Maria Luisa Rastello

Photometry, radiometry and 'the candela': evolution in the classical and quantum world

The metrological fields of photometry and radiometry and their associated units are closely linked through the current definition of the base unit of luminous intensity—the candela. These fields are important to a wide range of applications requiring precise and accurate measurements of electromagnetic radiation and, in particular, the amount of radiant energy (light) that is perceived by the human eye. The candela has been one of the base units since the inception of the International System of Units (SI) and is the only base unit that quantifies a fundamental biological process—human vision. This photobiological process spans an enormous dynamic range of light levels from a few-photon interaction involved in triggering the vision mechanism to a level of more than 1015 photons per second that is accommodated by the visual response under bright daylight conditions. This position paper, prepared by members of the Task Group on the SI of the Consultative Committee for Photometry and Radiometry Strategic Planning Working Group (CCPR WG-SP), reviews the evolution of these fields of optical radiation measurements and their consequent impact on definitions and realization of the candela. Over the past several decades, there have been significant developments in sources, detectors, measuring instruments and techniques, that have improved the measurement of photometric and radiometric quantities for classical applications in lighting design, manufacturing and quality control processes involving optical sources, detectors and materials. These improved realizations largely underpin the present (1979) definition of the candela. There is no consensus on whether this radiant-based definition fully satisfies the current and projected needs of the optical radiation community. There is also no consensus on whether a reformulation of the definition of the candela in terms of photon flux will be applicable to the lighting community. However, there have been significant recent advances in radiometry in the development of single-photon sources and single-photon detectors and the growth of associated technologies, such as quantum computing and quantum cryptography. The international acceptance of these new quantum-based technologies requires improved traceability and reliability of measurements at the level of a few photons. This review of the evolution of the candela and the impact of its possible reformulation might lead, in the future, to a reformulation in terms of quantum units (photons). This discussion is timely since redefinitions of four of the other SI base units are being considered now in terms of fundamental constants to provide a more universally realizable quantum-based SI system. This paper also introduces for the first time a fundamental constant for photometry.

Quantum dense key distribution

This paper proposes a protocol for quantum dense key distribution. This protocol embeds the benefits of a quantum dense coding and a quantum key distribution and is able to generate shared secret keys four times more efficiently than the Bennet-Brassard 1984 protocol. We hereinafter prove the security of this scheme against individual eavesdropping attacks, and we present preliminary experimental results, showing its feasibility.

Detection of multimode spatial correlation in PDC and application to the absolute calibration of a CCD camera

We propose and demonstrate experimentally a new method based on the spatial entanglement for the absolute calibration of analog detectors. The idea consists on measuring the sub-shot-noise intensity correlation between two branches of parametric down conversion, containing many pairwise correlated spatial modes. We calibrate a scientific CCD camera and a preliminary evaluation of the uncertainty indicates the metrological interest of the method.

Self consistent, absolute calibration technique for photon number resolving detectors

Well characterized photon number resolving detectors are a requirement for many applications ranging from quantum information and quantum metrology to the foundations of quantum mechanics. This prompts the necessity for reliable calibration techniques at the single photon level. In this paper we propose an innovative absolute calibration technique for photon number resolving detectors, using a pulsed heralded photon source based on parametric down conversion. The technique, being absolute, does not require reference standards and is independent upon the performances of the heralding detector. The method provides the results of quantum efficiency for the heralded detector as a function of detected photon numbers. Furthermore, we prove its validity by performing the calibration of a Transition Edge Sensor based detector, a real photon number resolving detector that has recently demonstrated its effectiveness in various quantum information protocols.

Single-photon detector calibration by means of conditional polarization rotation

We propose a new scheme for measuring the quantum efficiency of a single-photon detection apparatus by using polarization-entangled states. The scheme consists of measuring the polarization of a member of a polarization-entangled pair after a 90° polarization rotation conditional on the detection of the correlated photon after polarization selection. We present experimental results obtained with this scheme compared with traditional biphoton calibration. Our results show the interesting potentiality of the suggested scheme.

Minimax refining of wideband antireflection coatings for wide angular incidence

The design of antireflection coatings at any light incidence is a challenging task in optics. To this aim, a minimax method is presented: it minimizes the maximum deviation of the spectral reflectance from the desired specifications over the wavelength for a given set of incidence angles. Refining is limited to lossless coatings with assigned refractive indices and undetermined thicknesses; the algorithm consists of iterating appropriate linear optimization steps. In the examples some minimax-refined coatings are compared with coatings reported in the literature.

Minimax refining of optical multilayer systems

A new minimax method for refining optical multilayer systems is presented. It minimizes the maximum deviation of the spectral transmittance from the desired specifications. These are assigned in such a general way that any shape can be approximated. The algorithm consists of iterating optimization steps that are obtained by developing the transmittance in the Taylor expansion versus the known parameters and solved by piecewise-linear programming. The investigation is limited to the design of losslessmultilayers with assigned refractive indices and undetermined thicknesses. Some minimax-refined designs are compared favorably with those reported in the literature.

Prospects for improving the accuracy of silicon photodiode self-calibration with custom cryogenic photodiodes

This paper considers the possibility of improving the accuracy of the predictable quantum efficiency method (self-calibration) by using custom photodiodes at cryogenic temperatures. The photodiode quantum deficiency is partitioned into nine terms associated with different phenomenological loss mechanisms. The size of each term is estimated for operation of the photodiode at 72 K and 16 V reverse bias. Requirements for high-accuracy self-calibration of the value and uncertainty of each of the quantum deficiency terms are discussed.

Luminous-flux measurements by an absolute integrating sphere

We present an original implementation of the absolute-sphere method recently proposed by Ohno. The luminous-flux unit, the lumen, is realized by means of an integrating sphere with an opening calibrated by a luminous-intensity standard placed outside. The adapted experimental setup permits one to measure luminous-flux values between 5 and 2500 lm with a significant improvement with respect to the simulated performances reported in the literature. Traditionally, the luminous-flux unit, the lumen, is realized by goniophotometric techniques in which the luminous-intensity distribution is measured and integrated over the whole solid angle. Thus sphere results are compared with those obtained with the Istituto Elettrotecnico Nazionale goniophotometer. In particular, a set of standards, characterized by luminous-flux values of ~2000 lm, has been calibrated with both techniques. We highlight some of the problems encountered. Experimental results show that the agreement between the two methods is within the estimated uncertainty and suggest promising areas for future research.

Intercomparison of a correlated-photon-based method to measure detector quantum efficiency

We report on the absolute calibration of photodetector quantum efficiency by using correlated photon sources, performed independently at two laboratories, the National Institute of Standards and Technology and the Istituto Elettrotecnico Nazionale (IEN). The goal is to use an interlaboratory comparison to demonstrate the inherent absoluteness of the photon correlation technique by showing its independence from the particular experimental setup. We find that detector nonuniformity limited this comparison rather than uncertainty inherent in the method itself. The ultimate goal of these investigations is development of a robust measurement protocol that allows the uncertainties of individual measurements to be determined experimentally and verified operationally. Furthermore, to demonstrate the generality of the procedure, the IEN measurement setup was also used to calibrate a fiber-coupled avalanche photodiode module. Uncertainties are evaluated for the detector both with and without fiber coupling and differences are discussed. The current IEN setup using a thinner and higher transmittance nonlinear crystal for the generation of correlated photons shows a significant improvement in overall accuracy with respect to previously reported results from IEN [Metrologia 32, 501-503 (1996)].