Abstract

Spaceborne measurements pinned to international standards are needed to monitor the earth’s climate, quantify human influence thereon, and test forecasts of future climate change. The International System of Units (SI, from the French for Système International d’Unités) provides ideal measurement standards for radiometry as they can be realized anywhere, at any time in the future. The challenge is to credibly prove on-orbit accuracy at a claimed level against these international standards. The most accurate measurements of thermal infrared spectra are achieved with blackbody-based calibration. Thus, SI-traceability is obtained through the kelvin scale, making thermometry the foundation for on-orbit SI-traceable spectral infrared measurements. Thermodynamic phase transitions are well established as reproducible temperature standards and form the basis of the international practical temperature scale (International Temperature Scale of 1990, ITS-90). Appropriate phase transitions are known in the temperature range relevant to thermal infrared earth observation (190–330 K) that can be packaged such that they are chemically stable over the lifetime of a space mission, providing robust and traceable temperature calibrations. A prototype blackbody is presented that is compact, highly emissive, thermally stable and homogeneous, and incorporates a small gallium melting point cell. Precision thermal control of the blackbody allows the phase transition to be identified to within 5 mK. Based on these results, the viability of end-to-end thermometric calibration of both single-temperature and variable-temperature blackbodies on orbit by employing multiple-phase-change cells was demonstrated.

1. Introduction

Obtaining accurate measurements of infrared radiance from space can contribute greatly to our understanding of climate change and the earth system. The long-wave forcing of the climate, the climate’s response, and the long-wave feedbacks involved in that response bear characteristic signatures in a time series of thermal infrared spectra. The long-wave water vapor feedback, cloud feedback, and temperature change are uniquely discernable. For this reason, high spectral resolution thermal infrared time series constitute an effective benchmark of global climate change. Furthermore, such a time series should provide powerful constraints for climate models by improving the representation of feedbacks (Leroy et al. 2008).

To capture the spectral features containing information about greenhouse gas forcing and the response of the distribution of temperature, water vapor, and clouds, measurements are required to continuously cover at least the 200–2000 cm−1 spectral range at a resolution of better than or equal to 1 cm−1 (Ohring 2008). In this spectral window, global observations over all seasons will encounter radiance temperatures from 190 to 330 K. Various studies (Anderson et al. 2004; Ohring 2008; National Research Council 2007) have indicated that signal detection above natural variability for decadal climate signatures requires a threshold uncertainty of 0.05–0.1 K (1σ), or better, in radiance temperature. This is equivalent to a relative combined uncertainty of 1.5 × 10−3 (at 250 K at 750 cm−1) in radiance (1σ uncertainty values are used throughout this paper). Realizing such low uncertainty is routine for national meteorology institutes in a laboratory setting, but proving on-orbit uncertainty at this level has not yet been accomplished by space-based infrared sounders. Attaining a high-accuracy measurement from a satellite instrument that is defensible and credible by the scientific community will necessitate traceability to the International System of Units (SI, from the French for Système International d’Unités; see Dykema and Anderson 2006).

The International System of Units is linked to fundamental physical properties of matter such that any experimenter anywhere in the world can establish the bias of their observation tied to the applicable SI standard. The statement that a given measurement is SI traceable implies that it can be related to the base SI units through an unbroken chain of comparisons with accepted standards, all having stated uncertainties. In addition, certain principles must be followed to evaluate the uncertainty with which data are reported. For a satellite instrument, SI-traceable calibration achieved during prelaunch calibration cannot be assumed to be valid during the operational lifetime of the instrument. Demonstrating SI traceability on orbit is challenging because accepted standards with which the full dynamic range of expected measurements can be calibrated are not readily available, and the component uncertainties of the measurement (exclusive of the calibration standards) are not easily quantified. Demonstrating SI traceability on orbit, however, is essential, since it is the only rigorous path to establishing a high-accuracy time series.

