Irwin G. Priest, H. J. McNicholas, and M. Katherine Frehafer, "Some Tests of the Precision and Reliability of Measurements of Spectral Transmission by the Koenig-Martens Spectrophotometer1," J. Opt. Soc. Am. 8, 201-212 (1924)
The Koenig-Martens spectrophotometer as installed and used at the Bureau of Standards has been tested by measuring the transmissions of rotating sectored disks of known angular aperture. Measurements of the spectral transmission of blue filters by different observers have also been compared. The photometric probable error at various wave-lengths has been computed from the observations of three different observers.
From the data, which are presented in considerable detail in tables and graphs, the following conclusions are drawn:
1. For heterogeneous illumination, the probable error of a single observation (involving one reading each of θ1 and θ2) is about seven tenths of one percent of the transmission when measurements are made at the field brightness most favorable to accurate matching.
2. For homogeneous illumination the probable error of a single observation of transmission 0.37 is nearly constant and equal to about one percent of the transmission in the case of the following wave-lengths of mercury and helium: mercury, 435.8, 546.1 mμ; helium, 447.2, 492.2, 501.6, 667.8, 706.5 mμ.
3. For heterogeneous illumination, the actual error2 of the mean of ten observations for transmissions even as low as 0.015 and for wave-lengths between 430 and 700 mμ is usually less than one percent of the transmission, provided the transmission is not changing rapidly with wave-length.
4. There is no systematic error of measured transmission with respect to wave-length.
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B. S. Sectored Disk #8 (Six Slots)True Transmissions from Angular Calibration by B. S. Div. of Weights and MeasuresSlots 1 + 3 + 5 = 0.0078Slots 3 + 4 + 6 = 0.0076Total Transmission of Disc = 0.0154 ± .0002
Wave Length in millimicrons
Transmissions measured on Spectrophotometer
T
T
T
for slots 1 + 3 + 5 by M. K. F.
for slots 2 + 4+ 6 by M. K. F.
for 6 slots by R. H. S.
435.8
.00775
.00759
.01518
546.1
.00772
.00766
.01523
578.0
.01510
587.6
.00776
.00749
650.0
.00772
.00749
.01525
Table 2
Sectored Disk, B. S. 30547True transmission = 0.1009 from Angular Calibration by B. S. Division of Weights and Measures
Wave Length in millimicrons
T by I. G. P.
520
0.1006
0.1007
580
0.1002
600
0.1009
0.1009
620
0.1008
0.0996
Table 3
Sectored Disk, B. S. No. 22143 B, 4 and 3Td = 0.1029Heterogeneous Illumination
Observer
I. G. P.
H. J. M.
Wave-length in mμ
Collimator Slit Width
Ocular Slit Width
Tm
Tm
mechanical
spectral
Mechanical
spectral
in mm
in mμ
in mm
in mμ
430
0.5
3.8
0.3
2.3
0.1027
−0.002
±0.019
.1045
+.016
.016
460
0.3
3.1
0.2
2.1
.1028
−0.001
±.0076
.1016
−.013
.0096
490
0.1
1.3
0.2
2.6
.1020
−.009
.0043
520
0.1
1.7
0.2
3.4
.1021
−0.008
0.0038
.1034
+.005
.0032
.1041
+0.012
0.0023
560
0.1
2.2
0.2
4.4
.1033
+.004
.0024
600
0.1
2.8
0.2
5.6
.1036
+.007
.0030
640
0.1
3.5
0.2
7.0
.1035
+.006
.0036
660
0.2
3.8
0.2
3.8
.1029
.000
.0047
700
0.3
13.8
0.2
9.2
.1046
+.017
.0075
0.5
23.0
0.2
9.2
.1042
+0.013
0.0051
0.5
23.0
0.2
9.2
.1025
−0.004
0.0071
Alg. mean
+0.005
+0.002
Td is true transmission of the disk from angular calibration by B. S. Division of Weights and Measures.
Td is the true transmission of the disk from angular calibration, by B. S. Division of Weights and Measures.
Table 5
Ives-Brady Daylight Glass (Submitted by E. J. Brady, letter of Dec. 2. 1921)Particular care was taken always to use same part of specimen (see Fig. 1).Each tabulated value of transmission (T) is the mean of ten observations. The probable errors (P.E.)T are the probable errors of these means as derived from the ten residuals of θ1 and θ2 (see appendix) by propagation of error formulas.
Homogeneous Light
Red filter used over ocular to eliminate stray light
Tables (5)
Table 1
B. S. Sectored Disk #8 (Six Slots)True Transmissions from Angular Calibration by B. S. Div. of Weights and MeasuresSlots 1 + 3 + 5 = 0.0078Slots 3 + 4 + 6 = 0.0076Total Transmission of Disc = 0.0154 ± .0002
Wave Length in millimicrons
Transmissions measured on Spectrophotometer
T
T
T
for slots 1 + 3 + 5 by M. K. F.
for slots 2 + 4+ 6 by M. K. F.
for 6 slots by R. H. S.
435.8
.00775
.00759
.01518
546.1
.00772
.00766
.01523
578.0
.01510
587.6
.00776
.00749
650.0
.00772
.00749
.01525
Table 2
Sectored Disk, B. S. 30547True transmission = 0.1009 from Angular Calibration by B. S. Division of Weights and Measures
Wave Length in millimicrons
T by I. G. P.
520
0.1006
0.1007
580
0.1002
600
0.1009
0.1009
620
0.1008
0.0996
Table 3
Sectored Disk, B. S. No. 22143 B, 4 and 3Td = 0.1029Heterogeneous Illumination
Observer
I. G. P.
H. J. M.
Wave-length in mμ
Collimator Slit Width
Ocular Slit Width
Tm
Tm
mechanical
spectral
Mechanical
spectral
in mm
in mμ
in mm
in mμ
430
0.5
3.8
0.3
2.3
0.1027
−0.002
±0.019
.1045
+.016
.016
460
0.3
3.1
0.2
2.1
.1028
−0.001
±.0076
.1016
−.013
.0096
490
0.1
1.3
0.2
2.6
.1020
−.009
.0043
520
0.1
1.7
0.2
3.4
.1021
−0.008
0.0038
.1034
+.005
.0032
.1041
+0.012
0.0023
560
0.1
2.2
0.2
4.4
.1033
+.004
.0024
600
0.1
2.8
0.2
5.6
.1036
+.007
.0030
640
0.1
3.5
0.2
7.0
.1035
+.006
.0036
660
0.2
3.8
0.2
3.8
.1029
.000
.0047
700
0.3
13.8
0.2
9.2
.1046
+.017
.0075
0.5
23.0
0.2
9.2
.1042
+0.013
0.0051
0.5
23.0
0.2
9.2
.1025
−0.004
0.0071
Alg. mean
+0.005
+0.002
Td is true transmission of the disk from angular calibration by B. S. Division of Weights and Measures.
Td is the true transmission of the disk from angular calibration, by B. S. Division of Weights and Measures.
Table 5
Ives-Brady Daylight Glass (Submitted by E. J. Brady, letter of Dec. 2. 1921)Particular care was taken always to use same part of specimen (see Fig. 1).Each tabulated value of transmission (T) is the mean of ten observations. The probable errors (P.E.)T are the probable errors of these means as derived from the ten residuals of θ1 and θ2 (see appendix) by propagation of error formulas.