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