Germanium is a favorite material for infrared lens design. Its high refractive index, nominally, 4.0, allows for excellent correction of aberrations, and its relatively small dispersion in the 8.0-12.0 micron waveband results in acceptably small primary chromatic aberration for many applications. A singlet design is often satisfactory over reasonably wide wavebands without having to achromatize the design through use of a second lens element of greater dispersion, as is customarily done in achromat design.
In the 3.0-5.0 micron waveband, the dispersion characteristic of germanium shows a sharp increase in the rate of change of refractive index vs. wavelength and the resulting primary chromatic aberration requires correction.
While germanium is widely used for the above reasons, it unfortunately exhibits some negative aspects, as well. Significant changes in refractive index with temperature are a principal factor in lens thermal defocussing.
The first of the two accompanying articles addresses change in lens focal length with temperature, using first order thin-lens analysis The second article, Athermal IR Achromat Design, provides a mathematical background and methodology for simultaneously achromatizing an athermalizing a lens design for the 3.0-5.0 micron waveband.