Design of Glass Filter Combinations for Photometers

H. Wright; C. L. Sanders; D. Gignac

doi:10.1364/AO.8.002449

Applied Optics
Vol. 8,
Issue 12,
pp. 2449-2455
(1969)
•https://doi.org/10.1364/AO.8.002449

Design of Glass Filter Combinations for Photometers

H. Wright, C. L. Sanders, and D. Gignac

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H. Wright, C. L. Sanders, and D. Gignac, "Design of Glass Filter Combinations for Photometers," Appl. Opt. 8, 2449-2455 (1969)

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Abstract

Two nonlinear curve-fitting computer programs have been developed for designing subtractive glass filter combinations for use in photoelectric photometers. One program adjusts the filter thicknesses to minimize the sum of squares of errors at each wavelength and is thus useful in designing a general purpose instrument. The second program minimizes the errors in the photometric measurements of preselected light sources. Filters for correcting various photoelectric detectors to the CIE luminous efficiency function are specified. Several spectral response functions have been utilized including S-4, S-10, S-11, S-20 types, and those of typical silicon diodes, and selenium cells. Practical photometer designs with predicted measurement errors of less than 0.1% are presented.

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λ (nm)	Transmittance of filter combination	Modified spectral response of detector	V(λ) function	Deviation
380	0.0016	0.0060	0.0	−0.0060
90	0.0010	0.0044	0.0001	−0.0043
400	0.0005	0.0024	0.0004	−0.0020
10	0.0003	0.0013	0.0012	−0.0001
20	0.0003	0.0016	0.0040	0.0024
30	0.0007	0.0033	0.0116	0.0083
40	0.0019	0.0099	0.0230	0.0131
450	0.0056	0.0289	0.0380	0.0091
60	0.0093	0.0490	0.0600	0.0110
70	0.0193	0.1009	0.0910	−0.0099
80	0.0287	0.1498	0.1390	−0.0108
90	0.0413	0.2151	0.2080	−0.0071
500	0.0621	0.3217	0.3230	0.0013
10	0.0961	0.4940	0.5030	0.0090
20	0.1417	0.7133	0.7100	−0.0033
30	0.1754	0.8581	0.8620	0.0039
40	0.2004	0.9479	0.9540	0.0061
550	0.2194	0.9978	0.9950	−0.0028
60	0.2301	1.0027	0.9950	−0.0077
70	0.2339	0.9447	0.9520	0.0073
80	0.2247	0.8789	0.8700	−0.0089
90	0.2063	0.7628	0.7570	−0.0058
600	0.1837	0.6311	0.6310	−0.0001
10	0.1567	0.4957	0.5030	0.0073
20	0.1277	0.3664	0.3810	0.0146
30	0.1016	0.2611	0.2650	0.0039
40	0.0773	0.1751	0.1750	−0.0001
650	0.0576	0.1165	0.1070	−0.0095
60	0.0411	0.0713	0.0610	−0.0103
70	0.0290	0.0421	0.0320	−0.0101
80	0.0192	0.0229	0.0170	−0.0059
90	0.0122	0.0115	0.0082	−0.0033
700	0.0077	0.0055	0.0041	−0.0014
10	0.0048	0.0026	0.0021	−0.0005
20	0.0028	0.0011	0.0010	−0.0001
30	0.0016	0.0004	0.0005	0.0001
40	0.0010	0.0002	0.0002	0.0000
750	0.0005	0.0001	0.0001	0.0000
60	0.0003	0.0000	0.0001	0.0001
70	0.0002	0.0000	0.0	0.0000

Source No. K	Source type	Method

		Minimization of spectral errors S(K)	Minimization of photometric errors S(K)
		%	%
1	BB 2042 K	0.000	0.000
2	BB 2360 K	0.188	−0.015
3	BB 2854 K	0.366	−0.034
4	CIE Source C	0.772	−0.017
5	Fluorescent 3100 K	0.874	−0.022
6	Fluorescent 4400 K	0.934	−0.001
7	Fluorescent 7000 K	1.097	−0.008

