Linearity Characterization and Uncertainty Quantification of Spectroradiometers via Maximum Likelihood and the Non-parametric Bootstrap.

A technique for characterizing and correcting the linearity of radiometric instruments is known by the names the "flux-addition method" and the "combinatorial technique". In this paper, we develop a rigorous uncertainty quantification method for use with this technique and illustrate its use with both synthetic data and experimental data from a "beam conjoiner" instrument. We present a probabilistic model that relates the instrument readout to a set of unknown fluxes via a set of polynomial coefficients. Maximum likelihood estimates (MLEs) of the unknown fluxes and polynomial coefficients are recommended, while a non-parametric bootstrap algorithm enables uncertainty quantification including standard errors and confidence intervals. The synthetic data represent plausible outputs of a radiometric instrument and enable testing and validation of the method. The MLEs for these data are found to be approximately unbiased, and confidence intervals derived from the bootstrap replicates are found to be consistent with their target coverage of 95%. For the polynomial coefficients, the observed coverages range from 91% to 99%. The experimental data set illustrates how a complete calibration with uncertainties can be achieved using the method plus one well-known flux level. The uncertainty contribution attributable to estimation of the instrument's nonlinear response is less than 0.025% over most of its range.

Characterization and absolute calibration of an AERONET-OC radiometer.

The Ocean Color component of the global Aerosol Robotic Network (AERONET-OC) utilizes CE-318 sun photometers modified for above-water radiometry from fixed structures such as oil rigs, lighthouses, and service platforms. Primarily, AERONET-OC measurements allow determination of the water-leaving radiance required for the validation of ocean color satellite data products. One instrument from the AERONET-OC network, identified as AERONET #080, was studied in this work. A laser-illuminated integrating sphere of known radiance enabled determination of the linearity with flux and absolute radiance responsivity at multiple wavelengths within seven of the AERONET #080 filter bands. We compared the results to calibrations from the AERONET facility at the Goddard Space Flight Center of the National Aeronautics and Space Administration and from the Joint Research Centre of the European Commission. These results agree within the estimated mean comparison uncertainty of 1.88 % (k=2). We also assessed these results using calibrated lamp-illuminated integrating spheres and observed a spectral dependence to the comparison results that is unexplained.

Incandescent lamp-based facility for measuring the long-term radiometric stability of spectrographs.

The long-term temporal stability of a spectrograph is one of the most important characteristics affecting the spectrograph's radiometric performance. For many applications, from monitoring ocean color and lunar irradiance to laboratory irradiance measurement standards, the stability of a spectrograph is a primary factor in the overall measurement uncertainty and therefore is the major criterion for the suitability of the spectrograph as an optical-scale transfer standard. Here we report a facility built for testing the long-term radiometric stability of commercial, fiber-coupled spectrographs. The facility uses tungsten quartz-halogen irradiance standard lamps, type "FEL," of the National Institute of Standards and Technology (NIST) as light sources. To ensure the highest stability of these lamps during spectrograph tests, parameters such as lamp current, lamp voltage, and signals from an independent filter radiometer were continuously recorded to monitor any possible instability caused by such effects as lamp aging. Using this facility, we report the stability study of four spectrographs with spectral coverage from the UV to short-wave infrared over an interval of two months during which the lamp irradiance was stable to better than 0.02%. The tested spectrographs show good stability in general, ranging from 0.02% to 0.1% in the visible over a span of 11 days. For a longer two-month test, the variation in spectrograph responses increases by less than 0.1% with no discernable long-term drifts. In addition, we measured the response variation of two of the test spectrographs before and after they were sent to remote field locations and subjected to adverse environmental conditions. In this case, a larger response variation of up to 1.0% dependence on the wavelength was observed. We discuss the performance of the facility and the implications for using these spectrographs for several of NIST's remote sensing projects as radiometric transfer standards based on these stability measurements.

Improvements in the design of thermal-infrared radiation thermometers and sensors.

A new design for thermal-infrared radiation thermometer and sensors is described. Critical optical elements, such as the field stop, Lyot stop, collimating lens, and detector, are placed inside a thermally stabilized assembly that is controlled using thermo-electric coolers and thermistors. The assembled radiation thermometer is calibrated using both variable-temperature fluid-bath and heat-pipe blackbodies from -45 °C to 75 °C and the use of a modified-Planck function and these blackbodies. The size-of-source effect both with and without the Lyot stop has been measured. This new design, during operations without the need for cryogenic cooling, demonstrates sub millikelvin temperature measurement resolution with few millikelvin, week-long stable operations while measuring room-temperature objects.

Invited Article: Advances in tunable laser-based radiometric calibration applications at the National Institute of Standards and Technology, USA.

