Reflectances of transmissive sheets, calculated from the transmissions of one and two sheets, are compared with reflectances obtained by using the General Electric recording spectrophotometer. The expression used as a basis for calculation,
, in which Ra is the reflectance, and Ta and T2a are the transmissions of one and two sheets, respectively, of a, was derived by considering the infinite series of reflections undergone by light, or radiant energy in general, in passing through the two sheets. The expression was found to be valid and useful over a wide range of reflectances and wave-lengths, for materials such as paper, glass, and an organic plastic.
The method is an absolute one since it involves no reflectance standard. It involves no spherical or similar integrating device nor does it involve any reflecting surface other than that of the sample itself, as a fundamental part of the measurements. When transmission values for diffuse incidence are substituted into the expression, the reflectances thus calculated correspond to the conditions of diffuse incidence and diffuse viewing, and as such are somewhat higher than the usual directly measured reflectances for normal incidence and diffuse viewing (or diffuse incidence and normal viewing). For clear sheets, with normal incidence, specular reflectance may be calculated.
The method thus affords a means of determining, from two simple measurements, the specular-plus-diffuse reflectance of transmissive sheets for diffused light or radiant energy in general.
The expression as derived is theoretically inapplicable to diffusing sheets for light of normal incidence, but a compensation of errors allows close agreement over the visible range, at 365 millimicrons, and for “white” light, for all except tissue paper and other materials of like transmissivity. For diffuse incidence at 365, and to a certain extent, at 405 millimicrons, some papers show deviations from the simple theory because of fluorescence effects. This and other effects are discussed.
Reflectances in the infra-red region near 850 millimicrons are also calculated but no standard for comparison is available for these values. The sources of errors at the shorter wave-lengths, however, do not interfere in the infra-red region.
Transmissions of papers were found to be dependent upon the angle of incidence.
Reflectances throughout the visible region, measured at 45° from normal incidence were found to agree closely, for the type of papers studied, with those obtained using the General Electric recording spectrophotometer, which corresponds to the conditions of normal incidence and diffuse viewing.
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Comparison between reflectances of papers obtained from curves using the General Electric recording spectrophotometer, and those obtained by measuring reflectances at 45° from normal incidence.
Paper No.
405 mμ
436 mμ
546 mμ
623 mμ
G.E. %
45° %
G.E. %
45° %
G.E. %
45° %
G.E. %
45° %
1215
76.9
77.1
78.6
78.1
81.2
81.2
81.2
81.2
1214
66.5
65.6
69.5
69.9
73.6
74.2
73.8
73.1
1191
73.2
73.6
75.8
75.8
79.3
79.6
79.7
78.7
1170
63.0
62.4
67.9
67.3
73.2
73.2
73.6
72.2
1133
50.5
50.4
56.2
57.6
65.9
66.8
68.2
67.4
1136
54.6
55.6
61.4
62.5
71.9
72.9
74.1
73.7
Table II
Reflectances, calculated from the transmissions of one and two sheets, compared with the reflectances directly measured with a General Electric recording spectrophotometera and other equipment.
Used for values at 623, 546, 436 and 405 millimicrons for samples, Nos. 1215, 1214, 1191, 1170, 1133, 1136 and 200. See text for details.
Wave-length approximately 850 millimicrons. See text for details.
Heterogeneous light was that from a 100-watt, 110-volt tungsten lamp, after transmission through a 15-mm layer of 0.117 molar cupric chloride solution.
The first six papers were made in the Bureau paper mill (reference 13 in text). Numbers 128 and 198 were standard samples of the same number from the Government Printing Office. The papers were near-white or neutral gray unless otherwise specified.
“u.v.” stands for “unreal value” since the expression 1−(t02/t2a) had a negative value in these cases.
Reflectance was calculated from the refractive index for yellow light, n=1.5157.
Measured transmissions of diffusely incident radiant energy for one sheet are given as ta, for two sheets of the same material as t2a, and for the combination of the various materials with No. 128 as tab. This last combination was used for the first six papers at 436, 405 and 365 millimicrons. See text for further details.
These values were obtained with light of perpendicular incidence.
Table IV
Reflectance of receiving surface, Re, of light sensitive cell as a function of the angle of incidence, θ, at 578 millimicrons.
θ(degrees)
0
10
20
30
40
50
60
70
Rc
0.082
0.082
0.083
0.084
0.088
0.097
0.118
0.146
Table V
Transmission of papers as a function of angle of incident light at 578 millimicrons.
The increases in ta with θ at angles greater than 60° are reproducible but probably do not represent real characteristics of papers. They are apparently the result of the particular method of measurement, which consisted in varying the angle of the measuring cell and balancing the circuit at each angle with no paper. Beyond 60° the specular reflectance of the bare cell surface appears to increase much more rapidly with θ than that of the paper, so that the cell-response per unit of radiant flux is greater with than without the paper. At angles below 60°, however, such an effect would be negligible since the reflectance of the cell changes only slightly with θ at the smaller angles.
Table VI
Fluorescence of papers caused by 365-millimicron ultraviolet.
