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Frontiers in Optics

Two-Photon Optics: Imaging below the diffraction limit

Daniel Schlenk, Harald Weinfurter

Published Jan 1, 2006• 0 citations
Publisher

Abstract

Imaging properties of an optical system are limited by the wave nature of light. Entangled photons allow an improvement in resolution [1]. We show an experimental realisation using entangled photons from a Spontaneous Parametric Downconversion source.
DOI
10.1364/fio.2006.jwd117

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Entangled photons, generated by spontaneous parametric downconversion from a second-order nonlinear crystal, present a rich potential for imaging and image-processing applications. Since this source is an example of a three-wave mixing process, there is more flexibility in the choices of illumination and detection wavelengths and in the placement of object(s) to be imaged. Moreover, this source is entangled, a fact that allows for imaging configurations and capabilities that cannot be achieved by use of classical sources of light. We examine a number of imaging and image-processing configurations that can be realized with this source. The formalism that we utilize facilitates the determination of the dependence of imaging resolution on the physical parameters of the optical arrangement.
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Two-photon states generated through degenerate spontaneous parametric downconversion (SPDC) can exhibit sharp correlations in the transverse spatial coordinates. This property leads to unique free-space propagation features. Here, we show that a phase object placed in the image plane of the source affects the free space propagation of the SPDC in a way that is mathematically analogous to the Fresnel diffraction of a first-order coherent source. This effect can be observed via the extraction of correlation images. We demonstrate this prediction with an experiment where the diffraction of correlated bi-photons is detected using an event-based camera. The results allow us to reconstruct the phase structure of the sample via non-interferometric phase retrieval methods. We verify that the retrieved phase patterns exhibit a factor of two contrast enhancement due to the probe’s two-photon nature. Our findings offer a proof of principle application for quantitative phase imaging, particularly in regimes where low light conditions are required to prevent photo-damage and, at the same time, is desirable to preserve high resolution, contrast, and low noise.
We present another step in our efforts to expand far-field imaging beyond the diffraction limit and beyond the limitations imposed by fluorescent labels. The model system we examine is based on the exploitation of entangled photon pairs at 810 nm generated by spontaneous parametric down conversion (SPDC) of a 405 nm source to resolve the separations of the line pairs of a series of two-dimensional objects. A ghost-imaging optical system directs signal and idler photons along two paths, one of which contains the objects. Images are constructed using a covariance analysis of the entangled pairs using typically 106 frames collected with an EMCCD detector that was calibrated to account for the number of entangled pairs of photons, which is necessary for an accurate determination of the resolution and its comparison with the classical method. Conservation of momentum requires that there is inversion symmetry between the transverse k vectors of the photons passing through the target and their entangled counterparts directed along the targetless path. Our covariance analysis not only addresses this symmetry but also that the width of the covariance peak is broader than a single pixel owing to the nature of SPDC and the details of the optical arrangement. Consideration of this broadening provides significant improvement of the image quality. The Heisenberg limit (HL) is achieved within experimental error: using the same optical alignment, the resolution obtained with entangled pairs of 810 nm photons is, within experimental error, twice that obtained with classical 810 nm photons. More importantly, the error bars of measurements with 810 nm entangled pairs are quantified by the Cramér-Rao lower bound (CRLB) and compared with those of the classical measurements. While other workers have done quantum imaging on nonpoint sources, to our knowledge we are the first group that not only has done the quantum imaging but also has compared the CRLB and the measured error of the quantum and classical measurements for a series of different-sized objects. (Similar comparisons have, however, been made for systems that can be approximated as point sources, e.g., determining the separation of two laser beams).