Recent developments at the National Institute of Standards and Technology's facility for Spectral Irradiance and Radiance responsivity Calibrations using Uniform Sources (SIRCUS) are presented. The facility is predicated on the use of broadly tunable narrow-band lasers as light sources in two key radiometric calibration applications. In the first application, the tunable lasers are used to calibrate the spectral power responsivities of primary standard detectors against an absolute cryogenic radiometer (ACR). The second function is to calibrate the absolute radiance and irradiance responsivities of detectors with uniform light sources, typically generated by coupling the laser light into integrating spheres. The radiant flux from the uniform sources is determined by the ACR-calibrated primary standard detectors. Together these sources and detectors are used to transfer radiometric scales to a variety of optical instruments with low uncertainties. We describe methods for obtaining the stable, uniform light sources required for low uncertainty measurements along with advances in laser sources that facilitate tuning over broader wavelength ranges. Example applications include the development of a detector-based thermodynamic temperature scale, the calibration and characterization of spectrographs, and the use of a traveling version of SIRCUS (T-SIRCUS) to calibrate large aperture Earth observing instruments and astronomical telescopes.

Nonlinearity measurements of solar cells with an LED-based combinatorial flux addition method.

We present a light emitting diode (LED)-based system utilizing a combinatorial flux addition method to investigate the nonlinear relationship in solar cells between the output current of the cell and the incident irradiance level. The magnitude of the light flux is controlled by the supplied currents to two LEDs (or two sets of them) in a combinatorial fashion. The signals measured from the cell are arranged within a related overdetermined linear system of equations derived from an appropriately chosen Nth degree polynomial representing the relationship between the measured signals and the incident fluxes. The flux values and the polynomial coefficients are then solved for by linear least squares to obtain the best fit. The technique can be applied to any solar cell, under either monochromatic or broadband spectrum. For the unscaled solution, no reference detectors or prior calibrations of the light flux are required. However, if at least one calibrated irradiance value is known, then the entire curve can be scaled to an appropriate spectral responsivity value. Using this technique, a large number of data points can be obtained in a relatively short time scale over a large signal range.

Optical reflectance of pyrheliometer absorption cavities: progress toward SI-traceable measurements of solar irradiance.

We have accurately determined the absorptance of three pyrheliometer cavities at 532 nm by measuring the residual reflectance using an angle-resolved bidirectional reflectometer. Measurements were performed at a normal incidence as a function of the viewing angle and position on the cavity cone. By numerically integrating the measured angle-resolved scatter over both the direction and position and accounting for an obstructed view of the cavity, we determined that the effective cavity reflectance was between 8×10-4 and 9×10-4. Thus, the absorptance of the three cavities ranged from 0.99909±0.00014 to 0.99922±0.00012 (k=2 combined expanded uncertainties). These measurements, when extended over the spectral range of operation of the pyrheliometer, are required to establish SI traceability for absolute solar irradiance measurements.

Advances in thermometry.

The last 25 years have seen tremendous progress in thermometry in the moderate temperature range (1 K to 1235 K). Various primary thermometers - based on different physics -have uncovered errors in the International Temperature Scale of 1990 and set the stage for the planned redefinition of the kelvin.

Establishment and application of the 0/45 reflectance factor scale over the shortwave infrared.

This paper describes the establishment and application of the 0/45 reflectance factor scale in the shortwave infrared (SWIR) from 1100 to 2500 nm. Design, characterization, and the demonstration of a four-stage, extended indium-gallium-arsenide radiometer to perform reflectance measurements in the SWIR have been previously discussed. Here, we focus on the incorporation of the radiometer into the national reference reflectometer, its validation through comparison measurements, and the uncertainty budget. Next, this capability is applied to the measurement of three different diffuser materials. The 0/45 spectral reflectance factors for these materials are reported and compared to their respective 6/di spectral reflectance factors.

Large-area irradiance-mode spectral response measurements of solar cells by a light-emitting, diode-based integrating sphere source.

An irradiance-mode absolute differential spectral response (SR) measurement system based on a light emitting diode (LED) array is described. The LEDs are coupled to an integrating sphere whose output irradiance is uniform to better than 2% over an area of 160 mm by 160 mm. SR measurements of solar cells when subject to diffuse irradiation, as provided by the integrating sphere, are compared with collimated irradiance SR measurements. Issues originating from the differences in angular response of the reference versus the test cells are also investigated. The SR curves of large-area cells with dimensions of up to 155 mm are measured and then used to calculate the cell's short circuit current (I(sc)), if illuminated by a defined solar spectrum. The resulting values of I(sc) agree well with the values obtained from secondary measurements.

Absolute spectral responsivity measurements of solar cells by a hybrid optical technique.

An irradiance mode, absolute differential spectral response measurement system for solar cells is presented. The system is based on combining the monochromator-based approach of determining the power mode spectral responsivity of cells with an LED-based measurement to construct a curve representing the light-overfilled absolute spectral response of the entire cell. This curve can be used to predict the short-circuit current (I(sc)) of the cell under the AM 1.5 standard reference spectrum. The measurement system is SI-traceable via detectors with primary calibrations linked to the NIST absolute cryogenic radiometer. An uncertainty analysis of the methodology places the relative uncertainty of the calculated I(sc) at better than ±0.8%.

Versatile light-emitting-diode-based spectral response measurement system for photovoltaic device characterization.