Number of Paper
Fluorescent Light,a Expressed in Transmission Unitsb
1 Sheet
1 Sheet plus Paper No. 128
1215
0.002
0.003
1214
.004
.004
1191
.002
.003
1170
.006
.005
1133
.006
.004
1136
.005
.003
1002
.003
.003
128
.007
.007
The ultraviolet incident upon the papers was excluded from the measurements by means of a 10-mm layer, contained in a glass cell, of 0.65 molar cupric chloride solution at 26°C, which has the following transmittances (unpublished data): at 365 mμ, 0.0005; at 405 mμ, 0.176; at 436 mμ, 0.738; at 546 mμ, 0.788; at 578 mμ, 0.447; at 623 mμ, 0.041; at 691 mμ, 0.005; at 750 to 1400 mμ, 0.000.
The values in this table are expressed in the same units as those of Table III and thus may be subtracted directly from the values for ta, tab or t2a to obtain the corresponding transmission values for the incident ultraviolet.
Tables (6)
Table I
Comparison between reflectances of papers obtained from curves using the General Electric recording spectrophotometer, and those obtained by measuring reflectances at 45° from normal incidence.
Paper No.
405 mμ
436 mμ
546 mμ
623 mμ
G.E. %
45° %
G.E. %
45° %
G.E. %
45° %
G.E. %
45° %
1215
76.9
77.1
78.6
78.1
81.2
81.2
81.2
81.2
1214
66.5
65.6
69.5
69.9
73.6
74.2
73.8
73.1
1191
73.2
73.6
75.8
75.8
79.3
79.6
79.7
78.7
1170
63.0
62.4
67.9
67.3
73.2
73.2
73.6
72.2
1133
50.5
50.4
56.2
57.6
65.9
66.8
68.2
67.4
1136
54.6
55.6
61.4
62.5
71.9
72.9
74.1
73.7
Table II
Reflectances, calculated from the transmissions of one and two sheets, compared with the reflectances directly measured with a General Electric recording spectrophotometera and other equipment.
Used for values at 623, 546, 436 and 405 millimicrons for samples, Nos. 1215, 1214, 1191, 1170, 1133, 1136 and 200. See text for details.
Wave-length approximately 850 millimicrons. See text for details.
Heterogeneous light was that from a 100-watt, 110-volt tungsten lamp, after transmission through a 15-mm layer of 0.117 molar cupric chloride solution.
The first six papers were made in the Bureau paper mill (reference 13 in text). Numbers 128 and 198 were standard samples of the same number from the Government Printing Office. The papers were near-white or neutral gray unless otherwise specified.
“u.v.” stands for “unreal value” since the expression 1−(t02/t2a) had a negative value in these cases.
Reflectance was calculated from the refractive index for yellow light, n=1.5157.
Measured transmissions of diffusely incident radiant energy for one sheet are given as ta, for two sheets of the same material as t2a, and for the combination of the various materials with No. 128 as tab. This last combination was used for the first six papers at 436, 405 and 365 millimicrons. See text for further details.
These values were obtained with light of perpendicular incidence.
Table IV
Reflectance of receiving surface, Re, of light sensitive cell as a function of the angle of incidence, θ, at 578 millimicrons.
θ(degrees)
0
10
20
30
40
50
60
70
Rc
0.082
0.082
0.083
0.084
0.088
0.097
0.118
0.146
Table V
Transmission of papers as a function of angle of incident light at 578 millimicrons.
The increases in ta with θ at angles greater than 60° are reproducible but probably do not represent real characteristics of papers. They are apparently the result of the particular method of measurement, which consisted in varying the angle of the measuring cell and balancing the circuit at each angle with no paper. Beyond 60° the specular reflectance of the bare cell surface appears to increase much more rapidly with θ than that of the paper, so that the cell-response per unit of radiant flux is greater with than without the paper. At angles below 60°, however, such an effect would be negligible since the reflectance of the cell changes only slightly with θ at the smaller angles.
Table VI
Fluorescence of papers caused by 365-millimicron ultraviolet.
Number of Paper
Fluorescent Light,a Expressed in Transmission Unitsb
1 Sheet
1 Sheet plus Paper No. 128
1215
0.002
0.003
1214
.004
.004
1191
.002
.003
1170
.006
.005
1133
.006
.004
1136
.005
.003
1002
.003
.003
128
.007
.007
The ultraviolet incident upon the papers was excluded from the measurements by means of a 10-mm layer, contained in a glass cell, of 0.65 molar cupric chloride solution at 26°C, which has the following transmittances (unpublished data): at 365 mμ, 0.0005; at 405 mμ, 0.176; at 436 mμ, 0.738; at 546 mμ, 0.788; at 578 mμ, 0.447; at 623 mμ, 0.041; at 691 mμ, 0.005; at 750 to 1400 mμ, 0.000.
The values in this table are expressed in the same units as those of Table III and thus may be subtracted directly from the values for ta, tab or t2a to obtain the corresponding transmission values for the incident ultraviolet.