Suppose you want to take a picture of a building. Traditionally, you need to face your camera to the building, adjust the focus of the lens, and press the shutter. But with a technique known as ghost imaging, you can image the building by pointing a CCD ‘camera’ (without a lens) into the sun, rather than toward the building. We demonstrated the working principle of ghost imaging experimentally in 1995,1,2 using so-called entangled photon pairs as the light source. Proposed by Albert Einstein, Boris Podolsky, and Nathan Rosen in 1935,3 these entangled states were labeled ‘spooky action at a distance’ by Einstein for their apparent ability to immediately influence each other nonlocally. In our 1995 ghost-imaging experiment, one photon of the EPR pair—named for the initials of the discoverers—illuminated the object and the other triggered the CCD. We found, surprisingly, that observing one photon at a certain point on the object caused the other to be captured by a unique pixel in the CCD camera. Measuring the correlation of the EPR pairs revealed an image of the object even though the CCD was facing the light source instead of the scene. We named the 1995 experiment type I ghost imaging.
Figure 1. Ghost image of a toy figure.
Ten years later, we demonstrated type II ghost imaging, which does not require a special entangled photon source or even a camera lens. Instead, a large-angular-size thermal source, such as the sun, can reproduce ghost images directly onto a CCD. In type II ghost imaging, the thermal light simultaneously illuminates the object and a CCD array. Using a chaotic radiation or ‘pseudo-thermal’ light source, we found that if a CCD pixel is triggered by a photon, there exists a unique point on the object plane that has twice the chance of receiving another photon at the same time. By counting the coincidences between the CCD and a ‘bucket’ detector that receives the scattered and reflected photons from the object, a 50% contrast ghost image of the object can be captured by the CCD array (see Figure 1).4–6
Whether type I or II, the nonlocal point-to-point image-forming correlation is the result of interference between two photon amplitudes, corresponding to different yet indistinguishable alternative ways of triggering a joint photodetection event. As a result of multiphoton interference, ghost imaging has two peculiar features. It is nonlocal, and its spatial resolution differs from that of classical imaging. Consequently, ghost imaging using the sun as a light source could possibly achieve spatial resolution equivalent to that of a classical imaging system taking pictures at a distance of 10km with a 92m-diameter lens. Perhaps because of its unusual properties and their potential in certain practical applications, ghost imaging has attracted a great deal of attention.
In our everyday experience, we expect the light shining in California to behave independently of that in Maryland, especially given the distance between the two locations (i.e., we do not expect any correlation between them). Mathematically, this can be described by a factorizable function
where (r1, t1) and (r2, t2) are the space-time coordinates of the observations in California and Maryland, respectively. However, our intuitive experience is incorrect. For instance, in type II ghost imaging, the chaotic light that illuminates the object and that hitting the CCD array cannot be described by Equation 1. Instead, the situation is represented by a nonfactorizable function
i.e., we have twice the chance of observing light at and simultaneously. This nonfactorizable function enables reproduction of a ghost image of the target object at a distance. The nontrivial correlation function of Equation 2 is different by the constant of 1 from that of the entangled states, or the EPR correlation,
which means that the highest achievable contrast of a ghost image using thermal light is only 50%. The nonfactorizable correlation functions of Equations 2 or 3 cannot be achieved without taking multiphoton interference into account.
Is it possible to simulate the nonfactorizable functions of Equations 2 and 3 by classical factorizable functions? A number of classical simulations have been attempted since the first experimental demonstration of ghost imaging. In 2002, the group of Robert Boyd successfully simulated a ghost shadow by applying co-rotating laser beams, shot by shot.7 In 2004, Alessandra Gatti and her colleagues used classical imaging systems to achieve a factorizable speckle-to-speckle classical correlation between two distant planes, and , by imaging the speckles of the common thermal source onto the planes,8,9
where is the transverse coordinate in the plane of the light source. The original publications of Gatti's group chose 2f–2f classical imaging systems, characterized by 1/2f + 1/2f = 1/f (where f is the focal length), to image the speckles of the source onto both the object and ghost-image planes. Their speckle-to-speckle image-forming correlation, described by equation 4, is factorizable, which is very different from what we found in our experiments with lensless ghost imaging using thermal light.4,5
The work described here raises a fundamentally important question about whether the nonlocal ghost-imaging effect of ‘classical’ thermal light is caused by quantum-mechanical multiphoton interference. As our next steps, we intend to continue our investigations in this area, and to experimentally demonstrate sunlight-based ghost imaging.
This work was presented in the conference Quantum Communications and Quantum Imaging at the SPIE Optics + Photonics symposium in August 2009 in San Diego. Yanhua Shih is a chair of the conference.
Department of Physics
University of Maryland