Abstract
In the measurement of spectral distribution of fluorescent lamps, an error arises from the sensitivity of a spectroradiometer being influenced by the states of polarization of incident light.
The following equation for the transmission factor of a monochromator is derived from Fresnel's law.
Tθ=T (1+tcos 2θ), (1)
where Tθ is the transmission factor of a monochromator for radiant flux Φθ, the electric vector of which is on the plane inclined by an angle θ to the plane of incidence of the monochromator prism. Experimental results show that the radiant flux emitted by both tungsten lamps used as sub-standards of spectral distribution and fluorescent lamps is approximately expressed by the following equation,
Φθ=Φ [1+øcos (2θ+α)], (2)
where α is a phase difference.
For such receivers as phototubes and photomultipliers, their sensitivity for polarized light is approximately represented by
Sθ=S [1+s cos (2θ+β)], (3)
where Sθ is the sensitivity for radiant flux Φθ and β is a phase difference. This is an established expression used in past publications.
If Φθ enters the monochromator, the output i of the receiver is given by
i=∫2π0ΦθTθSθdθ=EST[1+φt/2cosα+st/2cosβ+φs/2cos(α-β)], (4)
where
i=∫2π0Φθdθ=2πΦ,
and E is the radiant flux.
Using the subscripts Wλ and Fλ to the above quantities concerning the sub-standard and the fluorescent lamps at wavelength λ respectively, one obtains the following equation.
EFλ/EWλ_??_iFλ/Wλ(1+Δλ) (5)
where
Δλ=tλ/2(φWλcosαWλ-φFλcosαFλ)+sλ/2{φWλcos(αWλ-βλ)-φFλcos(αFλ-βλ)}. (6)
The polarization error is represented by Δλ.
If Δλ does not vary with wavelength, no polarization error arises in the measurement of the relative value. However, Δλ varies usually with wavelength, and the polarization error is given by
(Δ)λ, λ'=|Δλ-Δλ|. (7)
If λ and λ' are given, the values of Δλ and (Δ)λ, λ' for any particular spectroradiometer are calculated by the equations (6) and (7). With the values 435.8mμ and 656.3mμ assigned to λ and λ' respectively, results of calculation are shown.
