is obtained by correlating the intensities measured by two detectors, one that does not view the object and another one that does view the object. More exactly, a high-resolution detector measures the intensity of a wave field emitted by a partially coherent source which has not interacted with the object to be imaged. A bucket (or single-pixel) detector collects the total (spatially-integrated) intensity of the wave field emitted by the same source that has interacted with the object. The correlation of the intensity measured at the high-resolution detector with the intensity measured by the bucket detector gives an image of the object. In this paper we analyze this imaging modality when the medium through which the waves propagate is random. We discuss the relation with time reversal focusing and with correlation-based imaging using ambient noise sources. We clarify the role of the partial coherence of the source and we study how scattering affects the resolution properties of the ghost imaging function in the paraxial regime: the image resolution is all the better as the source is less coherent, and all the worse as the medium is more scattering.
Citation: Josselin Garnier. Ghost imaging in the random paraxial regime. Inverse Problems & Imaging, 2016, 10 (2) : 409-432. doi: 10.3934/ipi.2016006
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