Table of contents

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.

The spectral radiant intensity of synchrotron radiation from electron storage rings can be calculated from basic electrodynamic relations (Schwinger equation) and it is directly proportional to the stored electron beam current, i.e. the number of stored electrons. With the necessary equipment installed to measure and control the electron beam current over a wide dynamic range, the radiant intensity of the synchrotron radiation can be adjusted accordingly without changing the spectrum.

This is done, e.g., at the Metrology Light Source (MLS), the dedicated electron storage ring of the Physikalisch-Technische Bundesanstalt. The MLS is operated as a primary radiation source standard from the near IR up to the soft x-ray region and its operational parameters can be adjusted and accurately measured in a wide range: the electron beam current can be varied from 1 pA (one stored electron) up to 200 mA and thus the radiant intensity can be changed by more than 11 decades. The photon flux or radiant power for typical angular acceptances can thus be varied from single photons to milliwatts. This is a very powerful tool, e.g., for the characterization of the linearity of the response of radiation detectors or for the calibration of photon counting detectors. In this article we present an overview of past, current and possible future activities exploiting this feature.

We present the experimental results of extremely precise timing in the sense of time-of-arrival measurements in a local time scale. The timing device designed and constructed in our laboratory is based on a new concept using a surface acoustic wave filter as a time interpolator. Construction of the device is briefly described. The experiments described were focused on evaluating the timing precision and stability. Low-jitter test pulses with a repetition frequency of 763 Hz were generated synchronously to the local time base and their times of arrival were measured. The resulting precision of a single measurement was typically 900 fs RMS, and a timing stability TDEV of 4 fs was achieved for time intervals in the range from 300 s to 2 h. To our knowledge this is the best value reported to date for the stability of a timing device. The experimental results are discussed and possible improvements are proposed.

New comparisons are reported of the triple-point temperatures, T_tp, of seven neon samples with different ²²Ne amount concentrations, ²²x, in cryogenic cells sealed by INRIM, NMIJ, NPL and PTB. This work stems from a collaboration between those laboratories aiming at establishing the relationship between T_tp and ²²x. Several problems remained unsolved in the published results. The new measurements supply more thermal data of lower uncertainty, to help solve some of these problems. The detailed results from 35 meltings are reported, characterized by improved uncertainty, and include an analysis of calorimetric, thermometric and sample-related effects. A broad range of collected and processed information is analysed in detail in order to confirm expanded uncertainty levels of the order of 30 µK for a single cell and 50 µK for a comparison of pairs of cells. The quality of the INRIM results is then discussed. In most cases the uncertainty budget for the INRIM measurements, including analysis of chemical impurities and the hydrostatic head correction, reached the targeted improved uncertainty. Finally, the results are discussed and compared with previous studies in support of the future assignment by the CCT of an accurate and reliable relationship T_tp versus ²²x. The paper discusses various improvements regarding the influence of the thermal measurements on both the uncertainty of the relationship and the ability to recognize either possible isotopic fractionation during sample preparation or incorrect assignment of ²²x values to some measured samples.

The absolute single-shot pulse energy of the SPring 8 extreme ultraviolet (EUV) free electron laser (FEL) was measured using a cryogenic radiometer with a relative standard uncertainty of 3%. The temperature change of the cavity in the cryogenic radiometer caused by an incident FEL pulse was determined using a lock-in amplifier and an ac Wheatstone bridge. The measured pulse energies were compared with a gas-monitor detector developed by Physikalisch-Technische Bundesanstalt/Deutsches Elektronen-Synchrotron/Ioffe Physico-Technical Institute (Ioffe) at a wavelength of 51.3 nm at the SPring-8 EUV-FEL in a shot-to-shot mode. The pulse energies measured using the two detectors agree within 2.0%.

Analysis of dynamic measurements is of growing importance in metrology as an increasing number of applications requires the determination of measurands showing a time-dependence. Often linear time-invariant (LTI) systems are appropriate for modelling the relation between the available measurement data and the required time-dependent values of the measurand. Estimation of the measurand is then carried out by deconvolution.

