Approximation of a melting plateau of large area HTFP cells used for
spectral irradiance realization

Yihang Xie; Caihong Dai; Yanfei Wang; Zhifeng Wu; Ling Li; Boris Khlevnoy; Boris Khlevnoy; Boris Khlevnoy; Irina Grigoryeva; Shufang He; Yandong Lin

doi:10.1364/AO.409631

Applied Optics
Vol. 60,
Issue 7,
pp. 1827-1833
(2021)
•https://doi.org/10.1364/AO.409631

Approximation of a melting plateau of large area HTFP cells used for spectral irradiance realization

Yihang Xie, Caihong Dai, Yanfei Wang, Zhifeng Wu, Ling Li, Boris Khlevnoy, Irina Grigoryeva, Shufang He, and Yandong Lin

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Yihang Xie, Caihong Dai, Yanfei Wang, Zhifeng Wu, Ling Li, Boris Khlevnoy, Irina Grigoryeva, Shufang He, and Yandong Lin, "Approximation of a melting plateau of large area HTFP cells used for spectral irradiance realization," Appl. Opt. 60, 1827-1833 (2021)

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Abstract

This paper adopted an approximation of a melting plateau to solve the problem that temperature data cannot be monitored continuously when measuring the spectral irradiance of a large area tungsten carbide–carbon high-temperature fixed-point blackbody at each measured wavelength. Tests with fully measured curves showed that the method has a rather small deviation from the measured data of 0.017 K maximum, which corresponds to the spectral irradiance deviation of 0.005% at 500 nm. The maximum relative deviation between the Akima fitting method and the measured temperature in terms of spectral irradiance was 0.002%, which was better than ${-}{0.067}\%$ of a single temperature of 3020.11 K method and 0.026% of a linear interpolation method.

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Plateau #,	K	Akima interpolation	Linear interpolation	Assumed single temperature of 3020.11 K	Spline interpolation	Bessel interpolation	B-spline interpolation	M-Akima interpolation
Cycle 1	MD	0.016	0.126	0.488	0.020	0.141	0.067	0.081
Cycle 1	RMSE	0.008	0.088	0.195	0.011	0.092	0.045	0.056
Cycle 2	MD	0.019	0.110	0.487	0.023	0.124	0.016	0.058
Cycle 2	RMSE	0.012	0.078	0.206	0.015	0.082	0.010	0.039
Cycle 3	MD	0.015	0.133	0.509	0.021	0.148	0.051	0.085
Cycle 3	RMSE	0.007	0.093	0.204	0.011	0.098	0.029	0.059
Average	MD	0.017	0.123	0.495	0.021	0.138	0.045	0.075
Average	RMSE	0.009	0.086	0.201	0.012	0.091	0.028	0.051

Plateau #, K	Akima interpolation	Linear interpolation	Assumed single temperature of 3020.11 K	Spline interpolation	Bessel interpolation	B-spline interpolation	M-Akima interpolation
C 1	0.003	0.115	\	0.007	0.183	0.088	0.117
C 2	0.011	0.035	\	0.019	0.249	0.043	0.033
C 3	0.001	0.111	\	0.011	0.196	0.001	0.111
Average	0.005	0.087	\	0.012	0.209	0.044	0.087

	Spectral irradiance of the large area WC-C HTFP blackbody, $µ W {c m}^{- 2} {n m}^{- 1}$				Relative deviation from the actual temperature
Wavelength, nm	Actual temperature	Temperature fitted by the Akima fitting method	Assumed constant temperature of 3020.11 K	Temperature fitted by the linear interpolation	Temperature fitted by the Akima fitting method	Assumed constant temperature of 3020.11 K	Temperature fitted by the linear interpolation
390	3.4057 E-01	3.4057 E-01	3.4065 E-01	3.4059 E-01	0.001%	0.022%	0.006%
400	4.0727 E-01	4.0728 E-01	4.0734 E-01	4.0730 E-01	0.002%	0.016%	0.007%
450	8.4900 E-01	8.4901 E-01	8.4903 E-01	8.4911 E-01	0.001%	0.004%	0.013%
500	$1.4453 E + 00$	$1.4453 E + 00$	$1.4452 E + 00$	$1.4456 E + 00$	0.002%	−0.004%	0.019%
550	$2.1343 E + 00$	$2.1343 E + 00$	$2.1340 E + 00$	$2.1348 E + 00$	0.001%	−0.012%	0.024%
600	$2.8439 E + 00$	$2.8439 E + 00$	$2.8433 E + 00$	$2.8446 E + 00$	0.000%	−0.020%	0.025%
650	$3.5117 E + 00$	$3.5117 E + 00$	$3.5108 E + 00$	$3.5126 E + 00$	0.000%	−0.028%	0.026%
700	$4.0944 E + 00$	$4.0944 E + 00$	$4.0929 E + 00$	$4.0954 E + 00$	0.000%	−0.036%	0.025%
800	$4.9248 E + 00$	$4.9247 E + 00$	$4.9225 E + 00$	$4.9256 E + 00$	0.000%	−0.045%	0.018%
900	$5.3099 E + 00$	$5.3099 E + 00$	$5.3070 E + 00$	$5.3105 E + 00$	0.000%	−0.055%	0.012%
1000	$5.3429 E + 00$	$5.3429 E + 00$	$5.3393 E + 00$	$5.3430 E + 00$	0.001%	−0.067%	0.003%

Plateau #,	K	Akima interpolation	Linear interpolation	Assumed single temperature of 3020.11 K	Spline interpolation	Bessel interpolation	B-spline interpolation	M-Akima interpolation
Cycle 1	MD	0.016	0.126	0.488	0.020	0.141	0.067	0.081
Cycle 1	RMSE	0.008	0.088	0.195	0.011	0.092	0.045	0.056
Cycle 2	MD	0.019	0.110	0.487	0.023	0.124	0.016	0.058
Cycle 2	RMSE	0.012	0.078	0.206	0.015	0.082	0.010	0.039
Cycle 3	MD	0.015	0.133	0.509	0.021	0.148	0.051	0.085
Cycle 3	RMSE	0.007	0.093	0.204	0.011	0.098	0.029	0.059
Average	MD	0.017	0.123	0.495	0.021	0.138	0.045	0.075
Average	RMSE	0.009	0.086	0.201	0.012	0.091	0.028	0.051

Plateau #, K	Akima interpolation	Linear interpolation	Assumed single temperature of 3020.11 K	Spline interpolation	Bessel interpolation	B-spline interpolation	M-Akima interpolation
C 1	0.003	0.115	\	0.007	0.183	0.088	0.117
C 2	0.011	0.035	\	0.019	0.249	0.043	0.033
C 3	0.001	0.111	\	0.011	0.196	0.001	0.111
Average	0.005	0.087	\	0.012	0.209	0.044	0.087

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Applied Optics