For many applications, a simple approximate equation for blackbody radiation can be more useful than is the Planck blackbody equation. An intermediate region exists where both the Rayleigh-Jeans equation and the Wien equation for blackbody radiation are inaccurate approximations to the Planck equation. Several approximate equations of simple mathematical form have been obtained that are more accurate in this intermediate region. These equations are applied to optical pyrometry to obtain formulas for brightness temperature and color temperature that can be used in the intermediate region.
D. E. Erminy, "Some Approximations to the Planck Function in the Intermediate Region with Applications in Optical Pyrometry," Appl. Opt. 6, 107-117 (1967)