There are two common methods to realize an SI-traceable infrared radiance scale. One is detector based through electrical substitution radiometry, which is based on SI electrological standards and the principle of equivalence between the optical watt and the electrical watt (Martin et al. 1985). The other is source based through the use of blackbodies with SI-traceable thermometry whose radiance can be described by the Planck function for blackbody radiation (Fox 2000). Although national meteorology institutes have built their primary radiometric scales around the detector-based method, on spaceborne infrared sounders lower uncertainties may be achieved with source-based methods. A review of remote sensing calibration by National Institute of Standards and Technology (NIST) meteorologists suggests that large systematic errors can occur in practical blackbodies (Rice and Johnson 2001). The attainment of the low uncertainties required for climate measurements therefore necessitates blackbodies with an SI-traceable emission scale.

The spectral radiance Bν̃(T) emitted by a blackbody cavity of uniform temperature T with an infinitesimal aperture is described by the Planck function:

 
formula

where h is Planck’s constant, c is the speed of light in a vacuum, kB is the Boltzmann constant, and ν̃ is the spectral index (in cm−1). The spectral radiance Iν̃ emitted by a cavity with a finite aperture with Lambertian reflectance is

 
formula

where ɛν̃ is the cavity spectral emissivity and Teff is the effective temperature of the radiation from the background environment. The second term on the right-hand side of this equation is a simplification valid for spatially isotropic and isothermal background radiation. The values of the physical constants that appear in the Planck function are known with much lower uncertainties than is required for remote sensing applications. Thus, the dominant source of uncertainty in a well-designed blackbody is in the measurement of the cavity temperature, as well as the effect of the nonunity emissivity of a practical blackbody with a macroscopic aperture. Temperature probes can exhibit drift over time periods of years, readout electronics can degrade, and cavity surface preparations can be altered though oxidation in the low earth orbit environment. The realization of the Planck function can thus become inaccurate following preflight calibration. Current and planned operational infrared sounders have no means to directly measure this drift; therefore, they have no means to ascertain the accuracy of their calibration targets during the flight mission. This results in a calibration error of unknown magnitude that varies with time on orbit.

To address this problem, we have developed a blackbody design that implements SI-traceable thermometry, throughout the lifetime of a satellite instrument, by realizing the primary SI temperature scale on orbit. The base SI unit of temperature is the kelvin, and the basic meteorological temperature scale is the International Temperature Scale of 1990. ITS-90 is defined in relation to the fixed points of pure elements, which are immutable physical constants (Rusby et al. 1991). Our design incorporates a simple gallium melting point standard into a calibration blackbody. The gallium melting point remains constant over time and is a defining point of the ITS-90. It is used as a benchmark to calibrate the onboard thermometers. This method allows accurate determination of a blackbody temperature during the lifetime of the satellite instrument on orbit, directly traceable to the base SI temperature scale. To fully constrain the blackbody radiance, an accurate determination of the effective cavity emissivity is also necessary. This is the subject of Gero et al. (2008; manuscript submitted to J. Atmos. Oceanic Technol.). Here, we describe the operation of the blackbody with an embedded melting point standard for calibrating thermometers. In section 2 we describe the details of the experimental apparatus, specifically the thermal and optical design elements of the blackbody and the operation of the gallium melting point standard. In section 3 we discuss the experimental results obtained with the blackbody. In section 4 we discuss the implications of these results for implementing a three-point calibration of temperature sensors on orbit. We summarize our conclusions in section 5.

