Coincidence imaging is a technique that extracts an image of a test system from the statistics of photons transmitted by a reference system when the two systems are illuminated by a source possessing appropriate correlations. It has recently been argued that quantum entangled sources are necessary for the implementation of this technique. We show that this technique does not require entanglement, and we provide an experimental demonstration of coincidence imaging using a classical source. We further find that any kind of coincidence imaging technique which uses a "bucket" detector in the test arm is incapable of imaging phase-only objects, whether a classical or quantum source is employed.
Coincidence imaging is a technique that extracts an image of a test system from the statistics of photons transmitted by a reference system when the two systems are illuminated by a source possessing appropriate correlations. It has recently been argued that quantum entangled sources are necessary for the implementation of this technique. We show that this technique does not require entanglement, and we provide an experimental demonstration of coincidence imaging using a classical source. We further find that any kind of coincidence imaging technique which uses a "bucket" detector in the test arm is incapable of imaging phase-only objects, whether a classical or quantum source is employed.
Entangled-photon coincidence imaging is a method to nonlocally image an object by transmitting a pair of entangled photons through the object and a reference optical system, respectively. The image of the object can be extracted from the coincidence rate of these two photons. From a classical perspective, the image is proportional to the fourth-order correlation function of the wave field. Using classical statistical optics, we study a particular aspect of coincidence imaging with incoherent sources. As an application, we give a proposal to realize lensless Fourier-transform imaging, and discuss its applicability in x-ray diffraction.
Coincidence, or ghost, imaging is a technique that uses two correlated optical fields to form an image of an object. In this work we identify aspects of coincidence imaging which can be performed with classically correlated light sources and aspects which require quantum entanglement. We find that entangled photons allow high-contrast, high-resolution imaging to be performed at any distance from the light source. We demonstrate this fact by forming ghost images in the near and far fields of an entangled photon source, noting that the product of the resolutions of these images is a factor of 3 better than that which is allowed by classical diffraction theory.
It has been claimed that ``the use of entangled photons in an imaging system can exhibit effects that cannot be mimicked by any other two-photon source, whatever strength of the correlations between the two photons'' [A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 87, 123602 (2001)]. While we believe that the cited statement is true, we show that the method proposed in that paper, with ``bucket detection'' of one of the photons, will give identical results for entangled states as for appropriately prepared classically correlated states.
Abstract Losses should be accounted for in a complete description of quantum imaging systems, and yet they are often treated as undesirable and largely neglected. In conventional quantum imaging, images are built up by coincidence detection of spatially entangled photon pairs (biphotons) transmitted through an object. However, as real objects are non-unitary (absorptive), part of the transmitted state contains only a single photon, which is overlooked in traditional coincidence measurements. The single-photon part has a drastically different spatial distribution than the two-photon part. It contains information about both the object, and, remarkably, the spatial entanglement properties of the incident biphotons. Here, we image the one- and two-photon parts of the transmitted state using an electron multiplying CCD array, treating it both as a traditional camera and as a massively parallel coincidence counting apparatus, and demonstrate agreement with theoretical predictions of non-unitary quantum optics. This work may prove useful for photon-number imaging and may lead to techniques for entanglement characterization that do not require coincidence measurements.
Imaging is the estimation of the spatial distribution of a physical object by measuring the optical radiation it emits, or by making use of an optical wave that interacts with the object, via reflection or transmission, for example, before being measured by a detector. The resolution of an imaging system is limited by the inability to localize the optical field at points of the object. Under otherwise ideal conditions, resolution is limited by diffraction. The sensitivity of an imaging system is limited by the uncertainty in the measurement. Under ideal conditions, this is determined by photon noise, which depends on the statistical fluctuations of the light. In conventional imaging systems, an extended detector, such as a CCD camera or an array detector, measures the spatial distribution of the optical intensity, which is proportional to the photon flux density. In interferometric systems, the spatial distribution of the optical field is inferred from measurements of the optical intensity. With the emergence of coherence theory, imaging systems based on measurements of the second-order coherence function at pairs of points in the detection plane were developed. An example is the imaging of an incoherent object based on the van Cittert-Zernike theorem. Imaging systems based on measurement of intensity correlation, or the photon coincidence rate, at pairs of points, were developed in the 1960s. A classic example of the photon-correlation imaging of an object emitting thermal light is stellar imaging using a Hanbury-Brown-Twiss intensity-correlation interferometer. More recently, two-photon light, which may be generated via spontaneous parametric downconversion in a second-order nonlinear optical crystal, has been used for imaging. This type of two-photon (or biphoton) imaging, which has come to be called quantum imaging, is also based on the measurement of photon coincidence by the use of photon-counting array detectors or by scanning two photon-counting detectors at pairs of points. To compare the resolution and sensitivity of imaging systems based on the aforementioned types of measurements, it is necessary to derive expressions for the measured quantities in terms of the object distribution. The point-spread functions based on such expressions can be used to assess the resolution. One measure of the sensitivity of the imaging process is the signal-to-noise ratio (SNR) of the measured variables. The statistical nature of the light source must be known in order to determine the SNR. The purpose of this chapter is to compare the resolution and sensitivity of photon-correlation imaging systems that make use of thermal light and two-photon light. We will henceforth refer to these two imaging modalities as classical and quantum photon-correlation imaging, or simply classical and quantum imaging, respectively. Clearly, light in other quantum states can also be used for imaging.
We present a theoretical framework for super-resolution imaging based on quantum coincidence detection. By comparing the classical Airy point spread function with the two-photon wavefunction of entangled photon pairs, we derive that coincidence detection yields an effective narrowing of the point spread function by a factor of two or the square root of two, depending on the maintenance of correlation. This model highlights the role of transverse phase accumulation in the image plane and predicts a quantum resolution limit that is half of the classical diffraction limit when correlation is maintained. The results offer clear insight into recent experimental demonstrations of quantum imaging beyond the classical diffraction limit.