An absolute differential spectral response measurement system for solar cells is presented. The system couples an array of light emitting diodes with an optical waveguide to provide large area illumination. Two unique yet complementary measurement methods were developed and tested with the same measurement apparatus. Good agreement was observed between the two methods based on testing of a variety of solar cells. The first method is a lock-in technique that can be performed over a broad pulse frequency range. The second method is based on synchronous multifrequency optical excitation and electrical detection. An innovative scheme for providing light bias during each measurement method is discussed.

Thermodynamic-temperature determinations of the Ag and Au freezing temperatures using a detector-based radiation thermometer.

The development of a radiation thermometer calibrated for spectral radiance responsivity using cryogenic, electrical-substitution radiometry to determine the thermodynamic temperatures of the Ag- and Au-freezing temperatures is described. The absolute spectral radiance responsivity of the radiation thermometer is measured in the NIST Spectral Irradiance and Radiance Responsivity Calibrations using Uniform Sources (SIRCUS) facility with a total uncertainty of 0.15% (k=2) and is traceable to the electrical watt, and thus the thermodynamic temperature of any blackbody can be determined by using Planck radiation law and the measured optical power. The thermodynamic temperatures of the Ag- and Au-freezing temperatures are determined to be 1234.956 K (+/-0.110 K) (k=2) and 1337.344 K(+/-0.129 K) (k=2) differing from the International Temperature Scale of 1990 (ITS-90) assignments by 26 mK and 14 mK, respectively, within the stated uncertainties. The temperatures were systematically corrected for the size- of-source effect, the nonlinearity of the preamplifier and the emissivity of the blackbody. The ultimate goal of these thermodynamic temperature measurements is to disseminate temperature scales with lower uncertainties than those of the ITS-90. These results indicate that direct disseminations of thermodynamic temperature scales are possible.

Synchrotron radiation-based irradiance calibration from 200 to 400 nm at the Synchrotron Ultraviolet Radiation Facility III.

A new facility for measuring irradiance in the UV was commissioned recently at the National Institute of Standards and Technology (NIST). The facility uses the calculable radiation from the Synchrotron Ultraviolet Radiation Facility as the primary standard. To measure the irradiance from a source under test, an integrating sphere spectrometer-detector system measures both the source under test and the synchrotron radiation sequentially, and the irradiance from the source under test can be determined. In particular, we discuss the calibration of deuterium lamps using this facility from 200 to 400 nm. This facility improves the current NIST UV irradiance scale to a relative measurement uncertainty of 1.2% (k=2).

"Once is Enough" in Radiometric Calibrations.

The successful development of an Optical Technology Division quality system for optical radiation measurement services has provided the opportunity to reconsider the existing calibration procedures to improve quality and reduce costs. We have instituted procedures in our calibration programs to eliminate uninformative repetitive measurements by concentrating our efforts on controlling and understanding the measurement process. The first program in our calibration services to undergo these revisions is described in this paper.

Long-term temporal stability of the National Institute of Standards and Technology spectral irradiance scale determined with absolute filter radiometers.

The temporal stability of the National Institute of Standards and Technology (NIST) spectral irradiance scale as measured with broadband filter radiometers calibrated for absolute spectral irradiance responsivity is described. The working standard free-electron laser (FEL) lamps and the check standard FEL lamps have been monitored with radiometers in the ultraviolet and the visible wavelength regions. The measurements made with these two radiometers reveal that the NIST spectral irradiance scale as compared with an absolute thermodynamic scale has not changed by more than 1.5% in the visible from 1993 to 1999. Similar measurements in the ultraviolet reveal that the corresponding change is less than 1.5% from 1995 to 1999. Furthermore, a check of the spectral irradiance scale by six different filter radiometers calibrated for absolute spectral irradiance responsivity based on the high-accuracy cryogenic radiometer shows that the agreement between the present scale and the detector-based scale is better than 1.3% throughout the visible to the near-infrared wavelength region. These results validate the assigned spectral irradiance of the widely disseminated NIST or NIST-traceable standard sources.

Realization of the National Institute of Standards and Technology detector-based spectral irradiance scale.

A detector-based spectral irradiance scale has been realized at the National Institute of Standards and Technology (NIST). Unlike the previous NIST spectral irradiance scales, the new scale is generated with filter radiometers calibrated for absolute spectral power responsivity traceable to the NIST high-accuracy cryogenic radiometer instead of with the gold freezing-point blackbody. The calibrated filter radiometers are then used to establish the radiance temperature of a high-temperature blackbody (HTBB) operating near 3,000 K The spectral irradiance of the HTBB is then determined with knowledge of the geometric factors and is used to assign the spectral irradiances of a group of 1,000-W free-electron laser lamps. The detector-based spectral irradiance scale results in the reduction of the uncertainties from the previous source-based spectral irradiance scale by at least a factor of 2 in the ultraviolet and visible wavelength regions. The new detector-based spectral irradiance scale also leads to a reduction in the uncertainties in the shortwave infrared wavelength region by at least a factor of 2-10, depending on the wavelength. Following the establishment of the spectral irradiance scale in the early 1960s, the detector-based spectral irradiance scale represents a fundamental change in the way that the NIST spectral irradiance scale is realized.