2. Experiment description

The design strategy employed in this experiment was to construct a blackbody that obeyed the Planck function [Eq. (1)] with an uncertainty in radiance dominated by the uncertainty from temperature measurement. This strategy required that the errors in radiance temperature from cavity temperature nonuniformity and nonunity cavity emissivity be less than the thermometry error. In the following sections we outline the thermal and optical designs, respectively, that were used to meet these requirements. This is followed by a description of the gallium melting point standard that confers SI traceability to the blackbody temperature. The performance of the blackbody–gallium cell system was tested in a vacuum chamber simulating the low earth orbit environment.

a. Thermal design

Figure 1 depicts the cylindrical cavity geometry that was chosen for the blackbody, with a 60° reentrant cone at the base. The aperture, the cone, and the cylinder were designed as independent interlocking aluminum modules that are held together using compression. Temperature homogeneity is achieved by carefully controlling several design elements. A large thermal mass is used, with 13-mm-thick walls, in order to enhance the thermal conductivity and minimize temperature gradients along the cavity. The blackbody exterior is covered with layers of Kapton, Nomex, and aluminized Mylar to insulate against radiative thermal losses to the environment. The full blackbody module is mounted on an optical table with highly rigid and insulating G10 fiberglass stands to reduce thermal losses in the mounting mechanism. Each blackbody module is outfitted with a Kapton thermofoil heater (Minco, Minneapolis, Minnesota). The power dissipation in each can be manually controlled to ensure temperature homogeneity across the entire cavity. The heaters are regulated using an analog proportional-integral-derivative controller (Wavelength Electronics, Bozeman, Montana). A thermistor placed in proximity to the reentrant cone provides the closed-loop feedback for the controller. The operational blackbody has a setpoint accuracy of 5 mK, temperature stability better than 1 mK h−1, and cavity inhomogeneity of 10 mK along its length, depending on the difference between the blackbody setpoint and the ambient temperature.

Fig. 1.

Cross-sectional view of the blackbody with the embedded gallium cell (shaded in gray). The blackbody has cylindrical geometry. All component modules (except the gallium cell) are made of aluminum 6061 and the cavity interior is coated with Aeroglaze Z306. The interior length is 229 mm, the inner diameter is 51 mm, and the entrance aperture diameter is 38 mm. All components are held together using compression. Thermal grease is used as indicated to enhance conduction between the gallium cell and the blackbody. Thermistors, labeled 1–6, are placed into the narrow cylindrical wells to monitor the temperature along the length of the cavity. Thermistors 1, 2, and 6 are referred to as the gallium, cone, and aperture thermistors, respectively.

Fig. 1.

Cross-sectional view of the blackbody with the embedded gallium cell (shaded in gray). The blackbody has cylindrical geometry. All component modules (except the gallium cell) are made of aluminum 6061 and the cavity interior is coated with Aeroglaze Z306. The interior length is 229 mm, the inner diameter is 51 mm, and the entrance aperture diameter is 38 mm. All components are held together using compression. Thermal grease is used as indicated to enhance conduction between the gallium cell and the blackbody. Thermistors, labeled 1–6, are placed into the narrow cylindrical wells to monitor the temperature along the length of the cavity. Thermistors 1, 2, and 6 are referred to as the gallium, cone, and aperture thermistors, respectively.

The temperatures of each blackbody module and the gallium cell are monitored using thermistors (Thermometrics, Edison, New Jersey). They are potted with thermal grease in deep narrow cylindrical cavities 2–5 mm from the blackbody interior surface. The exact locations of the six thermistors used are shown in Fig. 1.

The resistance of the thermistor is measured with a Hart Scientific 1575 SuperThermometer (American Fork, Utah). This apparatus applies a constant current of 10 μA and measures the voltage across the resistive sensor, comparing it to the voltage across a well-characterized internal reference resistor. The measurement is performed twice with the current in alternating directions, in order to eliminate offset voltages, including those arising from thermal electromotive forces (EMFs). Using this approach, errors from driving current imprecision, voltage offsets, amplifier and analog-to-digital converter (ADC) inaccuracies, and drift in the physical properties of electronic components are avoided because these all affect the voltage samples equally (Hart Scientific 1999). Lead resistance errors are eliminated by using a four-wire circuit. In this arrangement, the sensor is driven with current from one pair of wires and the resulting EMF is sensed with a second pair of wires. The signal is passed to an amplifier with very high input impedance that draws negligible current from the sensor. As a result, no measurable voltage develops along the EMF sensing wires. Electrical noise remains the chief source of measurement uncertainty. The ultimate accuracy of the SuperThermometer in measuring resistance is two parts in 105, or 0.5 mK between 25° and 50°C (Hart Scientific 1999). Table 1 lists the component uncertainty budget.

