As any optical system is subjected to higher or lower temperatures several things happen: the lens elements expand or contract, the housing expands or contracts, and the refractive index of the lens materials increases or decreases. While the lens and housing relative expansion can sometimes be a problem, the primary problem with infrared systems is the very large change in refractive index as a function of temperature, or dn/ dt. Germanium has a dn/ dt of 0.000396/ C. For comparison, BK7 glass has a dn/ dt of 3.6 0E-6. It can be shown for a simple lens that

where df is the change in focal length and ? t is the change in temperature in degrees Celsius.

Consider the following example: Assume that we have a 75-mm-diameter f/1.5 germanium lens with a focal length of 112.5 mm. Applying the previous relationship yields a change in focal length of 0.599 mm for a 40 C ? t thermal soak. For reference, the Rayleigh criteria for one-quarter wave of defocus is 0.046 mm, so the preceding defocus value equates to 3.3 waves of defocus, which is 13.1 Rayleigh criteria depths of focus, a huge amount! This issue can, and often is, a very serious problem in thermal infrared systems. In this example, if we were to control the temperature so as to stay within a one-quarter wave of defocus, we would need to control the temperature to within 3 C.

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