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Determining the temperature of a blackbody based on a spectral comparison<br />
with a fixed temperature blackbody<br />
T. Zama and I. Saito<br />
National Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology<br />
(NMIJ/AIST). AIST Tsukuba Central 3, 1-1, Umezono 1-Chome, Tsukuba-shi, Ibaraki-ken 305-8563 Japan<br />
Abstract. The temperature of a blackbody has been<br />
determined from a spectral radiance comparison between<br />
the blackbody and a fixed temperature blackbody (whose<br />
temperature is copper freezing point). A multichannel<br />
spectroradiometer was used for the comparison. The<br />
spectral resolution and bandpass property of the<br />
spectroradiometer was evaluated and the signal to noise<br />
ratio of the spectroradiometer was measured. The<br />
uncertainty of the spectral radiance comparison was<br />
evaluated from the signal to noise ratio, the bandpass<br />
property and the spectral distribution difference between<br />
two blackbodies. The result of spectral radiance<br />
comparison was fitted to Planck’s low and the temperature<br />
of the blackbody was determined. The fitting curve agreed<br />
well with the measurement result in longer wavelength<br />
region, but did not agreed with that in shorter wavelength<br />
region. The bandwidth and the signal noise of the<br />
multichannel spectroradiometer caused the disagreement.<br />
Introduction<br />
Blackbody is widely used for establishing scales, for<br />
example spectral irradiance or radiance. For using a<br />
blackbody as primary standard light source, evaluating the<br />
blackbody’s temperature is required. The temperature is<br />
evaluated by (a) radiant flux comparison between the<br />
blackbody and other blackbody whose absolute<br />
temperature is well known or (b) absolute spectral radiance<br />
measurement by an absolute detector. For the comparison<br />
of (a), a fixed temperature blackbody is required. For the<br />
measurement of (b), absolute filter radiometer is required.<br />
In this paper, we introduce a method for determining<br />
blackbody’s temperature according to (a) comparison. A<br />
spectral comparison has been conducted from 600 nm to<br />
780 nm by using a multichannel spectroradiometer. We<br />
compared a blackbody whose operative temperature is<br />
variable from 1300 K to 3300 K (HTBB) with a<br />
copper-freezing-point blackbody (CUBB). The CUBB was<br />
used as the blackbody whose absolute temperature is well<br />
known.<br />
Equipment for Measurement<br />
The multichannel spectroradiometer consists of a<br />
polychromator and a silicon photodiode array detector and<br />
offers a spectral measurement from 380 nm to 780 nm with<br />
increment of 2 nm. The image of an object is focused onto<br />
the entrance slit of the polychromator. The signal from<br />
each pixel of the array is converted to 16-bit digital value<br />
and recorded by a computer. A filter, which has low<br />
transmittance, has been used for avoiding saturation of a<br />
signal on measuring HTBB.<br />
The temperature change of the HTBB is monitored by<br />
a radiation thermometer. The temperature of the HTBB is<br />
kept constant by a feedback from the signal of the<br />
radiation thermometer.<br />
We have used the CUBB, which is operated copper<br />
freezing point, for temperature standard.<br />
Principle of Temperature Determination<br />
The HTBB and CUBB have been measured by the<br />
multichannel spectroradiometer. The spectral radiant flux<br />
of each blackbody was converted into a spectral data. The<br />
spectral data is shown as follows.<br />
( ) ( ) ( ) (1)<br />
L M<br />
λ , T = L λ,<br />
T S λ0,<br />
λ dλ<br />
Where L M (λ 0 , Τ) is spectral data of the multichannel<br />
spectroradiometer at λ 0 nm (that is dimensionless, because<br />
the output data of the spectroradiometer is simply<br />
numerical data), L(λ, Τ) is spectral irradiance of blackbody<br />
whose temperature is Τ at λ nm (whose unit is W m -2 sr -1<br />
nm -1 ) and the function L(λ, Τ) is given by Planck’s law and<br />
S(λ 0 , λ) is spectral radiance responsivity of the<br />
multichannel spectroradiometer (whose unit is sr m 2 W -1 ).<br />
The S(λ 0 , λ) represents bandpass property of the<br />
multichannel spectroradiometer.<br />
The HTBB temperature T is determined from the<br />
CUBB temperature T 0 . Expressing the ratio of HTBB<br />
spectral radiance to CUBB spectral radiance as C λ , the<br />
following equation is derived.<br />
hc / λkT0<br />
L(<br />
λ,<br />
T ) e −1<br />
Cλ<br />
= =<br />
hc / λkT<br />
L(<br />
λ,<br />
T0<br />
) e −1<br />
hc 1<br />
T =<br />
(2)<br />
hc λkT<br />
λk<br />
0<br />
⎛ e −1<br />
⎞<br />
ln<br />
⎜ + 1<br />
⎟<br />
⎝ Cλ<br />
⎠<br />
As mentioned above, the spectral data we can measure<br />
by the multichannel spectroradiometer is shown as (1), and<br />
hence the measurable ratio is not C λ but C M,λ0 that is<br />
expressed as follows.<br />
C<br />
M , λ0<br />
0 ∫<br />
L<br />
=<br />
L<br />
M<br />
M<br />
( λ0<br />
, T )<br />
( λ , T )<br />
0<br />
0<br />
=<br />
∫<br />
∫<br />
L<br />
( λ,<br />
T ) S( λ0<br />
, λ)<br />
( λ,<br />
T ) S( λ , λ)<br />
L<br />
Where L M (λ 0 , Τ) and L M (λ 0 , T 0 ) are the measured spectral<br />
data of HTBB and CUBB respectively.<br />
If spectral radiance of HTBB L(λ, Τ) and CUBB<br />
L(λ, T 0 ) has a similar shape, the influence of the bandpass<br />
property of the multichannel spectroradiometer will be<br />
small and C M,λ0 is almost equal to C λ0. However, the<br />
spectral shape of L(λ, Τ) and L(λ, T 0 ) is considerably<br />
different in shorter wavelength (while the CUBB is<br />
operated copper freezing point 1357.77 K, we operate the<br />
HTBB at about 3000 K); and there is no assurance that the<br />
influence of the bandpass property is negligible.<br />
In order to clarify the relation between C M,λ0 and C λ ,<br />
expanding L(λ, Τ) near λ 0 and introducing new valuable<br />
Λ = λ - λ 0 , the following equation is derived.<br />
0<br />
0<br />
dλ<br />
dλ<br />
(3)<br />
Proceedings NEWRAD, 17-19 October 2005, Davos, Switzerland 281