Because the index of refraction is temperature dependent, a temperatur
e gradient across a window causes image blur and bore sight error. Pri
or to this paper, there have been no direct temperature-dependent meas
urements reported on the mid-infrared refractive index for sapphire, a
popular infrared window material of high durability. Measurements of
dn/dT are reported on the ordinary ray of sapphire in the 4 mu m regio
n for the first time. Accurate temperature and frequency dependent ref
ractive index models can now be constructed from visible measurements
of the refractive index, far-infrared reflectance measurements, thermo
-optic coefficient measurements, and infrared measurements of the abso
rption coefficient. Visible measurements determine the contribution to
the refractive index from electronic transitions. Far-infrared measur
ements determine the contributions from fundamental lattice vibrations
(phonons). Infrared absorption data are used to determine parameters
in a multiphonon sum band model. By applying the Hilbert transform to
this multiphonon absorption model, a model for the multiphonon refract
ivity is obtained. Two- and three-phonon contributions to the refracti
ve index are important for an accurate model that includes temperature
dependence. Results for the ordinary- and extraordinary-rays are obta
ined. (C) 1998 Elsevier Science B.V. All rights reserved.