Table 1.

Component uncertainties (1σ) of the gallium cell blackbody.

Component uncertainties (1σ) of the gallium cell blackbody.
Component uncertainties (1σ) of the gallium cell blackbody.

The thermistors are individually calibrated in a highly stable and homogenous thermal bath (Hart Scientific 7080 Calibration Bath). They are placed in a calibration fluid mixture composed of 50% water and 50% ethylene glycol, and their resistance values are measured at seven different temperatures from −30°C to 50°C. At each setpoint, the bath temperature is held constant for 30 min while the thermistor resistances are logged. The bath temperature is determined using a standard platinum resistance thermometer (SPRT; Hart Scientific 5681 SPRT) with a traceable calibration to the ITS-90 temperature scale. The resulting temperature and resistance data are fitted to the Steinhart–Hart equation in order to determine the calibration coefficients of each thermistor. The fit residuals to the Steinhart–Hart equation are less than ±3 mK over the entire range.

The experiment was conducted in a vacuum chamber to simulate the thermal environment of low earth orbit. The chamber was evacuated to <1 × 10−5 mb, where convection is negligible and radiation is the dominant mechanism of heat transfer.

b. Optical design

The aperture, the cone, and the cylinder were designed as independent interlocking aluminum modules. The 60° reentrant cone at the base of the blackbody ensures that an incident ray undergoes a large number of specular reflections before exiting the cavity. The blackbody cavity may be assembled with an arbitrary number of cylindrical modules, thereby providing a range of aspect ratios, defined as the ratio of cavity depth to aperture diameter. Higher aspect ratios lead to higher effective emissivities and will more closely approximate the ideal blackbody (Gouffé 1945; Quinn 1967; Chandos and Chandos 1974; Usadi 2006). Based on preliminary emissivity modeling, an aspect ratio of 6 was chosen, with a cavity length of 229 mm and an aperture diameter of 38 mm.

The interior surface of the cavity was sandblasted to create micron-scale roughness. The surface was primed with Aeroglaze 9947 primer, and coated with Aeroglaze Z306 diffuse black paint (Lord Corp., Erie, Pennsylvania). This paint has characteristically high emissivity in the infrared, low outgassing rates, and is qualified for spaceborne applications. A thin 0.06-mm coat of paint was applied in order to keep temperature gradients across the insulating paint to a minimum (Best et al. 2003).

The directional–hemispherical reflectance of a witness sample of the blackbody surface preparation was determined with a reflectometer. The apparatus employed a quantum cascade laser at 8 μm in pulsed mode. The hemispherically reflected laser light from a surface sample was collected in a gold-coated integrating sphere (Labsphere, North Sutton, New Hampshire) and the signal amplitude was measured synchronously with a mercury–cadmium–telluride (MCT) detector (Kolmar, Newburyport, Massachusetts), then compared to a surface sample with known reflectance in order to calculate the absolute reflectance. The surface reflectance of the witness sample was measured to be 0.031 ± 0.001, with measurement precision being the dominant source of uncertainty.

The effective emissivity of the blackbody cavity was modeled using a Monte Carlo method (Sapritsky and Prokhorov 1992; Sapritsky and Prokhorov 1995; Prokhorov 1998). The statistical ray-tracing calculation provides estimates of normal spectral effective emissivity for blackbody cavities of arbitrary cylindrical geometry and temperature distribution. The average normal ray-viewing condition with a beam diameter of 25 mm was employed to correspond to the size of the image of the detectors in the plane of the blackbody aperture. The simulations were run with 107 rays, leading to an uncertainty of one part in 106 resulting from ray truncation.

