Raju U. Datla

Statistical analysis of CIPM key comparisons based on the ISO Guide

An international Advisory Group on Uncertainties has published guidelines for the statistical analysis of a simple key comparison carried out by the Consultative Committees of the International Committee of Weights and Measures (CIPM) where a travelling standard of a stable value is circulated among the participants. We discuss several concerns regarding these guidelines. Then, we describe a statistical model based on the Guide to the Expression of Uncertainty in Measurement to establish the key comparison reference value, the degrees of equivalence, and their associated standard uncertainties on the basis of the data submitted by the participants. The proposed statistical model applies to all those CIPM key comparisons where the submitted results are mutually comparable and appropriate for determining the key comparison reference value and the submitted uncertainties are sufficiently reliable.

Combined result and associated uncertainty from interlaboratory evaluations based on the ISO Guide

We address the problem of determining the combined result and its associated uncertainty in the measurement of a common measurand by a group of competent laboratories. Most data analyses of interlaboratory evaluations are based on the assumption that the expected values of the individual laboratory results are all equal to the value of the common measurand. This means that the laboratory results are subject to random effects only with respect to the value of the measurand. This assumption is frequently unjustified. We use the more realistic assumption that the laboratory results are subject to both random and systematic effects with respect to the value of the measurand. In this case, the value of the measurand may fall anywhere within the range of results. Therefore, a combined result and its associated standard uncertainty that place a non-negligible fraction of the results outside the 2-standard-uncertainty interval are unsatisfactory representations of the value of the common measurand provided by the set of laboratory results. The more realistic assumption requires us to deal with the uncertainty arising from possible systematic effects in the laboratory results. Following the approach of the ISO Guide to deal with systematic effects, we propose a three-step method to determine a combined result and its associated standard uncertainty such that the 2-standard-uncertainty interval would include a sufficiently large fraction of the results. When the interlaboratory evaluation is an International Committee for Weights and Measures (CIPM) key comparison, we suggest that the combined result and its associated standard uncertainty determined by the three-step method be identified with the key comparison reference value and its associated standard uncertainty. These quantities can then be used to specify the degree of equivalence of the individual laboratory results. We illustrate the three-step method by applying it to the results of an international comparison of cryogenic radiometers recently organized by the Consultative Committee for Photometry and Radiometry (CCPR).

Testing the radiometric accuracy of Fourier transform infrared transmittance measurements

We have investigated the ordinate scale accuracy of ambient temperature transmittance measurements made with a Fourier transform infrared (FT-IR) spectrophotometer over the wavelength range of 2-10 mum. Two approaches are used: (1) measurements of Si wafers whose index of refraction are well known from 2 to 5 mum, in which case the FT-IR result is compared with calculated values; (2) comparison of FT-IR and laser transmittance measurements at 3.39 and 10.6 mum on nominally neutral-density filters that are free of etaloning effects. Various schemes are employed to estimate and reduce systematic error sources in both the FT-IR and laser measurements, and quantitative uncertainty analyses are performed.

Active cavity absolute radiometer based on high-Tc superconductors

To implement the detector-based radiometric scale in the new Medium Background Infrared (MBIR) facility at the National Institute of Standards and Technology (NIST), we have developed an electrical-substitution cavity radiometer that can be operated just above liquid-nitrogen temperature. This MBIR active cavity radiometer (ACR) utilizes a temperature-controlled receiver cone and an independently temperature-controlled heat sink. Being a thermal-type detector, low noise and drift of the radiometer signal depends mainly on low-noise temperature control of the receiver and heat sink. Using high critical-temperature (Tc) superconducting thin-film temperature sensors in the active control loops, we have achieved closed-loop temperature controllability of better than 10 µK at 89 K for a receiver having an open-loop thermal time constant of about 75 s. For a flux level of 1 µW to 10 µW, the rms noise floor over a measurement cycle time is below 20 nW. This is the lowest noise level yet reported for a liquid-nitrogen-cooled electrical-substitution radiometer, and it is the first demonstration of the use of high-Tc superconductors in such a radiometer. Potential uses for this ACR in the MBIR facility include absolute measurement of the broadband radiance of large-area 300 K cryogenic black-body sources, and absolute measurement of the spectral radiance of laser-illuminated integrating spheres for improved spectral responsivity measurements of infrared transfer standard radiometers.

ACR II: Improved absolute cryogenic radiometer for low background infrared calibrations

A second-generation absolute cryogenic radiometer (ACR II) was developed for use at the Low Background Infrared calibration facility at the National Institute of Standards and Technology. The need for spectral calibrations of very sensitive [D* = 10(14) cm (Hz)1/2W(-1)] infrared detectors necessitated the use of a cryogenic infrared monochromator and a more sensitive radiometer. The improved low-power performance of the ACR II compared with the older absolute cryogenic radiometer (ACR) has also made it useful as the primary standard for the calibration of cryogenic blackbody sources that are used as low-power infrared sources. The responsivity of the new radiometers receiver is 210 K/mW with a type A (random component) standard uncertainty of at most 7 pW when making power measurements of less than 10 nW. The original ACR has a responsivity of 29 K/mW and has a type A standard uncertainty of approximately 100 pW when making a similar low-noise-power measurement. Other properties of the radiometers are also described and compared.

