Page 266 - Modern Optical Engineering The Design of Optical Systems

246 Chapter Eleven

Figure 11.5 Transmission of typical evaporated interference filters plotted
against wavelength in arbitrary units. (Upper left) Short-pass filter (note
that dashed portion of curve must be blocked by another filter if low long
wavelength transmission is necessary). (Upper right) Long-pass filter.
(Lower left) Bandpass filter. (Lower right) Narrow bandpass (spike) filter.

the characteristics can be shifted up or down the spectrum as described
in the preceding paragraph. Most interference filters are very nearly
100 percent efficient, so that the reflection for a film is equal to one
minus the transmission (except in regions where the materials used
become absorbing). Since the characteristics of an interference filter
depend on the thickness of the films, the characteristics will change
when the angle of incidence is changed. This is in great measure due to
the fact that the optical path through a film is increased when the light
passes through obliquely. For moderate obliquity angles the effect is usually
to shift the spectral characteristics to a slightly shorter wavelength. The
wavelength shift with obliquity is approximated by

0 2
2
n s in
n
where is the shifted wavelength at an angle of incidence of , 0 is the
wavelength for normal incidence, and n is the “effective index” for the
coating stack (n is typically in the range of 1.5 to 1.9 for most coatings).
Coatings also shift wavelength effects with temperature; this shift is to
the order of one- or two-tenths of an angstrom per degree Celsius.