Using the measured temperature distributions along the cavity (10–18-mK gradient along the cylinder as measured by the thermistors) and a surface reflectance of 0.031 (as measured at 8 μm with the reflectometer), the modeled effective cavity emissivity was 0.999 883 ± 0.000 003. The dominant source of error is the uncertainty in the surface reflectance. For a cavity heated to 50°C in an effective ambient background of 27°C, this results in a radiance temperature of 49.9976°C, a 2.4-mK deviation from an ideal blackbody. If the cavity temperature were isothermal, its radiance temperature under these conditions would be 49.9977°C, 0.1 mK different compared to the observed case. These errors are less than the 3.1-mK cumulative thermometry measurement error; thus, the model results indicate that the blackbody should exhibit excellent radiometric performance.

c. Gallium melting point standard

The SRM 1968 gallium melting point standard—http://ts.nist.gov/MeasurementServices/ReferenceMaterials/archived_certificates/1968.%20June%201977.pdf (NIST, Gaithersburg, Maryland)—consists of approximately 25 g of high-purity gallium in a chemically stable epoxy-sealed Teflon crucible. The cylindrical cell is 117 mm tall and 23 mm in diameter, with the geometry shown in Fig. 2. It allows simple realization of the gallium melting point at 29.7646 ± 0.0007°C, which is a defining point of the ITS-90 temperature scale (Thornton 1977). The cell was designed for calibrating small temperature probes up to 3.6 mm in diameter.

Fig. 2.

Cross-sectional view of the gallium melting point standard. The cell has cylindrical geometry and is 117 mm long and 23 mm in diameter. The temperature probe is inserted into the well down the middle of the cell, where it is in good thermal contact with the melting gallium. The cell contains 25 g of gallium with a nominal purity of 99.999 99%.

Fig. 2.

Cross-sectional view of the gallium melting point standard. The cell has cylindrical geometry and is 117 mm long and 23 mm in diameter. The temperature probe is inserted into the well down the middle of the cell, where it is in good thermal contact with the melting gallium. The cell contains 25 g of gallium with a nominal purity of 99.999 99%.

The standard operation of the gallium melting point standard is to begin with the gallium in its solid phase and immerse the cell in a liquid bath at a temperature just above the melting point. As the gallium begins to melt, the temperature inside the well reaches the melting point and remains stable at that temperature while the material is undergoing melting (shown in Fig. 3). The length of the melting plateau is inversely proportional to the temperature difference between the bath temperature and the melting point. With the bath set to 29.9°C, the plateau lasts approximately 10 h.

Fig. 3.

A full gallium melting point transition in a thermal bath. The cell, initially at room temperature, was immersed in a liquid bath held at 29.92°C. The temperature inside the cell plateaued at the gallium melting point for about 10 h, before equilibrating with the bath temperature.

Fig. 3.

A full gallium melting point transition in a thermal bath. The cell, initially at room temperature, was immersed in a liquid bath held at 29.92°C. The temperature inside the cell plateaued at the gallium melting point for about 10 h, before equilibrating with the bath temperature.

In this experimental setup, the laboratory blackbody in good thermal contact with the cell acts as the temperature bath. A mechanical mount was designed to place the cell adjacent to the reentrant cone in close proximity to the primary emitting surface (shown in Fig. 1). Good thermal contact between the aluminum and the cell was ensured by using thermal grease.

3. Experimental results

Figure 4 shows the temperature of the gallium cell and the blackbody during a full gallium phase transition. Here, the temperature of the blackbody was first stabilized below the gallium melt point at 29.18°C. Then, constant power was applied to the heaters to gradually raise the temperature above the melt point. Around time index equal to 410 min, the temperature of the gallium cell plateaued, while the surrounding blackbody continued to increase in temperature, albeit at a lower rate. The melt plateau lasted about 120 min, after which the gallium began to warm up and eventually reequilibrated with the rest of the blackbody.

Fig. 4.

