MePK absolute primary radiometric thermometry
Section 1: Absolute (spectralband) radiometry (radiation thermometry)
Authors: Graham Machin (NPL, chair), Klaus Anhalt (PTB), Pieter Bloembergen (NIM, formerly NMIJ & VSL) Juergen Hartmann (PTB), Peter Saunders (MSL), Emma Woolliams (NPL), Yoshiro Yamada (NMIJ), Howard Yoon (NIST)
Version 5.1
Date: 26 July 2012
Introduction
The determination of thermodynamic temperatures through absolute primary radiometry requires the following:

A blackbody with a known (high) spectral emissivity.

A measurement of the spectral radiance of the blackbody traceable to the units of the SI.
Blackbody sources
The spectral radiance of a blackbody, L_{b}_{,}_{}^{1}, that is the power emitted per unit area per solid angle per unit wavelength interval, is given by Planck’s law:
, (1)
where T is the thermodynamic temperature,^{ }k is the Boltzmann constant, h is the Planck constant, c the speed of light in a vacuum, n is the refractive index of the gas in the optical path, is the wavelength in that gas, and is the spectral emissivity of the blackbody. The units of the spectral radiance are W m^{–2} sr^{–1} nm^{–1}
The measurement of thermodynamic temperature by absolute primary filter radiometry
The implementation of absolute primary radiometry requires that the quantities involved are traceable to the units of the SI. Hence, the power measurement must be traceable to the definition of the watt; wavelength, area and distance to the definition of the metre.
Basic principles of absolute primary radiometry
The components of a radiometric system for the measurement of thermodynamic temperatures are a blackbody source and a detector with a known spectral responsivity. The source and the detector areas are limited by coaligned, circular apertures with radii r_{1} and r_{2}, respectively, separated by distance d. The incident spectral power, _{}(), at the detector is given by
, (2)
where L_{} is the spectral radiance of the source and is the throughput of the setup. The throughput is related to the configuration factor (also known as the geometric or form factor), F, and the source aperture area, A_{1}
, (3)
where the configuration factor is
. (4)
The term is also known as the ‘geometric factor’ in the literature.
The spectral irradiance, E_{}, is simply given by the incident power at the plane of the detector aperture divided by the detector aperture area, ,
. (5)
Absolute primary spectralband (or filter) radiometry
The spectral power is determined using a detector of known spectral responsivity in a particular waveband and in a defined solid angle. In principle, there are a number of different filter radiometry implementations. But in practice the filter radiometer is comprised of a detector, a spectrally selective filter and a geometric/optical system with at least one defining aperture; in addition, at least one lens has to be added for imaging systems.
Different practical implementations of absolute primary spectralband radiometry are possible, but all require the following common calibration infrastructure:

A trap detector calibrated at distinct wavelengths by monochromatic radiation from a laser or monochromator, using a cryogenic electrical substitution radiometer and a continuous spectral power responsivity scale obtained by interpolating these values by a physical model. This provides power traceability to the watt.

The calibration of the spectral responsivity, at discrete wavelengths, of the filter radiometer by comparison with the trap detector. This requires a monochromatic source, tuneable across the bandwidth of the filter radiometer. This is often achieved using a tuneable laser illuminating an integrating sphere or, alternatively, a monochromatorbased source. For a spectral radiance responsivity calibration, the source must be Lambertian. The wavelength determination of the laser, or the wavelength scale calibration of the monochromator, provides traceability to the metre.