Low-background temperature calibration of infrared blackbodies

The Low Background Infrared (LBIR) facility at the National Institute of Standards and Technology (NIST) has performed ten radiance temperature calibrations of low-background blackbodies since 2001, when both the calibration facility and method of calibrating blackbodies were significantly improved. Data from nine of these blackbody calibrations are presented, showing a surprisingly large spread in blackbody performance. While some blackbodies performed relatively well, in no case did the measured radiance temperature agree with the temperature sensors in the blackbody core to within 0.3 K over the entire operating temperature range of the blackbody. Of the nine blackbodies reported, five showed temperature errors greater than 1 K at some point in their operating temperature range. The various sources of uncertainty, such as optical geometry and detector standard uncertainty, are presented with examples to support the stated calibration accuracy. Generic blackbody cavity design features, such as cavity thermal mass, cavity volume and defining aperture placement are discussed and correlated with blackbody performance. Data are also presented on the performance of the absolute cryogenic radiometers (ACRs) that are used as detector standards in the calibration of blackbodies. Recent intercomparisons of all the LBIR ACRs with a trap detector calibrated against the NIST primary optical power measurement standard show that ACRs used to calibrate blackbodies are suitable detector standards and contribute less than 0.02% uncertainty (k = 1) to radiance temperature measurements of the blackbody cavities.

Absolute cryogenic radiometer and solid-state trap detectors for IR power scales down to 1 pW with 0.1% uncertainty

Commercially available absolute cryogenic radiometers (ACRs) have combined uncertainties that grow rapidly above 1% (k = 1) at power levels below 10 nW. There are solid state detectors, however, used in sensors and radiometers that cannot be calibrated at levels as high as 10 nW because they begin to saturate. For this reason new detector-based standards are being developed to provide the low-background infrared calibration community with absolute traceability to powers down to 1 pW with ~0.1% (k = 1) combined uncertainty. The scale will be established using an ACR with a combined uncertainty of the order of 1 fW and a trap detector based on arsenic-doped silicon blocked impurity band devices with similar noise floor performance.

Polarization-dependent angular reflectance of silicon and germanium in the infrared

We have investigated the reflectance of crystalline silicon and germanium samples for infrared radiation polarized parallel and perpendicular to the plane of incidence. A Fourier transform infrared (FT-IR) spectrometer was employed to measure the specular reflectance at angles of incidence from 20° to 60° in the wavelength range between 2 μm and 25 μm. The measurements agree with the theoretical analysis to within the experimental uncertainty. At large angles of incidence, the reflectance depends strongly on polarization. Since the beam in a spectrometer generally exhibits partial polarization, the measured reflectance without a polarizer may differ from the average reflectance for the two polarization states. This work demonstrates that silicon and germanium can be used as standard reference materials for specular reflectance in the mid-infrared region.

Calibration of low-background temperature IR test chambers used to calibrate space sensors

The low-background infrared (LBIR) facility at the US National Institute of Standards and Technology (NIST) has been calibrating infrared test chambers that are used to calibrate spacebased remote sensors. These test chambers typically operate at temperatures of 20 K to 80 K and have collimators in them to simulate faint objects at great distances in a low-background environment. Since 2001 the LBIR facility has used a transfer radiometer, the BXR, to calibrate nine IR test chambers. The BXR has shown that the output of these chambers can differ from the modelled output by ±10%. In this paper the methodology of the BXR calibration activity will be described along with specific examples to highlight important calibration performance parameters of the BXR and of other hardware in the calibration chain from the primary standard.

Infrared transfer radiometer for broadband and spectral calibration of space chambers

The Low-Background Infrared (LBIR) facility at NIST has recently completed construction of an infrared transfer radiometer with an integrated cryogenic Fourier transform spectrometer (Cryo-FTS). This mobile system can be deployed to customer sites for broadband and spectral calibrations of space chambers and low-background HWIL testbeds. The Missile Defense Transfer Radiometer (MDXR) has many of the capabilities of a complete IR calibration facility and will replace our existing filter-based transfer radiometer (BXR) as the NIST standard detector deployed to MDA facilities. The MDXR features numerous improvements over the BXR, including: a cryogenic Fourier transform spectrometer, an on-board absolute cryogenic radiometer (ACR), an internal blackbody reference, and an integrated collimator. The Cryo-FTS can be used to measure high resolution spectra from 4 to 20 micrometers, using a Si:As blocked-impurity-band (BIB) detector. The on-board ACR can be used for self-calibration of the MDXR BIB as well as for absolute measurements of infrared sources. A set of filter wheels and a rotating polarizer within the MDXR allow for filter-based and polarization-sensitive measurements. The optical design of the MDXR makes both radiance and irradiance measurements possible and enables calibration of both divergent and collimated sources. Details of the various MDXR components will be presented as well as initial testing data on their performance.