A full melting transition of the gallium cell blackbody. (top) The temperature of the blackbody cone (thermistor 2) and the gallium cell (thermistor 1) during the melt. The blackbody temperature was first stabilized below the gallium melting point; then, constant power was applied to the blackbody heaters after approximately 370 min. The gallium melting point was reached around time index 410 min, at which point the temperature inside the cell remained constant for the next 120 min. After the melt, the temperature of the cell reequilibrated with the rest of the blackbody. The other parts of the blackbody (thermistors 3–6) were all within 10 mK of each other under equilibrium conditions prior to the melt, and they reached a maximum gradient of 90 mK between the aperture and the cone near the end of the melt plateau. (bottom) The rate of change of temperature for the blackbody cone and the gallium cell.

Fig. 4.

A full melting transition of the gallium cell blackbody. (top) The temperature of the blackbody cone (thermistor 2) and the gallium cell (thermistor 1) during the melt. The blackbody temperature was first stabilized below the gallium melting point; then, constant power was applied to the blackbody heaters after approximately 370 min. The gallium melting point was reached around time index 410 min, at which point the temperature inside the cell remained constant for the next 120 min. After the melt, the temperature of the cell reequilibrated with the rest of the blackbody. The other parts of the blackbody (thermistors 3–6) were all within 10 mK of each other under equilibrium conditions prior to the melt, and they reached a maximum gradient of 90 mK between the aperture and the cone near the end of the melt plateau. (bottom) The rate of change of temperature for the blackbody cone and the gallium cell.

Under equilibrium conditions, a thermal gradient was present between the blackbody cone and the temperature inside the gallium cell. The gallium cell was found to be 25–60 mK colder than the cone, under various experimental conditions. This was partly due to the 7.5-mm layer of Teflon separating the aluminum cavity and the melting material. Furthermore, because of the geometry, heat was only directly applied to one end of the cylindrical cell, while the other end equilibrated with the surrounding (colder) thermal environment.

The onset of the melt plateau was more clearly identified by raising the temperature of the blackbody in small 5–15-mK steps. In this method of operation the initiation of the melting point was extremely distinct and could be best identified by looking at the temperature difference between the cone and the gallium thermistors (shown in Fig. 5). While the gallium was solid, this temperature difference approached a constant value that was nearly independent of the temperature (∼40 mK). In this regime the equilibrium temperature distribution is determined by the thermal conductivity of the blackbody–gallium cell system. Once the melting was initiated, the temperature difference between the cone and the gallium thermistors increased, as the melting of the gallium perturbed the thermal equilibrium, acting as an additional reservoir for thermal energy. This can be clearly identified in Fig. 5 at time index 180 min. The temperature of the surrounding blackbody is 29.805°C at this point, 41 mK above the gallium melting point. The temperature inside the cell stabilized at 29.762 88°C ± 0.000 04 over the next 23 h, while the surrounding blackbody was at 29.835°C. The small offset from the true gallium melting point was within the thermistor uncertainty (±3.1 mK; see Table 1).

Fig. 5.

Onset of the gallium melting point with the blackbody operated in step mode. (top) The temperature of the blackbody cone and the gallium cell; (bottom) the temperature difference between the two. The temperature of the blackbody is stepped up at 5–15-mK intervals, then allowed to equilibrate for an hour. The temperature difference equilibrates to approximately 40 mK prior to the melt, but increases once the melt is initiated. The transition point between the two regimes is clearly discernable at time index 180 min.

Fig. 5.

Onset of the gallium melting point with the blackbody operated in step mode. (top) The temperature of the blackbody cone and the gallium cell; (bottom) the temperature difference between the two. The temperature of the blackbody is stepped up at 5–15-mK intervals, then allowed to equilibrate for an hour. The temperature difference equilibrates to approximately 40 mK prior to the melt, but increases once the melt is initiated. The transition point between the two regimes is clearly discernable at time index 180 min.