λ (nm)	Transmittance of filter combination	Modified spectral response of detector	V(λ)	Deviation
380	0.0045	0.0110	0.0	−0.0110
90	0.0019	0.0056	0.0001	−0.0055
400	0.0007	0.0020	0.0004	−0.0016
10	0.0003	0.0009	0.0012	0.0003
20	0.0003	0.0010	0.0040	0.0030
30	0.0008	0.0026	0.0116	0.0090
40	0.0029	0.0095	0.0230	0.0135
450	0.0096	0.0322	0.0380	0.0058
60	0.0156	0.0529	0.0600	0.0071
70	0.0332	0.1126	0.0910	−0.0216
80	0.0454	0.1535	0.1390	−0.0145
90	0.0617	0.2086	0.2080	−0.0006
500	0.0906	0.3041	0.3230	0.0189
10	0.1452	0.4834	0.5030	0.0196
20	0.2213	0.7220	0.7100	−0.0120
30	0.2741	0.8691	0.8620	−0.0071
40	0 3135	0.9609	0.9540	−0.0079
550	0.3425	1.0091	0.9950	−0.0141
60	0.3563	1.0060	0.9950	−0.0110
70	0.3611	0.9447	0.9520	0.0073
80	0.3459	0.8768	0.8700	−0.0068
90	0.3185	0.7631	0.7570	−0.0061
600	0.2838	0.6316	0.6310	−0.0006
10	0.2413	0.4944	0.5030	0.0086
20	0.1950	0.3625	0.3810	0.0185
30	0.1542	0.2568	0.2650	0.0082
40	0.1156	0.1697	0.1750	0.0053
650	0.0839	0.1101	0.1070	−0.0031
60	0.0579	0.0651	0.0610	−0.0041
70	0.0392	0.0369	0.0320	−0.0049
80	0.0249	0.0193	0.0170	−0.0023
90	0.0153	0.0094	0.0082	−0.0012
700	0.0091	0.0043	0.0041	−0.0002
10	0.0053	0.0019	0.0021	0.0002
20	0.0030	0.0008	0.0010	0.0002
30	0.0017	0.0003	0.0005	0.0002
40	0.0009	0.0001	0.0002	0.0001
750	0.0005	0.0000	0.0001	0.0001
60	0.0003	0.0000	0.0001	0.0001
70	0.0002	0.0000	0.0	−0.0000

Detector and S-type		Number of filters for best combination	Sum of squares Q	Sum of squares of photometric errors PES	Maximum photometric error S(K)
1	RCA6217	4	0.0022	1.65	1.20
1	S-10	4	0.0045	0.0007	0.030
2	RCA6217	4	0.0033	6.59	2.44
2	S-10	4	0.0062	0.0040	0.050
3	RCA1P21	4	0.0119	1.77	1.14
3	S-4	3	0.0420	0.0047	0.070
4	EMI9588	4	0.0021	1.71	1.25
4	S-20	4	0.0047	0.0009	0.034
5	Barrier-	4	0.0025	2.31	0.302
5	layer cell	3	0.0054	0.0090	0.113
6	Silicon	5	0.0048	2.93	1.71
6	diode	4	0.0078	0.0016	0.052
7	EMI9524	4	0.0449	55.45	6.57
7	S-11	3	0.0763	0.4659	0.600
8	Gillod Boutry cell,	4	0.0017	1.63	1.17
8	Ag-Bi-O-Cs	4	0.0026	0.0007	0.031
9	Rank Cintell	4	0.0018	1.26	1.10
9	VB 59, Ag-Bi-O-Cs	4	0.0032	0.0009	0.034

λ (nm)	Transmittance of filter combination	Modified spectral response of detector	V(λ) function	Deviation
380	0.0016	0.0060	0.0	−0.0060
90	0.0010	0.0044	0.0001	−0.0043
400	0.0005	0.0024	0.0004	−0.0020
10	0.0003	0.0013	0.0012	−0.0001
20	0.0003	0.0016	0.0040	0.0024
30	0.0007	0.0033	0.0116	0.0083
40	0.0019	0.0099	0.0230	0.0131
450	0.0056	0.0289	0.0380	0.0091
60	0.0093	0.0490	0.0600	0.0110
70	0.0193	0.1009	0.0910	−0.0099
80	0.0287	0.1498	0.1390	−0.0108
90	0.0413	0.2151	0.2080	−0.0071
500	0.0621	0.3217	0.3230	0.0013
10	0.0961	0.4940	0.5030	0.0090
20	0.1417	0.7133	0.7100	−0.0033
30	0.1754	0.8581	0.8620	0.0039
40	0.2004	0.9479	0.9540	0.0061
550	0.2194	0.9978	0.9950	−0.0028
60	0.2301	1.0027	0.9950	−0.0077
70	0.2339	0.9447	0.9520	0.0073
80	0.2247	0.8789	0.8700	−0.0089
90	0.2063	0.7628	0.7570	−0.0058
600	0.1837	0.6311	0.6310	−0.0001
10	0.1567	0.4957	0.5030	0.0073
20	0.1277	0.3664	0.3810	0.0146
30	0.1016	0.2611	0.2650	0.0039
40	0.0773	0.1751	0.1750	−0.0001
650	0.0576	0.1165	0.1070	−0.0095
60	0.0411	0.0713	0.0610	−0.0103
70	0.0290	0.0421	0.0320	−0.0101
80	0.0192	0.0229	0.0170	−0.0059
90	0.0122	0.0115	0.0082	−0.0033
700	0.0077	0.0055	0.0041	−0.0014
10	0.0048	0.0026	0.0021	−0.0005
20	0.0028	0.0011	0.0010	−0.0001
30	0.0016	0.0004	0.0005	0.0001
40	0.0010	0.0002	0.0002	0.0000
750	0.0005	0.0001	0.0001	0.0000
60	0.0003	0.0000	0.0001	0.0001
70	0.0002	0.0000	0.0	0.0000

Abstract

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Figures (7)

Tables (4)

Equations (6)

Applied Optics