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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Two-Photon Optics: Imaging below the diffraction limit

Daniel Schlenk, Harald Weinfurter

Published Jun 1, 2007• 0 citations
Publisher

Abstract

The properties of imaging systems can be described by the point-spread function, which is determined by diffraction. A shorter wavelength results in a smaller diffraction pattern and therefore allows (in principle) a better resolution. It has been shown that entangled n-photon states have diffraction properties of the wavelength divided by n if a n-photon detection is performed. Here we use this feature to enhance the resolution of an imaging system.

DOI
10.1109/cleoe-iqec.2007.4386904

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The properties of imaging systems can be described by the point-spread function, which is determined by diffraction. A shorter wavelength results in a smaller diffraction pattern and therefore allows (in principle) a better resolution. It has been shown that entangled n-photon states have diffraction properties of the wavelength divided by n if a n-photon detection is performed. Here we use this feature to enhance the resolution of an imaging system.
Quantum imaging emerged quite recently as a breakthrough technology of overcoming the diffraction limit in microscopy and enhancement of optical resolution without the necessity to use hard radiation or perform scanning in the near field [1] , [2] . Both, the quantum imaging itself and the more “classical” techniques inspired by it (for example, super-resolution optical fluctuations imaging – SOFI [3] ), rely on detection and analysis of photon (intensity) correlations. Typically, it is believed that the more correlated illuminating light is used and the higher order of the correlations is measured, the larger super-resolution can be achieved. That conclusion is based on efficient narrowing of the point-spread function, which, however, does not necessarily imply better resolution as the ability to reconstruct smaller features of the investigated object successfully.
Quantum imaging with undetected photons is a recently introduced technique that goes significantly beyond what was previously possible. In this technique, images are formed without detecting the light that interacted with the object that is imaged. Given this unique advantage over the existing imaging schemes, it is now of utmost importance to understand its resolution limits, in particular what governs the maximal achievable spatial resolution. We show both theoretically and experimentally that the momentum correlation between the detected and undetected photons governs the spatial resolution — a stronger correlation results in a higher resolution. In our experiment, the momentum correlation plays the dominating role in determining the resolution compared to the effect of diffraction. We find that the resolution is determined by the wavelength of the undetected light rather than the wavelength of the detected light. Our results thus show that it is in principle possible to obtain resolution characterized by a wavelength much shorter than the detected wavelength.
Quantum imaging with undetected photons is a recently introduced technique that goes significantly beyond what was previously possible.In this technique, images are formed without detecting the light that interacted with the object that is imaged.Given this unique advantage over the existing imaging schemes, it is now of utmost importance to understand its resolution limits, in particular what governs the maximal achievable spatial resolution.We show both theoretically and experimentally that the momentum correlation between the detected and undetected photons governs the spatial resolution -a stronger correlation results in a higher resolution.In our experiment, the momentum correlation plays the dominating role in determining the resolution compared to the effect of diffraction.We find that the resolution is determined by the wavelength of the undetected light rather than the wavelength of the detected light.Our results thus show that it is in principle possible to obtain resolution characterized by a wavelength much shorter than the detected wavelength.
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.
Although questions regarding fundamental issues of quantum theory still exist, quantum entanglement has started to play important roles in practical engineering applications. Quantum imaging is one of these exciting areas. Quantum imaging has so far demonstrated three peculiar features: enhancing the spatial resolution of imaging beyond the diffraction limit; reproducing ghost images in a “nonlocal” manner; and dispersion-cancelation or turbulence-free imaging. The enhanced spatial resolution apparently “violates” the uncertainty principle. The ghost imaging is considered as a “nonlocal” phenomenon due to a point-to-point correlation of two interaction-free photons at distance. All the peculiar features are the results of two-photon interference, which involves the superposition of two-photon amplitudes, a nonclassical entity corresponding to different yet indistinguishable alternative ways of creating a joint-detection event. The effect of turbulence on a classic image can be easily seen from the blurring of the images.