4. Discussion

Using this methodology, the accuracy of blackbody thermometry can be determined on board a satellite instrument, traceable to the ITS-90 temperature scale. Since the gallium is hermetically sealed and its physical properties are not subject to long-term drift, such a cell can be used to test thermometer drift over the lifetime of a satellite instrument. To achieve this operationally, the fixed-point temperature must be related thermally to the temperature probes embedded in the blackbody. The main obstacle encountered in the laboratory experiments was the 25–60-mK gradient between the phase-change material and the thermistor near the radiating surface. This gradient can be reduced by improving heat transfer between the blackbody and the gallium, and by employing a mechanical design that completely surrounds the cell within the heated blackbody. Any remaining gradient can be treated as a constant bias that can be accounted for with a thermal model of the blackbody. The exact onset of the phase transition needs to be identified. This can be achieved with either the step or the ramp method used in this paper. With the step method, a thermometer must directly measure the temperature of the melt material, as the onset is determined using the difference between the temperature of the phase-change material and the temperature measured by the thermometer to be calibrated. This requires good active control of the blackbody to maintain it at a steady temperature. The accuracy of realizing the temperature at the onset of the phase transition is dependent on the smallest achievable temperature step size. In this paper the realization accuracy was 5–15 mK. With the ramp method, the onset of the melting point can be identified by looking at the signature of a perturbed rate of change of heating in any thermometer embedded in the blackbody. This method requires good thermal control of the blackbody, as the accuracy of identifying the melting point improves with lower temperature ramp rates. It has been demonstrated that melting point signatures can be identified to 5-mK accuracy using a ramp rate of about 0.02 mK s−1 (Best et al. 2007).

Thermometers suitable for space applications, such as thermistors and encapsulated platinum resistance thermometers, can have their calibration coefficients determined using a minimum of three temperature points. The relation between the resistance R and the temperature T for a thermistor is best described by the Steinhart–Hart equation (Steinhart and Hart 1968):

 
formula

where A, B, and C are empirically derived calibration coefficients. For a platinum resistance thermometer, the resistance–temperature relation is best approximated by the Callendar–van Dusen equation (Callendar 1887; van Dusen 1925):

 
formula

where R0 is the resistance at 0°C. In both cases the three coefficients A, B, and C can be calculated by measuring a minimum of three distinct resistance–temperature pairs and performing a linear regression.

For a spaceborne blackbody that operates near a single temperature throughout its mission, closely spaced fixed points may be used to calibrate the thermometer over a narrow temperature range. The fixed points of gallium and its eutectic alloys (shown in Fig. 6) would be suitable for this application (Krutikov et al. 2006). For a climate instrument with the mission to measure SI-traceable radiance over a broad radiance temperature range corresponding to various earth-observing conditions, a variable-temperature blackbody is needed. In this case the fixed points of mercury, water, and gallium can be used to calibrate a temperature probe in the range spanning 234–303 K (Best et al. 2007).

Fig. 6.

Phase-change fixed points within the radiance temperature range of earth observations of infrared radiance (190–330 K); all values are in kelvins. Three defining points of the ITS-90 lie in this range (indicated by circles): the triple point of mercury, the triple point of water, and the melting point of gallium. Three eutectic alloys of gallium—GaIn, GaSn, and GaZn (indicated by diamonds)—also have well-defined melting points that may be used in this application.

Fig. 6.

Phase-change fixed points within the radiance temperature range of earth observations of infrared radiance (190–330 K); all values are in kelvins. Three defining points of the ITS-90 lie in this range (indicated by circles): the triple point of mercury, the triple point of water, and the melting point of gallium. Three eutectic alloys of gallium—GaIn, GaSn, and GaZn (indicated by diamonds)—also have well-defined melting points that may be used in this application.