This paper is a tutorial about the application of digital deconvolution filters to reconstruct a time-variable measurand from the measurement signal of a LTI measurement apparatus. The goal of the paper is to make metrologists aware of the potentialities of digital signal processing in such cases. A range of techniques is available for the construction of a digital deconvolution filter. Here we compare various approaches for a form of dynamic model that is relevant to many metrological applications and we discuss the consequences for these approaches of the different ways in which information about the LTI system may be expressed. We consider specifically the methods of minimum-phase all pass decomposition, asynchronous time reversal using the exact inverse filter and the construction of stable infinite impulse response and finite impulse response approximate inverse filters by a least squares approach in the frequency domain. The methods are compared qualitatively by assessing their numerical complexity and quantitatively in terms of their performance for a simulated measurement task.

Taking into account numerical complexity and underlying assumptions of the methods, we conclude that when a continuous model of the LTI system is available, or when the starting point is a set of measurements of the frequency response of a system, application of least squares in the frequency domain for the construction of an approximate inverse filter is to be preferred. On the other hand, asynchronous time reversal filtering using the exact inverse filter appears superior when a discrete model of the LTI system is available and when causality of the deconvolution filter is not an issue.

We perform 3D finite element calculations of the fields in microwave cavities and analyse the distributed cavity phase (DCP) errors of atomic clocks that they produce. The fields of cylindrical cavities are treated as an azimuthal Fourier series. Each of the lowest components produces clock errors with unique characteristics that must be assessed to establish a clock's accuracy. We describe the errors and how to evaluate them. We prove that sharp structures in the cavity do not produce large frequency errors, even at moderately high powers, provided the atomic density varies slowly. We model the amplitude and phase imbalances of the feeds. For larger couplings, these can lead to increased phase errors. We show that phase imbalances produce a novel DCP error that depends on the cavity detuning. We also design improved cavities by optimizing the geometry and tuning the mode spectrum so that there are negligible phase variations, allowing this source of systematic error to be dramatically reduced.

Results are presented from a theoretical and experimental investigation of the frequency transfer uncertainty (FTU) in long-distance comparisons of frequency standards. The FTU can be an important component of the total uncertainty in such comparisons. The use of the Allan deviation in characterizing the FTU is analysed theoretically and it is shown that for certain noise types the Allan deviation is biased high. A potentially more accurate first difference statistic that can be used in certain situations is also discussed. In addition, an experimental determination of the noise types and levels in common transfer techniques is presented. It is shown that FTUs approaching 1 part in 10¹⁶ at 30 days are possible with current transfer methods. Finally, a method is presented for estimating the FTU in calibrating International Atomic Time (TAI) with a primary frequency standard.

The size-of-source effect (SSE) of a radiation thermometer is a critical uncertainty component in the fixed-point blackbody calibration of a transfer reference thermometer in the low-temperature range where the field of view is comparable to the size of the blackbody cavity opening. The SSE causes the signal difference between the melting and freezing plateaus to increase, and steepens the slopes of the plateaus. We propose a new method that can recover the signals of the melting and freezing curves that are deteriorated by the SSE, and thereby flatten the plateaus. The improvement has been successfully demonstrated using a tin-point blackbody. The signal difference between the melting and freezing plateaus was reduced from 81 mK to 18 mK, and the freezing-point signal was corrected by 1.30 K. In addition, the slopes on the plateaus have been dramatically flattened.

Test masses of absolute gravimeters contain prism or hollow retroreflectors. A rotation of such a retroreflector during free-fall can cause a bias in the measured g-value. In particular, prism retroreflectors produce phase shifts, which cannot be eliminated. Such an error is small if the rotation occurs about the optical centre of the retroreflector; however, under certain initial conditions the error can reach the microgal level. The contribution from these rotation-induced accelerations is calculated.

