Transmittance measurements for filters of optical density between one and ten

Z. M. Zhang; T. R. Gentile; A. L. Migdall; R. U. Datla

doi:10.1364/AO.36.008889

Transmittance measurements for filters of optical density between one and ten

Z. M. Zhang, T. R. Gentile, A. L. Migdall, and R. U. Datla

Applied Optics
Vol. 36,
Issue 34,
pp. 8889-8895
(1997)
•https://doi.org/10.1364/AO.36.008889

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Z. M. Zhang, T. R. Gentile, A. L. Migdall, and R. U. Datla, "Transmittance measurements for filters of optical density between one and ten," Appl. Opt. 36, 8889-8895 (1997)

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History
- Original Manuscript: March 5, 1997
- Revised Manuscript: June 16, 1997
- Published: December 1, 1997

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Abstract

We have developed a facility for measuring the transmittance of optical filters at a wavelength of 1064 nm, using a Nd:YAG laser, a power stabilizer, and linear photodiode detectors. A direct measurement method was used for filters with optical densities (OD’s) less than or equal to 4, and a reference substitution technique was used for filters with OD’s as great as 10. The apparatus and data-acquisition system are described. Measurement results for a set of filters are presented. The expanded uncertainties for the measured OD and deduced absorption coefficient are determined through a detailed analysis of all the uncertainty components.

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Nominal OD	Repeatability σ_repeat	Temperature Variation σ_temp	Reference σ_ref	Combined Standard Uncertainty σ_comb	Expanded Uncertainty 2σ_comb
1	0.00006	0.00007	NA	0.0041	0.0008
2	0.00006	0.00015	NA	0.00043	0.0009
3	0.00020	0.00022	NA	0.00050	0.0010
4	0.00067	0.00030	NA	0.00084	0.0017
5	0.00020	0.00038	0.00050	0.00077	0.0015
6	0.00020	0.00045	0.00050	0.00081	0.0016
7	0.00100	0.00053	0.00050	0.00130	0.0026
8	0.00100	0.00060	0.00084	0.00149	0.0030
9	0.00100	0.00067	0.00149	0.00197	0.0039
10	0.00600	0.00075	0.00149	0.00624	0.0125

Filter No.	d (mm)	Filter Temp. (°C)	σ_spatial	σ_interf	Optical Density OD ± ΔOD	Absorption Coefficient a ± Δa (mm^-1)
10-01	1.044	24.7	0.00129	0.0016	1.0111 ± 0.0042	2.1518 ± 0.0113
22-01	2.177	25.4	0.00065	0.0001	2.0785 ± 0.0016	2.1609 ± 0.0035
32-01	3.157	23.8	0.00021	NA	2.9931 ± 0.0011	2.1572 ± 0.0023
42-01	4.194	24.1	0.00072	NA	3.9679 ± 0.0022	2.1590 ± 0.0020
54-01	5.410	25.1	0.00026	NA	5.1140 ± 0.0016	2.1615 ± 0.0014
64-01	6.391	25.3	0.00023	NA	6.0325 ± 0.0017	2.1606 ± 0.0012
75-01	7.526	24.8	0.00160	NA	7.1015 ± 0.0041	2.1619 ± 0.0015
84-01	8.418	25.2	0.00960	NA	8.1084 ± 0.019	2.2082 ± 0.0054
94-01	9.413	24.9	0.00200	NA	9.1038 ± 0.0056	2.2183 ± 0.0016
105-01	10.549	24.7	0.00900	NA	10.1885 ± 0.022	2.2162 ± 0.0048

Nominal OD	Repeatability σ_repeat	Temperature Variation σ_temp	Reference σ_ref	Combined Standard Uncertainty σ_comb	Expanded Uncertainty 2σ_comb
1	0.00006	0.00007	NA	0.0041	0.0008
2	0.00006	0.00015	NA	0.00043	0.0009
3	0.00020	0.00022	NA	0.00050	0.0010
4	0.00067	0.00030	NA	0.00084	0.0017
5	0.00020	0.00038	0.00050	0.00077	0.0015
6	0.00020	0.00045	0.00050	0.00081	0.0016
7	0.00100	0.00053	0.00050	0.00130	0.0026
8	0.00100	0.00060	0.00084	0.00149	0.0030
9	0.00100	0.00067	0.00149	0.00197	0.0039
10	0.00600	0.00075	0.00149	0.00624	0.0125

Filter No.	d (mm)	Filter Temp. (°C)	σ_spatial	σ_interf	Optical Density OD ± ΔOD	Absorption Coefficient a ± Δa (mm^-1)
10-01	1.044	24.7	0.00129	0.0016	1.0111 ± 0.0042	2.1518 ± 0.0113
22-01	2.177	25.4	0.00065	0.0001	2.0785 ± 0.0016	2.1609 ± 0.0035
32-01	3.157	23.8	0.00021	NA	2.9931 ± 0.0011	2.1572 ± 0.0023
42-01	4.194	24.1	0.00072	NA	3.9679 ± 0.0022	2.1590 ± 0.0020
54-01	5.410	25.1	0.00026	NA	5.1140 ± 0.0016	2.1615 ± 0.0014
64-01	6.391	25.3	0.00023	NA	6.0325 ± 0.0017	2.1606 ± 0.0012
75-01	7.526	24.8	0.00160	NA	7.1015 ± 0.0041	2.1619 ± 0.0015
84-01	8.418	25.2	0.00960	NA	8.1084 ± 0.019	2.2082 ± 0.0054
94-01	9.413	24.9	0.00200	NA	9.1038 ± 0.0056	2.2183 ± 0.0016
105-01	10.549	24.7	0.00900	NA	10.1885 ± 0.022	2.2162 ± 0.0048

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