Imaging aims to create a correspondence between the distribution of light in an object plane, in which the objects of interest are placed, and in an image plane, where a sensor measures intensity. An imaging device is characterized by resolution, which determines how sharp is the correspondence between the two conjugate planes, and depth of field, which fixes the longitudinal distance range in which the object can move, while its image is still well focused on the sensor. Unfortunately, a natural tradeoff between resolution and depth of field entails that focusing a high-resolution image is much harder than focusing a low-resolution one. Moreover, standard imaging devices are not able to recover information on the out-of-focus planes after the acquisition. The goal of plenoptic imaging is to overcome this limitation, by retrieving combined information on both the spatial distribution and the direction of light in the scene of interest, which opens the possibility to refocus planes of the scene in a much wider range than the natural depth of field of the system, and also to change the point of view on the scene. Though plenoptic imaging is one of the most promising techniques for 3D imaging, in all the devices based on intensity measurements its advantages come at the expense of spatial resolution, which can no longer reach its diffraction limit. In this paper, we review the possibility to avoid loss of resolution by integrating second-order intensity correlation measurements in a simple single-lens imaging setup. The described device, based on the correlation plenoptic imaging (CPI) technique, enables one to perform either standard or plenoptic imaging, while keeping the resolution at the diffraction limit. We show that the proposed setup outperforms both standard imaging and first-order plenoptic imaging in terms of resolution and depth of field.
One of the most peculiar features of imaging systems is the trade-off between resolution and depth of field. Resolution can be improved by increasing the numerical aperture of the imaging system. However, the range of distances that can be put in sharp focus in a single shot decreases with the square of the numerical aperture. Plenoptic imaging (PI) devices are able to retrieve both spatial and directional information from the scene of interest, usually by placing a microlens array in front of the camera sensor. This feature entails the possibility to refocusing planes of the scene in a much wider range than the natural depth of field of the system, and also to change the point of view on the scene. Though plenoptic imaging is one of the most promising techniques for 3D imaging, its advantages come at the expense of spatial resolution, which can no longer reach the diffraction limit. We experimentally demonstrate that correlations of chaotic light can be exploited to overcome the inverse proportionality between depth of field and resolution, and perform plenoptic imaging at the diffraction limit. We retrieve images by correlating intensity fluctuations at different points of two parts of a sensor, which register spatial and angular information, respectively. Hence, our Correlation Plenoptic Imaging (CPI) protocol does not add any limitation to the native resolution of the imaging system. We show the experimental refocusing, through the CPI procedure, of widely out-of-focus parts of a transmissive test target. Moreover, we determine and test the theoretical limits of CPI in terms of resolution and depth of field, quantifying the improvement with respect to standard imaging and classical PI. We finally comment on future perspectives.
Plenoptic imaging (PI) is an optical technique to perform three-dimensional imaging in a single shot. It is enabled by the simultaneous measurement of both the location and the propagation direction of light in a given scene. Despite being very useful for extending the depth of field, such technique entails a strong trade- off between spatial and angular resolution. This makes the resolution and the maximum achievable depth of focus inversely proportional; hence, resolution cannot be diffraction-limited. We have recently proposed a new procedure, called Correlation Plenoptic Imaging (CPI), to overcome such fundamental limits by collecting plenoptic information through intensity correlation measurement. Using two correlated beams, from either a chaotic or an entangled photon source, we perform imaging in one arm and simultaneously obtain the angular information in the other arm. In this paper, we discuss the case in which the two correlated beams of light are generated by spontaneous parametric down-conversion. We review the principles of CPI with entangled photons and discuss its resolution and depth-of-field limits.
Plenoptic Imaging (PI) is a novel optical technique for achieving tridimensional imaging in a single shot. In conventional PI, a microlens array is inserted in the native image plane and the sensor array is moved behind the microlenses. On the one hand, the microlenses act as imaging pixels to reproduce the image of the scene; on the other hand, each microlens reproduces on the sensor array an image of the camera lens, thus providing the angular information associated with each imaging pixel. The recorded propagation direction is exploited, in post- processing, to computationally retrace the geometrical light path, thus enabling the refocusing of different planes within the scene, the extension of the depth of field of the acquired image, as well as the 3D reconstruction of the scene. However, a trade-off between spatial and angular resolution is built in the standard plenoptic imaging process. We demonstrate that the second-order spatio-temporal correlation properties of light can be exploited to overcome this fundamental limitation. Using two correlated beams, from either a chaotic or an entangled photon source, we can perform imaging in one arm and simultaneously obtain the angular information in the other arm. In fact, we show that the second order correlation function possesses plenoptic imaging properties (i.e., it encodes both spatial and angular information), and is thus characterized by a key re-focusing and 3D imaging capability. From a fundamental standpoint, the plenoptic application is the first situation where the counterintuitive properties of correlated systems are effectively used to beat intrinsic limits of standard imaging systems. From a practical standpoint, our protocol can dramatically enhance the potentials of PI, paving the way towards its promising applications.
We present a novel factorization algorithm which can be computed using an analogue computer based on a
polychromatic source with a given wavelength bandwidth, a multi-path interferometer and a spectrometer. The
core of this algorithm stands on the measurement of the periodicity of a "factoring" function given by an
exponential sum at continuous argument by recording a sequence of interferograms associated with suitable
units of displacement in the inteferometer. A remarking rescaling property of such interferograms allows, in
principle, the prime number decomposition of several large integers. The information about factors is encoded
in the location of the inteferogram maxima.
We exploit the remarkable phenomena of interference in physics together with aspects of number theory in
order to factorize large numbers. In particular, the introduction of continuous truncated exponential sums
(CTES) allows us to develop a new algorithm for factoring several large numbers by a single measurement of
the periodicity of a CTES interferogram. Such an interferogram can be obtained by measuring the interference
pattern produced by polychromatic light interacting with an interferometer with variable optical paths.
We will describe a new factorization algorithm based on the reproduction of continuous exponential sums, using
the interference pattern produced by polychromatic light interacting with an interferometer with variable optical
paths. We will describe two possible interferometers: a generalized symmetric Michelson interferometer and a
liquid crystal grating. Such an algorithm allows, for the first time, to find all the factors of a number N in a
single run without precalculating the ratio N/l, where l are all the possible trial factors. It also allows to solve
the problem of ghost factors and to factorize different numbers using the same output interference pattern.
The so called NOON states are the main ingredient of many quantum optic schemes. The reliability of NOON-state
production protocols thus plays an important role in view of practical applications. In realistic situations,
the reliability of NOON-state sources strongly depends on the non-unitary photodetection efficiency of the single
photon detectors involved in the protocol. We discuss and compare the reliability of NOON-state schemes
based on both single-photon detection and non detection. Our result may be of great interest for practical
implementation of NOON-state schemes.