The MPG-2 (Max-Planck-Gravimeter) is a transportable absolute gravimeter built on a classical free-fall scheme to measure the local gravity value. With significant improvements and further investigations in recent years, the standard deviation of the mean for a typical measurement over 12 h to 24 h is 1.0 µGal to 3.0 µGal (1 µGal = 10⁻⁸ m s⁻²), and the combined standard uncertainty is estimated to be less than 10 µGal. The major improvements include the new interferometer design and alignment, longer drop length, reduced recoil effects and demagnetization of the falling body. The revised uncertainty budget and new measurement results of MPG-2 are reported. The results of observations at the reference gravity station Bad Homburg confirmed the revised uncertainty budget.

In all indexes of the accuracy of gears, the measurement of the error of an involute tooth profile is a difficult technical problem. A double-disc instrument for measuring an involute is introduced, the measuring principle of which is the same as the 'rolling artefact method' developed by PTB. In this paper, the measurement error caused by deviation of the measurement point is analysed. In order to increase the position accuracy of the measurement point, a novel method called the 'error compensation method' is introduced, which searches for the best position of the stylus by tentatively compensating the measurement error caused by deviation of the measurement point. According to analysis and experiment, the stylus's adjustment deviation by the 'error compensation method' is 8 µm.

Acoustic thermometry using a gas-filled quasi-spherical resonator (QSR) is one of the most promising techniques for measuring the Boltzmann constant k_B with low uncertainty. Dimensional metrology with coordinate measurement machines (CMMs) can be used to determine the resonator's volume, either directly or in combination with measurements of the resonator's microwave spectra. We assessed the uncertainty achievable when using a CMM to characterize the shape and volume of three QSRs. The resonators differed significantly in their design and construction: their inner volumes ranged between 524 cm³ and 2225 cm³, while the QSR geometries ranged from a diamond-turned triaxial ellipsoid to the variable misalignment of spheroidal hemispheres. Comparative coordinate measurements of two solid spherical density standards were used to identify and estimate type B uncertainties.

We tested the regression of the CMM data to spherical harmonic expansions and determined the volume of a QSR directly with a relative uncertainty u_R < 30 parts in 10⁶. Additionally, spherical harmonic regression of the CMM data can place uncertainty bounds on the eccentricity parameters, ε₁ and ε₂, typically with a relative uncertainty u_R ≈ 0.02. This is sufficient to determine corrections to both the acoustic and the microwave resonance frequencies of the QSR with a relative uncertainty u_R < 1 part in 10⁶ for all resonances. These figures assume that the enclosed volume of an assembled QSR is equal to the sum of the volumes of its two component 'hemispheres'. In practice this cannot be strictly true and the additional uncertainties in the volume of the assembled QSR are discussed.

This paper has two purposes: first, as a tutorial on the use of generalized autocovariances for deriving covariance properties of phase-noise models with power-law spectra; second, to connect the subject to the theory of generalized functions, also called tempered distributions. Proofs of theorems are available in an online supplement (http://stacks.iop.org/0026-1394/47/605/mmedia).

We investigate some statistical properties of ac voltages from a white noise source measured with a digital lock-in amplifier equipped with finite impulse response output filters which introduce correlations between successive voltage values. The main goal of this work is to propose simple solutions to account for correlations when calculating the standard deviation of the mean (SDM) for a sequence of measurement data acquired using such an instrument. The problem is treated by time series analysis based on a moving average model of the filtering process. Theoretical expressions are derived for the power spectral density (PSD), the autocorrelation function, the equivalent noise bandwidth and the Allan variance; all are related to the SDM. At most three parameters suffice to specify any of the above quantities: the filter time constant, the time between successive measurements (both set by the lock-in operator) and the PSD of the white noise input, h₀. Our white noise source is a resistor so that the PSD is easily calculated; there are no free parameters. Theoretical expressions are checked against their respective sample estimates and, with the exception of two of the bandwidth estimates, agreement to within 11% or better is found.