Athermats are lenses that are designed to compensate for the focus shift that occurs with temperature excursions. The changing parameters of an optical element are the radius, the thickness, and the index of refraction. The spacing of the lens from the detector also changes and is a function of the coefficient of expansion of the housing material1.
9.2 Focus Shift of a Refractive Element
The power (reciprocal of the focal length f) of a thin lens is given by Ï=(nâ1)(1 R 1 â1 R 2 ), where n = index of refraction, and R 1 andR 2 are the surface radii. Differentiation of Eq. (9.1) with respect to temperature yields dÏ dt =(nâ1)[(â1 R 2 1 )(d R 1 )â(â1 R 2 2 )(d R 2 )]+(1 R 1 â1 R 2 )dn dt .
We recognize in this equation that (1âR 1 )(dR 1 âdt)=(1âR 2 )(dR 2 âdt)=Î± L , , the thermal coefficient of the lens material. Therefore, dÏ dt =(nâ1)(â1 R 1 Î± L +1 R 2 Î± L )+(1 R 1 â1 R 2 )dn dt .
Rearranging and making use of Eq. (9.1) results in dÏ dt =[Ï (nâ1) ]dn dt .
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