A series of 26 selenium glass filters with cutoffs uniformly paced over the visible spectrum is used as the basic set of filters to determine the relative spectral sensitivity function of a given photoelectric receiver. Certain characteristics of these filters, such as non-uniformity of transmittance across the filter surface and temperature dependence, impair the precision of the transmittance measurements as well as photocell-response measurements. Nevertheless it is possible to derive fairly well-conditioned matrices of difference functions obtained from the basic set of cutoff filters, which will allow a satisfactory determination of a spectral sensitivity function. Experimental as well as numerical implications are discussed in detail on the basis of a practical example.
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All filters but No. 3 are from Tokyo Shibura Company, Tokyo, Japan. No. 3 is a Schott glass.
Corning filters. The number following solidus ( / ) gives thickness in mm.
Schott filter. The number following( / ) gives thickness in mm.
Table II
Location of central wavelength λj and corresponding width of wavelength band Δλi.
T8
T14
T23
j
λj
Δλj
j
λj
Δλi
j
λj
Δj
j
λj
Δλj
1
407
38
1
410
20
1
406
32
13
549
10
2
445
38
2
430
20
2
429
14
14
560
12
3
483
38
3
450
20
3
441
10
15
572
12
4
521
38
4
470
20
4
451
10
16
585
14
5
559
38
5
490
20
5
461
10
17
598
12
6
597
38
6
510
20
6
471
10
18
609
10
7
635
38
7
530
20
7
481
10
19
619
10
8
673
38
8
550
20
8
490
10
20
631
14
9
570
20
9
500
12
21
645
14
10
590
20
10
513
12
22
660
18
11
610
20
11
526
12
23
685
30
12
630
20
12
538
12
13
650
20
14
670
20
Table III
Errors ∊(Pj)(14) (in percent) as a function of ∊(ΔRi)=+5%.a The errors ∊(ΔRi) were introduced one at a time.
j
1
2
3
4
5
6
7
8
9
10
11
12
13
14
i
1
9.7
−1.4
2
−4.4
8.1
−0.2
3
−2.0
6.1
4
−0.5
0.7
−2.2
8.6
0.1
5
0.2
−0.3
1.0
−3.3
6.5
−0.8
0.1
6
0.3
−2.2
8.0
−1.4
0.1
7
0.2
−0.5
0.6
−2.4
7.4
−0.6
8
−0.1
−0.1
0.3
−1.4
6.8
−0.7
0.2
9
−0.1
−0.1
0.3
−1.6
7.2
−2.7
0.3
−0.1
10
0.4
−1.0
9.9
−1.1
0.2
−0.1
11
−0.1
0.3
−2.0
6.7
−1.5
0.7
12
−0.1
−1.0
8.3
−4.5
0.1
13
−0.3
0.2
−2.1
10.1
14
−0.1
0.1
−1.3
4.9
Empty spaces denote zeros or near zeros.
Table IV
Average errors
(Pj) (in percent) for j=i, j=i+1, and j=i−1 as a function of ∊(ΔRi)=+5%. The errors ∊(ΔRi) were introduced one at a time.
Matrix
(Pj) j=i
(Pj) j=i+1
(Pj) j=i−1
T8
5.7
0.1
0.9
T14
7.7
1.1
2.1
T23
15.4
6.1
8.6
Table V
Errors ∊[Pj(14)] (in percent) as a function of ∊(τij)=−5%. Only errors of diagonal elements (i=j) were introduced one at a time.a
j
1
2
3
4
5
6
7
8
9
10
11
12
13
14
i
1
5.4
−0.8
2
−3.0
3.0
−0.1
3
−0.1
−1.6
5.1
4
0.3
−0.5
1.4
−5.1
5
0.1
−0.2
0.8
−2.4
5.1
−0.6
0.1
6
0.1
0.2
−1.5
5.5
−1.0
0.1
7
0.1
−0.4
−0.5
−1.8
5.4
−0.4
8
−0.1
0.2
−1.1
5.2
−0.5
0.2
9
−0.1
0.3
−1.2
5.5
−2.1
0.2
10
0.2
−1.1
5.6
−0.6
0.1
−0.1
11
0.2
−1.6
5.3
−1.2
0.6
12
−0.1
−0.7
5.8
−3.2
0.1
13
−0.2
0.1
1.2
5.6
14
−0.1
0.1
−1.3
5.0
Empty spaces denote zeros or near zeros.
