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JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY
VOLUME 25
A Blackbody Design for SI-Traceable Radiometry for Earth Observation
P. JONATHAN GERO, JOHN A. DYKEMA,
AND
JAMES G. ANDERSON
School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts
(Manuscript received 10 December 2007, in final form 22 April 2008)
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-phasechange 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
Corresponding author address: Dr. P. Jonathan Gero, School of
Engineering and Applied Sciences, Harvard University, 12 Oxford St., Cambridge, MA 02138.
E-mail: gero@huarp.harvard.edu
DOI: 10.1175/2008JTECHA1100.1
© 2008 American Meteorological Society
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 (1␴), 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 (1␴ 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).
NOVEMBER 2008
2047
GERO ET AL.
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 SItraceable 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 B␯˜ (T ) emitted by a blackbody
cavity of uniform temperature T with an infinitesimal
aperture is described by the Planck function:
B␯˜ 共T 兲 ⫽
2hc2␯˜ 3
,
hc␯˜
exp
⫺1
kBT
冉 冊
共1兲
where h is Planck’s constant, c is the speed of light in a
vacuum, kB is the Boltzmann constant, and ␯˜ is the
spectral index (in cm⫺1). The spectral radiance I␯˜ emit-
ted by a cavity with a finite aperture with Lambertian
reflectance is
I␯˜ ⫽ ␧␯˜ B␯˜ 共T 兲 ⫹ 共1 ⫺ ␧␯˜ 兲 B␯˜ 共T eff兲,
共2兲
where ␧␯˜ is the cavity spectral emissivity and T is the
effective temperature of the radiation from the background environment. The second term on the righthand 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
eff
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VOLUME 25
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.
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.
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 ␮A and measures the voltage across the resistive
sensor, comparing it to the voltage across a wellcharacterized internal reference resistor. The measurement is performed twice with the current in alternating
directions, in order to eliminate offset voltages, includ-
NOVEMBER 2008
GERO ET AL.
TABLE 1. Component uncertainties (1␴) of the gallium cell
blackbody.
Component
Thermometry
Readout electronics
Calibration standard
Calibration fitting
Blackbody
Homogeneity
Emissivity
Uncertainty
(mK)
0.5
0.4
3.0
0.1
2.1
ing those arising from thermal electromotive forces
(EMFs). Using this approach, errors from driving current imprecision, voltage offsets, amplifier and analogto-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.
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.
2049
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 ␮m 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
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JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY
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%.
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 ␮m 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 2.4mK 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.
VOLUME 25
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.
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.
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.
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 epoxysealed 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.
The standard operation of the gallium melting point
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.
NOVEMBER 2008
GERO ET AL.
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
2051
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.
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).
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 im-
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JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY
proving 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):
T ⫺1 ⫽ A ⫹ B log共R兲 ⫹ C 关log共R兲兴3,
共3兲
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):
R ⫽ R0关1 ⫹ AT ⫹ BT 2 ⫹ C共T ⫺ 100兲T 3兴,
共4兲
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
VOLUME 25
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.
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 earthobserving 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).
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 elec-
NOVEMBER 2008
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GERO ET AL.
TABLE 2. Component uncertainties (1␴) 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.
Temperature
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-k⍀ thermistor using the
fixed points of Hg, H2O, and Ga (indicated by the vertical lines of
symbols). (bottom) The uncertainty for a 30-k⍀ thermistor calibrated at the fixed points of GaSn, GaZn, and Ga.
tronics, including reference resistors, thermistor selfheating, 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 1␴ root-sum-ofsquares 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.
5. Conclusions
An in situ fixed-point evaluation of the calibration
uncertainty of thermometers was performed in a highemissivity, 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
Component
234 K
273 K
303 K
Thermistor self-heating
Readout electronics
Reference resistors
ADC resolution (12 bit)
0.01 mK
0.2 ⍀
0.2 ⍀
153.4 ⍀
0.11 mK
0.2 ⍀
0.2 ⍀
8.3 ⍀
0.39 mK
0.2 ⍀
0.2 ⍀
3.4 ⍀
the blackbody can be calibrated on orbit, during the
lifetime of the instrument, with traceability to the ITS90 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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