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, Ra = (1 - Ta2/T2a)½, 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.
HERBERT F. LAUNER, "Reflection-Transmission Relationships in Sheet Materials," J. Opt. Soc. Am. 32, 84-92 (1942)