Polynomial Representation of Transmittance Models

Joseph H. Pierluissi

doi:10.1364/AO.12.000776

Applied Optics
Vol. 12,
Issue 4,
pp. 776-778
(1973)
•https://doi.org/10.1364/AO.12.000776

Polynomial Representation of Transmittance Models

Joseph H. Pierluissi

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Joseph H. Pierluissi, "Polynomial Representation of Transmittance Models," Appl. Opt. 12, 776-778 (1973)

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Abstract

A quadratic formula that accurately represents general absorptance is both developed for 5 cm⁻¹ data on the 4ν₂ + ν₃ band of CO₂ centered at 4853.58cm⁻¹ and generalized to a polynomial function of the weak- and strong-line limits of known models.

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Wavenumber Interval (cm⁻¹)						Mean Absolute Deviation of Models (X103)
	Coefficients of Five-Parameter Formula					Five parameter	Zachor	Modified Mayer-Goody	Modified Elsasser	Mayer-Goody
	n	C	B_W	B_S	B_WS	Five parameter	Zachor	Modified Mayer-Goody	Modified Elsasser	Mayer-Goody
4795.0–4800.0	0.784	6.2165-04	4.4765+06	0.792	−4.8265+02	8.32	9.37	12.37	12.86	17.95
4800.0–4805.0	0.835	5.8545-04	7.7505+06	0.820	7.0695+01	6.60	7.49	13.26	12.12	16.85
4805.0–4810.0	1.137	5.7105-04	1.1355+07	0.641	−1.5105+03	6.32	8.71	14.36	18.10	11.79
4810.0–4815.0	0.917	8.9855-04	3.0295+06	0.808	−6.0225+02	4.15	6.82	7.49	15.15	9.00
4815.0–4820.0	0.881	1.1155-03	7.8025+05	0.800	−1.2035+02	6.55	11.00	14.13	16.02	18.42
4820.0–4825.0	0.855	1.5085-03	2.8715+05	0.823	−2.0535+02	4.82	9.90	10.40	16.86	13.85
4825.0–4830.0	0.785	1.2855-03	1.3975+05	0.863	−1.9555+02	7.30	10.23	10.17	15.65	15.59
4830.0–4836.4	0.681	1.7665-03	6.1535+04	0.840	−1.8875+02	9.83	12.19	12.45	15.74	18.45
4836.4–4841.5	0.559	1.5815-03	4.6615+04	0.901	−6.5245+01	10.88	11.41	11.42	12.18	24.50
4841.5–4846.4	0.554	1.4845-03	5.7845+04	0.941	−4.6805+00	9.50	9.86	9.93	10.57	25.10
4846.4–4851.2	0.668	1.2065-03	1.4775+05	0.937	−3.0795+01	7.56	7.94	8.69	10.01	18.29
4851.2–4856.7	0.611	4.7085-04	5.9695+05	0.710	−9.9825+02	5.82	12.17	11.58	11.87	24.93
4856.7–4861.2	0.603	1.5825-03	8.1545+04	0.935	−3.8135+01	8.78	9.17	9.32	11.10	23.79
4861.2–4866.2	0.562	2.2345-03	3.5095+04	0.944	7.8735+00	8.06	8.38	8.88	10.44	22.82
4866.2–4871.1	0.626	2.4735-03	3.3955+04	0.982	2.5805+01	8.06	7.96	8.51	9.29	24.79
4871.1-4876.4	0.803	2.6615-03	5.8865+04	0.992	2.7555+01	10.11	9.96	10.06	12.89	17.44
4876.4–4881.3	0.798	1.70022-03	1.5315+05	0.874	−1.6375+02	7.52	8.25	8.42	12.72	13.71
4881.3–4886.0	0.828	8.6035-04	8.1005+05	0.729	−4.6735+02	6.49	13.24	14.83	15.41	19.87
4886.0–4890.4	0.834	5.6915-04	5.5355+06	0.825	−7.8415+02	5.94	6.54	8.11	13.95	10.81
4890.4-4894.8	0.845	4.9075-04	1.2605+07	0.804	3.4075+02	4.79	5.07	13.59	12.36	17.28
4894.8–4900.3	0.862	3.6815-04	1.2355+07	0.786	−8.4745+02	5.85	6.51	9.80	11.46	13.09
4900.3–4905.2	0.869	3.2805-04	1.3055+07	0.642	−2.5195+03	5.94	7.91	10.23	12.05	13.13
					Mean	7.24	9.09	10.82	13.13	17.79

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Applied Optics