Table VI
Average errors
(Pj) (in percent) for j=i, j=i+1, and j=i−1 as a function of ∊(ij)=−5%. Only errors of diagonal elements (i=j) were introduced one at a time.
Matrix
(Pj) j=i
(Pj) j=i+1
(Pj) j=i−1
T8
5.0
0.1
0.8
T14
5.2
0.8
1.5
T23
7.7
3.2
4.3
Tables (6)
Table I
Specifications of cutoff filters, auxiliary filters, and filter combinations.
All filters but No. 3 are from Tokyo Shibura Company, Tokyo, Japan. No. 3 is a Schott glass.
Corning filters. The number following solidus ( / ) gives thickness in mm.
Schott filter. The number following( / ) gives thickness in mm.
Table II
Location of central wavelength λj and corresponding width of wavelength band Δλi.
T8
T14
T23
j
λj
Δλj
j
λj
Δλi
j
λj
Δj
j
λj
Δλj
1
407
38
1
410
20
1
406
32
13
549
10
2
445
38
2
430
20
2
429
14
14
560
12
3
483
38
3
450
20
3
441
10
15
572
12
4
521
38
4
470
20
4
451
10
16
585
14
5
559
38
5
490
20
5
461
10
17
598
12
6
597
38
6
510
20
6
471
10
18
609
10
7
635
38
7
530
20
7
481
10
19
619
10
8
673
38
8
550
20
8
490
10
20
631
14
9
570
20
9
500
12
21
645
14
10
590
20
10
513
12
22
660
18
11
610
20
11
526
12
23
685
30
12
630
20
12
538
12
13
650
20
14
670
20
Table III
Errors ∊(Pj)(14) (in percent) as a function of ∊(ΔRi)=+5%.a The errors ∊(ΔRi) were introduced one at a time.
j
1
2
3
4
5
6
7
8
9
10
11
12
13
14
i
1
9.7
−1.4
2
−4.4
8.1
−0.2
3
−2.0
6.1
4
−0.5
0.7
−2.2
8.6
0.1
5
0.2
−0.3
1.0
−3.3
6.5
−0.8
0.1
6
0.3
−2.2
8.0
−1.4
0.1
7
0.2
−0.5
0.6
−2.4
7.4
−0.6
8
−0.1
−0.1
0.3
−1.4
6.8
−0.7
0.2
9
−0.1
−0.1
0.3
−1.6
7.2
−2.7
0.3
−0.1
10
0.4
−1.0
9.9
−1.1
0.2
−0.1
11
−0.1
0.3
−2.0
6.7
−1.5
0.7
12
−0.1
−1.0
8.3
−4.5
0.1
13
−0.3
0.2
−2.1
10.1
14
−0.1
0.1
−1.3
4.9
Empty spaces denote zeros or near zeros.
Table IV
Average errors
(Pj) (in percent) for j=i, j=i+1, and j=i−1 as a function of ∊(ΔRi)=+5%. The errors ∊(ΔRi) were introduced one at a time.
Matrix
(Pj) j=i
(Pj) j=i+1
(Pj) j=i−1
T8
5.7
0.1
0.9
T14
7.7
1.1
2.1
T23
15.4
6.1
8.6
Table V
Errors ∊[Pj(14)] (in percent) as a function of ∊(τij)=−5%. Only errors of diagonal elements (i=j) were introduced one at a time.a
j
1
2
3
4
5
6
7
8
9
10
11
12
13
14
i
1
5.4
−0.8
2
−3.0
3.0
−0.1
3
−0.1
−1.6
5.1
4
0.3
−0.5
1.4
−5.1
5
0.1
−0.2
0.8
−2.4
5.1
−0.6
0.1
6
0.1
0.2
−1.5
5.5
−1.0
0.1
7
0.1
−0.4
−0.5
−1.8
5.4
−0.4
8
−0.1
0.2
−1.1
5.2
−0.5
0.2
9
−0.1
0.3
−1.2
5.5
−2.1
0.2
10
0.2
−1.1
5.6
−0.6
0.1
−0.1
11
0.2
−1.6
5.3
−1.2
0.6
12
−0.1
−0.7
5.8
−3.2
0.1
13
−0.2
0.1
1.2
5.6
14
−0.1
0.1
−1.3
5.0
Empty spaces denote zeros or near zeros.
Table VI
Average errors
(Pj) (in percent) for j=i, j=i+1, and j=i−1 as a function of ∊(ij)=−5%. Only errors of diagonal elements (i=j) were introduced one at a time.