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European Quantum Electronics Conference (EQEC)

Quantum fluctuations in superresolving Fourier-microscopy

Pierre Scotto, Pere Colet, Mikhail I. Kolobov, Maxi San Miguel

Published Jan 1, 2003• 0 citations
Publisher

Abstract

A new scheme, superresolving Fourier-microscopy is proposed, which detects the spatial Fourier spectrum of the image created by an additional Fourier lens. This procedure amounts in directly imaging on the observation plane the field coming through the pupil, and all the field transmitted by the pupil is again concentrated on a finite region of space. Using decomposition on the basis of the prolate spheroidal functions, object reconstruction is shown to be in principle possible. The gain in superresolution achieved in this scheme over the classical Rayleigh limit is investigated numerically.

DOI
10.1109/eqec.2003.1314230

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A new scheme, superresolving Fourier-microscopy is proposed, which detects the spatial Fourier spectrum of the image created by an additional Fourier lens. This procedure amounts in directly imaging on the observation plane the field coming through the pupil, and all the field transmitted by the pupil is again concentrated on a finite region of space. Using decomposition on the basis of the prolate spheroidal functions, object reconstruction is shown to be in principle possible. The gain in superresolution achieved in this scheme over the classical Rayleigh limit is investigated numerically.
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Far-field optical imaging inevitably involves low-pass spatial filtering, limiting the resolution. Moreover, conventional imaging suppresses high spatial frequency components close to the cutoff, making them invisible under noise, particularly the shot noise arising from discrete and random nature of quantum light. Here we propose and implement a method for reducing the effect of this noise by optically pre-processing the incoming light prior to detection, thereby optimizing the quantum measurement performed on it. Our scheme, termed Fourier Domain Division (FDD), partitions the Fourier plane into multiple regions for independent detection and subsequent post-processing for image reconstruction. By analyzing the quantum and classical Fisher information, we show that our method is advantageous with respect to direct imaging for high spatial-frequency components. As a result, the number of photons required to achieve a certain signal-to-noise-ratio in the Fourier domain is reduced, thus enhancing the overall resolution in the photon-starved regime. We demonstrate our method in microscopy, achieving 5-fold improvement of Fisher information on high spatial-frequency components. Unlike active super-resolution methods, FDD is passive, making it broadly applicable in microscopy and other imaging scenarios where active illumination is impractical, including astronomy and remote sensing. Our work establishes a general strategy for designing quantum optimized superresolution imaging systems, bridging fundamental quantum limits, practical image analysis and computer vision applications.
We propose a source of multimode squeezed light that can be used for the superresolving microscopy beyond the standard quantum limit. This source is an optical parametric amplifier with a properly chosen diaphragm on its output and a Fourier lens. We demonstrate that such an arrangement produces squeezed prolate spheroidal waves which are the eigen modes of the optical imaging scheme used in microscopy. The degree of squeezing and the number of spatial modes in illuminating light, necessary for the effective object field reconstruction, are evaluated
We numerically investigate the role of quantum fluctuations in superresolution of optical objects. First, we confirm that when quantum fluctuations are not taken into account, one can easily improve the resolution by one order of magnitude beyond the diffraction limit. Then we investigate the standard quantum limit of superresolution which is achieved for illumination of an object by a light wave in a coherent state. We demonstrate that this limit can be beyond the diffraction limit. Finally, we show that further improvement of superresolution beyond the standard quantum limit is possible using the object illumination by a multimode squeezed light.
We present a detailed quantum-statistical analysis of superresolution for optical systems with circular symmetry based on our previous paper [Opt. Commun. 264, 9 (2006)].We consider as example an imaging system with two Fourier lenses; however, our approach can be easily generalized for more complex paraxial systems with circular symmetry. We present an original and very effective algorithm for numerical evaluation of the circular prolate spheroidal functions, which are the eigenmodes of our system. We investigate in detail the two-dimensional reconstruction point-spread function and provide examples of superresolution for rotationally symmetric and angularly dependent objects. Finally, we investigate the role of the local quantum fluctuations in the superresolution process and evaluate the local noise figure for the reconstruction process.