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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Reduction of quantum noise in image estimation by use of twin-photon beams

Majeed M. Hayat, Bahaa E. A. Saleh, John A. Gubner

Published Oct 25, 1996• 0 citations
Publisher

Abstract

An estimate of the transmittance of an object is examined in a twin-photon beam setup. The estimate is based on observing both the photons of one beam and the photons of the twin beam after passage through the object. The performance of the estimate (bias, variance, and mean-square error) is compared to the conventional single-beam measurement. The improvement depends on the photon flux, the counting time, the quantum efficiencies of the detectors, and the value of the measured transmittance itself. In general, a performance advantage is achieved for sufficiently high photon flux or long counting time.

DOI
10.1117/12.255087

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An estimate of the transmittance of an object is examined in a twin-photon beam setup. The estimate is based on observing both the photons of one beam and the photons of the twin beam after passage through the object. The performance of the estimate (bias, variance, and mean-square error) is compared to the conventional single-beam measurement. The improvement depends on the photon flux, the counting time, the quantum efficiencies of the detectors, and the value of the measured transmittance itself. In general, a performance advantage is achieved for sufficiently high photon flux or long counting time.
The accuracy of optical measurements at low light levels is limited by the quantum noise of the source and by the random nature of the interaction with the measured object. The source noise may be reduced by use of nonclassical photon-number squeezed light. We consider the use of two photon-correlated beams (generated, for example, by spontaneous parametric downconversion) to measure the optical transmittance of an object. The photons of each beam obey a random Poisson process but are synchronized in time. One beam is used to probe the object, and the other is used as a reference providing information on the realization of the random arrival of photons at the object. The additional information available by such measurement may be exploited to improve the accuracy of the measurement. Various estimators, including the maximum-likelihood estimator, are considered, and their performance is evaluated and compared with the measurement based on a single-beam conventional (Poissonian) source and a maximally squeezed (fixed-photon-number) source. The performance advantage that is established depends on parameters such as the intensity of the source, the transmittance of the object, the quantum efficiency of the detectors, the background noise, and the degree of correlation of the photon numbers in the two beams.
The accuracy of optical measurements at low light levels is limited by the quantum noise of the source and by the random nature of the interaction with the measured object. The source noise may be reduced by use of nonclassical photon-number squeezed light. This paper considers the use of two photon-correlated beams (generated, for example, by spontaneous parametric downconversion) to measure the optical transmittance of an object. The photons of each beam obey a random Poisson process, but are synchronized in time. One beam is used to probe the object while the other is used as a reference providing information on the realization of the random arrival of photons at the object. The additional information available by such measurement may be exploited to improve the accuracy of the measurement. Various estimators, including the maximum likelihood estimator, are considered and their performance is evaluated and compared with the measurement based on single-beam conventional (Poisson) source and maximally squeezed (fixed photon number) source. The performance advantage established in this paper depends on parameters such as the intensity of the source, the transmittance of the object, the quantum efficiency of the detectors, the background noise, and the degree of correlation of the photon numbers in the two beams.
Quantum-intensity-correlated twin beams of light can be used to measure absorption with precision beyond the classical shot-noise limit. The degree to which this can be achieved with a given estimator is defined by the quality of the twin-beam intensity correlations, which is quantified by the noise reduction factor. We derive an analytical model of twin-beam experiments, incorporating experimental parameters such as the relative detection efficiency of the beams, uncorrelated optical noise, and uncorrelated detector noise. We show that for twin beams without excessive noise, measured correlations can be improved by increasing the detection efficiency of each beam; notwithstanding, this may unbalance detection efficiency. However, for beams with excess intensity or other experimental noise, one should balance detection efficiency, even at the cost of reducing detection efficiency—we specifically define these noise conditions and verify our results with statistical simulation. This has application in design and optimization of absorption spectroscopy and imaging experiments.
We show that it is possible to estimate the shape of an object by measuring only the fluctuations of a probing field, allowing us to expose the object to a minimal light intensity. This scheme, based on noise measurements through homodyne detection, is useful in the regime where the number of photons is low enough that direct detection with a photodiode is difficult but high enough such that photon counting is not an option. We generate a few-photon state of multi-spatial-mode vacuum-squeezed twin beams using four-wave mixing and direct one of these twin fields through a binary intensity mask whose shape is to be imaged. Exploiting either the classical fluctuations in a single beam or quantum correlations between the twin beams, we demonstrate that under some conditions quantum correlations can provide an enhancement in sensitivity when estimating the shape of the object.
Quantum-correlated photon sources provide a means of suppressing multiple photon emission and thus improving the security and efficiency of quasi single-photon quantum key distribution systems. We present illustrative photon-counting statistics for a Poissonian source conditioned by photon number measurements on a fully correlated twin beam with a non-ideal photon counter. We show that high photon counting efficiency is needed to obtain significant improvement in channel efficiency (bits per symbol) and/or security (in the form of reduced Shannon entropy leakage) over a single beam source.
A nonclassical light source is used to demonstrate experimentally the absolute efficiency calibration of a photon-number-resolving detector. The photon-pair detector calibration method developed by Klyshko for single-photon detectors is generalized to take advantage of the higher dynamic range and additional information provided by photon-number-resolving detectors. This enables the use of brighter twin-beam sources including amplified pulse pumped sources, which increases the relevant signal and provides measurement redundancy, making the calibration more robust.