handbook of modern sensors

128 4 Optical Components of Sensors
reduce losses, optical materials are often given antireflective coatings, which have
refractive indices and thickness geared to specific wavelengths.
The radiant energy balance Eq. (3.134) should be modified to account for two
reflections in an optical material:
ρ 2 + α + γ = 1, (4.9)
where α is a coefficient of absorption and γ is a coefficient of transmittance. In a
transparency region, α ≈ 0, therefore, transmittance is:
γ = 1 − ρ z ≈
2n
n 2 + 1 . (4.10)
Equation (4.10) specifies the maximum theoretically possible transmittance of the
optical plate. In the above example, transmittance of a glass plate is 88.6% (visible),
whereas transmittance of a germanium plate is 41% (far IR). In the visible range,
germanium transmittance is zero, which means that 100% of light is reflected and
absorbed. Figure 4.5 shows reflectance and transmittance of a thin plate as functions
of refractive indices. Here, a plate means any optical device (like a window or a
lens) operating within its useful spectral range, [i.e., where its absorptive loss is small
(α ≈ 0)].
Figure 4.6 shows an energy distribution within an optical plate when incident
light flux 0 strikes its surface. A part of incident flux, ρ , is reflected, another part,
α , is absorbed by the material, and the third part, γ , is transmitted through. The
Fig. 4.5. Reflectance and transmittance of a thin plate as functions of a refractive index.