The overall temperature uncertainty of performing such an in situ calibration of a thermistor with three fixed-point cells was modeled and the results are shown in Fig. 7. The calculation was done with a model for thermistor calibration using the Steinhart–Hart equation, and a half-bridge topology for measuring the thermistor resistance, similar to the one employed by Keith et al. (2001) in the Interferometer for Emission and Solar Absorption (INTESA) flight instrument. Component uncertainties arising from the readout electronics, including reference resistors, thermistor self-heating, and analog-to-digital converter resolution, were accounted for in the model, and are listed in Table 2. The overall uncertainty in the temperature is evaluated from an ensemble of 104 Monte Carlo simulations of the calibration model, where the variance of the random variables was specified by the 1σ root-sum-of-squares measurement uncertainties. The results show that within the region bounded by the fixed points the combined thermometric uncertainty is dominated by the uncertainty in temperature determination. These results suggest that with sufficient accuracy in temperature determination, it is possible to calibrate temperature probes on a satellite instrument on orbit, with adequately low uncertainties to meet the demands of climate observations.

Fig. 7.

Combined temperature uncertainty of a modeled in situ calibration of blackbody thermistors using three fixed-point cells. (top) The uncertainty in calibrating a 10-kΩ thermistor using the fixed points of Hg, H2O, and Ga (indicated by the vertical lines of symbols). (bottom) The uncertainty for a 30-kΩ thermistor calibrated at the fixed points of GaSn, GaZn, and Ga.

Fig. 7.

Combined temperature uncertainty of a modeled in situ calibration of blackbody thermistors using three fixed-point cells. (top) The uncertainty in calibrating a 10-kΩ thermistor using the fixed points of Hg, H2O, and Ga (indicated by the vertical lines of symbols). (bottom) The uncertainty for a 30-kΩ thermistor calibrated at the fixed points of GaSn, GaZn, and Ga.

Table 2.

Component uncertainties (1σ) of the thermometry readout electronics for a modeled flight blackbody design. The uncertainty in the realization and identification of the fixed points was varied over the values of 0, 5, 10, and 15 mK.

Component uncertainties (1σ) of the thermometry readout electronics for a modeled flight blackbody design. The uncertainty in the realization and identification of the fixed points was varied over the values of 0, 5, 10, and 15 mK.
Component uncertainties (1σ) of the thermometry readout electronics for a modeled flight blackbody design. The uncertainty in the realization and identification of the fixed points was varied over the values of 0, 5, 10, and 15 mK.

5. Conclusions

An in situ fixed-point evaluation of the calibration uncertainty of thermometers was performed in a high-emissivity, thermally stable, compact blackbody with an embedded gallium melting point cell. The design is evolvable into a lightweight flight version. Two methods have been investigated for realizing the phase transition for the purposes of thermometer calibration. Using these methods, thermometry accurate to 5 mK may be achieved. By extending the methodology employed in this experiment to multiple fixed-point cells within a single blackbody, the temperature probes embedded in the blackbody can be calibrated on orbit, during the lifetime of the instrument, with traceability to the ITS-90 temperature scale in the temperature range 234–303 K. Since the practically achievable pathway for the traceability of infrared radiance to the SI is through Planck’s law and the definition of the kelvin, this methodology allows unprecedented accuracy in the remote sensing of spectral infrared radiance. This is an improvement over previous methods for infrared radiance calibration, which have appealed to engineering formulas or intercomparison campaigns capable only of testing system–level uncertainty. This methodology provides an end-to-end calibration of all aspects of thermometry, including thermometer coefficients and electronics readout.

Acknowledgments

The authors acknowledge the engineering support of L. Lapson, M. Greenberg, J. Demusz, M. Rivero, and T. Martin. The authors would also like to thank F. Best and his coinvestigators for helpful discussions and S. Mekhontsev for suggestions on the practical realization of the fixed-point concept.

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Footnotes

Corresponding author address: Dr. P. Jonathan Gero, School of Engineering and Applied Sciences, Harvard University, 12 Oxford St., Cambridge, MA 02138. Email: gero@huarp.harvard.edu