Abstract
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.
Highlights
In this paper we study an imaging modality called ghost imaging introduced recently in the literature
In this paper we study ghost imaging in the paraxial regime, that is the regime in which the propagation distance is much larger than the correlation length of the medium, which is itself much larger than the typical wavelength, as in the previous section
In this paper we have addressed transmission-based ghost imaging
Summary
In this paper we study an imaging modality called ghost imaging introduced recently in the literature. As shown by the expression (9) in Proposition 1, the products of two Green’s functions (one of them being complex conjugated) play a central role in the understanding of ghost imaging and we will describe their statistical properties in the random paraxial regime . The result (23) on the first-order moment shows that any coherent wave imaging method cannot give good images if the propagation distance is larger than the scattering mean free path:. C20 z 2 ic ri2cω is the formula for the square radius of a Gaussian beam that undergoes classical diffraction in a homogeneous medium with speed of propagation c0
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