Two precision circular apertures with known diameter and separation. The areas of these apertures and separation distance provide traceability to the metre.
Examples of practical implementations of absolute primary spectralband radiometry are described below, each having a slightly different calibration method. These are given as a guide only, and the realisation of an absolute primary thermometry scale will depend on local requirements and constraints.
The first two methods are nonimaging, and the third and fourth use optics to facilitate the measurement of small sources.
Nonimaging methods
The power mode
If the radiometer is calibrated for spectral power responsivity, , the photocurrent measured by the radiometer is
. (6)
The power responsivity is determined by calibration against a source that underfills the radiometer, and then a geometric system with two apertures is added to measure the radiance of the blackbody (see Figure 1). For this method the homogeneity of the detector is very important.
Figure 1: The power method.
The irradiance mode
If the radiometer is calibrated for spectral irradiance responsivity, _{ }, the photocurrent measured by the radiometer is
. (7)
The spectral irradiance responsivity of the filter radiometer with mounted aperture is determined by comparison to a trap detector (calibrated a priori against a cryogenic radiometer) with a calibrated entrance aperture, defining the effective area of the trap detector. The spectral irradiance responsivity can be determined with a monochromatorbased or a laserbased system.
During measurement, an aperture at known distance from the radiometer aperture is added in front of the blackbody to create the geometric system needed to convert from irradiance to radiance, i.e. to define the solid angle (see Figure 2). However as diffraction losses increase drastically for a decreasing diameter of the blackbody aperture, so the method has been adapted, as below, for determining the temperature of small sources (e.g. HTFPs).
Figure 2: The irradiance method.
Imaging methods The hybrid method (irradiance mode)
The irradiance approach can be applied to smaller blackbody cavities by introducing a single lens. The calibration is usually performed “in parts”, with the irradiance responsivity of the filter radiometer determined as above, and the transmittance of the lens determined separately. An additional known aperture is added to the lens, at a known distance from the radiometer aperture, to form the geometric system for spectral radiance (see Figure 3). Formally, the method can be considered to be equivalent to the irradiance method (above) – but is capable of measuring sources with small apertures. The absolute sizeofsource effect must be corrected for. The instrument can also be calibrated for use in radiance mode.
Figure 3: The hybrid method.
The radiance mode
An appropriately designed imaging radiometer can be calibrated traceable to primary units as a filter radiometer (see Figure 4). The more complex optical system of the thermometer (e.g. several lenses and appropriate baffling) can lead to an extremely low sizeofsource effect.
If this imaging radiometer, or radiation thermometer, is calibrated for spectral radiance responsivity, _{ }, the photocurrent measured by the radiometer is
. (8)
The calibration of such a system is by comparison with a source of known radiance. The instrument can then determine the blackbody radiance directly.
Figure 4: The radiance method.
Summary of absolute primary radiometry methods
Several different absolute primary radiometry methods could be employed to generate thermodynamic temperature, directly traceable to SI units. Four have been outlined here for illustrative purposes, but radiometrists should not be constrained by these methods and should use whichever variant their own laboratory circumstances permit.
By comparing ITS90 with absolute primary radiometry [1, Annex 2], it is clear that for those laboratories capable of radiometry at the highest level, advantage will be gained through realising and disseminating T directly instead of the T_{90} proxy.
More details are to be found in [1, 2, 3, 4, 5] and references therein.
References
[1] Machin, G., Bloembergen, P., Anhalt, K., Hartmann, J., Sadli, M., Saunders, P., Woolliams, E., Yamada, Y.,Yoon^{ }H., “Realisation and dissemination of thermodynamic temperature above 1234.93 K”, CCT/1012.
[2] Yoon, H.W., Gibson, C.E., Eppeldauer, G.P., Smith, A.W., Brown, S.W., Lykke, K.R., “Thermodynamic radiation thermometry using radiometers calibrated for radiance responsivity”, Int. J. Thermophys., 32, 22172229, 2011.
[3] Woolliams, E., Dury, M., Burnitt, T., Alexander, P.E.R., Winkler, R., Hartree, W., Salim, S., Machin, G., “Primary radiometry for the miseenpratique for the definition of the kelvin: the hybrid method”, Int. J. Thermophys., 32, 1  11, 2011.
[4] Hartmann, J., Anhalt, K., Taubert, D.R., Hollandt J. “Absolute radiometry for the MeP: the irradiance measurement method”, Int. J. Thermophys., 32, 17071718.
[5] Machin, G., Bloembergen, P., Anhalt, K., Hartmann, J., Sadli, M., Saunders, P., Woolliams, E., Yamada, Y.,Yoon^{ }H., “Practical implementation of the miseenpratique for the definition of the kelvin above the silver point”, Int. J. Thermophys., 31, 17791788, 2010.
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