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arXiv:quant-ph/0402160 · Physical Review A

Ghost imaging using homodyne detection

Morten Bache, E. Brambilla, A. Gatti, Luigi A. Lugiato

Published Aug 31, 2004• 44 citations
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Abstract

We present a theoretical study of ghost imaging based on correlated beams arising from parametric down-conversion, and which uses balanced homodyne detection to measure both the signal and idler fields. We analytically show that the signal-idler correlations contain the full amplitude and phase information about an object located in the signal path, both in the near-field and the far-field case. To this end we discuss how to optimize the optical setups in the two imaging paths, including the crucial point regarding how to engineer the phase of the idler local oscillator as to observe the desired orthogonal quadrature components of the image. As is well known, the near-field image resolution is inherently linked to the far-field bandwidth of the image, determined by the bandwidth of the source of the correlated beams. We show how to circumvent this limitation by using a spatial averaging technique which dramatically improves the imaging bandwidth of the far-field correlations as well as speeds up the convergence rate. The results are backed up by numerical simulations taking into account the finite size and duration of the pump pulse.

DOI
10.1103/physreva.70.023823

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We present a theoretical study of ghost imaging based on correlated beams arising from parametric down-conversion, and which uses balanced homodyne detection to measure both the signal and idler fields. We analytically show that the signal-idler correlations contain the full amplitude and phase information about an object located in the signal path, both in the near-field and the far-field case. To this end we discuss how to optimize the optical setups in the two imaging paths, including the crucial point regarding how to engineer the phase of the idler local oscillator as to observe the desired orthogonal quadrature components of the image. As is well known, the near-field image resolution is inherently linked to the far-field bandwidth of the image, determined by the bandwidth of the source of the correlated beams. We show how to circumvent this limitation by using a spatial averaging technique which dramatically improves the imaging bandwidth of the far-field correlations as well as speeds up the convergence rate. The results are backed up by numerical simulations taking into account the finite size and duration of the pump pulse.
In ghost imaging schemes information about an object is extracted by measuring the correlation between a beam that passed the object and a reference beam. We present a spatial averaging technique that substantially improves the imaging bandwidth of such schemes, which implies that information about high-frequency Fourier components can be observed in the reconstructed diffraction pattern. In the many-photon regime the averaging can be done in parallel and we show that this leads to a much faster convergence of the correlations. We also consider the reconstruction of the object image, and discuss the differences between a pixel-like detector and a bucket detector in the object arm. Finally, it is shown how to non-locally make spatial filtering of a reconstructed image. The results are presented using entangled beams created by parametric down-conversion, but they are general and can be extended also to the important case of using classically correlated thermal-like beams.
Abstract. The field of Quantum Imaging exploits the quantum nature of light and the intrinsic parallelism of optical signals to devise novel techniques for optical imaging and for parallel information processing at the quantum level (see [1] and references quoted therein). In this presentation, we will shortly discuss two topics in this area: the first is the so-called ghost imaging which, however, is not necessarily quantum; the second is the detection of faint amplitude objects with a sensitivity beyond the standard quantum limit, and in this case we are fully in the quantum domain. Both topics are related to the phenomenon of optical parametric down-conversion (PDC), in which a fraction of the pump photons of a laser beam, injected into a crystal with a quadratic non-linearity, are down-converted to a pair of signal and idler photons, with conservation of total energy and total momentum. A feature of paramount importance is that the signal and idler beams are spatially correlated both in the near field (position correlation) and in the far field (momentum correlation).The simultaneous presence of position and momentum correlation implies quantum entanglement, as it has been also observed experimentally [2]. 1. Ghost Imaging
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 quasi-thermal 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 new scenario for the discussion of what role the entanglement plays in correlated imaging.
Ghost imaging and ghost diffraction can be realized by using the spatial correlations between signal and idler photons produced by spontaneous parametric down-conversion. If an object is placed in the signal (idler) path, the spatial correlations between the transmitted photons as measured by a single, non-imaging, "bucket" detector and a scanning detector placed in the idler (signal) path can reveal either the image or diffraction pattern of the object, whereas neither detector signal on its own can. The details of the bucket detector, such as its collection area and numerical aperture, set the number of transverse modes supported by the system. For ghost imaging these details are less important, affecting mostly the sampling time required to produce the image. For ghost diffraction, however, the bucket detector must be filtered to a single, spatially coherent mode. We examine this difference in behavour by using either a multi-mode or single-mode fibre to define the detection aperture. Furthermore, instead of a scanning detector we use a heralded camera so that the image or diffraction pattern produced can be measured across the full field of view. The importance of a single mode detection in the observation of ghost diffraction is equivalent to the need within a classical diffraction experiment to illuminate the aperture with a spatially coherent mode.
Ghost imaging can be performed using either quantum or classical states of light that possess strong spatial correlations. In both cases, the image is formed by averaging over many optical events. Here we show that it is possible to distinguish an object from a preestablished basis set of objects by using a small number of position-correlated photon pairs produced by spontaneous parametric down-conversion. The signal photon is incident on one member of a set of spatially nonoverlapping objects. The "ghost" image information is impressed upon the spatially separated idler photon and is extracted by means of holographic filtering and coincidence detection. We were able to distinguish among sets of two and four spatially nonoverlapping objects with confidence levels higher than 87% and 81%, respectively. This method of ghost imaging can be performed in situations requiring extremely low light levels.
Correlated-photon imaging, popularly known as ghost imaging, is a technique whereby an image is formed from light that has never interacted with the object. In ghost imaging experiments two correlated light fields are produced. One of these fields illuminates the object, and the other field is measured by a spatially resolving detector. In the quantum regime, these correlated light fields are produced by entangled photons created by spontaneous parametric down-conversion. To date, all correlated-photon ghost-imaging experiments have scanned a single-pixel detector through the field of view to obtain the spatial information. However, scanning leads to a poor sampling efficiency, which scales inversely with the number of pixels, N, in the image. In this work we overcome this limitation by using a time-gated camera to record the single-photon events across the full scene. We obtain high-contrast images, 90%, in either the image plane or the far-field of the photon pair source, taking advantage of the EPR-like correlations in position and momentum of the photon pairs. Our images contain a large number of modes, >500, creating opportunities in low-light-level imaging and in quantum information processing.