We analytically show that it is possible to perform coherent imaging by using the classical correlation of two beams obtained by splitting incoherent thermal radiation. The case of such two classically correlated beams is treated in parallel with the configuration based on two entangled beams produced by parametric down-conversion, and a basic analogy is pointed out. The results are compared in a specific numerical example.The topic of entangled imaging has attracted noteworthy attention in recent years [1,2,3,4,5,6,7,8]. This tecnique exploits the quantum entaglement of the state generated by parametric down-conversion (PDC), in order to retrieve information about an unknown object. In the regime of single photon pair production of PDC, the photons of a pair are spatially separated and propagate through two distinct imaging systems. In the path of one of the photons an object is located. Information about the spatial distribution of the object is not obtained by detection of this photon, but rather by registering the coincidence counts as a function of the other photon position [1,2,3,4,5]. In the regime of a large number of photon pairs, this procedure is generalized to the measurement of the signal-idler spatial correlation function of intensity fluctuations [6]. Such a two-arm configuration provides more flexibility in comparison with standard imaging procedures, as e.g. the possibility of illuminating the object with one light frequency and performing a spatially resolved detection in the other arm with a different light frequency, or of processing the information from the object by only operating on the imaging system of arm 2 [5,6]. In addition, it opens the possibility of performing coherent imaging by using, in a sense, spatially incoherent light, since each of the two down-converted beams taken separately is described by a thermal-like mixture and only the two-beam state is pure(see e.g. [5] and [6]).In this paper we show that it is possible to implement such a scheme using a truly incoherent light, as the radiation produced by a thermal (or quasi-thermal) source. A comparison between thermal and biphoton emission is performed in [9], where an underlying duality accompanies the mathematical similarity between the two cases. Here, we considerCorrelated imaging with incoherent thermal light. The thermal beam a is splitted into two beams which travel through two distinct imaging systems, described by their impulse response functions h1 and h2. Arm 1 includes an object. Detector D1 is either a point-like detector or a bucket detector. Beam 2 is detected by an array of pixel detectors. v is a vacuum field. a different scheme (Fig.1), appropriate for correlated imaging, in which a thermal beam is divided by a beam-splitter (BS) and the two outgoing beams are handled in the same way as the PDC beams in entangled imaging. A basic analogy between the PDC and the thermal case emerges from our analysis. Currently there is a debate whether quantum entanglement is necessary to perform correlated imaging [5,6,7,8]. ...

High-resolution ghost image and ghost diffraction experiments are performed by using a single classical source of pseudothermal speckle light divided by a beam splitter. Passing from the image to the diffraction result solely relies on changing the optical setup in the reference arm, while leaving the object arm untouched. The product of spatial resolutions of the ghost image and ghost diffraction experiments is shown to overcome a limit which seemed to be achievable only with entangled photons.

We analytically show that it is possible to perform coherent imaging by using the classical correlation of two beams obtained by splitting incoherent thermal radiation. A formal analogy is demonstrated between two such classically correlated beams and two entangled beams produced by parametric down-conversion. Because of this analogy, the classical beams can mimic qualitatively all the imaging properties of the entangled beams, even in ways which up to now were not believed possible. A key feature is that these classical beams are spatially correlated both in the near field and in the far field. Using realistic numerical simulations the performances of a quasithermal and a parametric down-conversion source are shown to be closely similar, both for what concerns the resolution and statistical properties. The results of this paper provide a scenario for the discussion of what role the entanglement plays in correlated imaging

No abstract

Using a 1 GW, 1 ps pump laser pulse in high-gain parametric down conversion allows us to detect sub-shot-noise spatial quantum correlation with up to 100 photoelectrons per mode by means of a high efficiency charge coupled device. The statistics is performed in single shot over independent spatial replica of the system. Evident quantum correlations were observed between symmetrical signal and idler spatial areas in the far field. In accordance with the predictions of numerical calculations, the observed transition from the quantum to the classical regime is interpreted as a consequence of the narrowing of the down-converted beams in the very high-gain regime.