The Refractive index, real part, n (dimensionless) may be expressed as a function of both wavelength and temperature by using an expression of the form

The wavelength-dependent (non-temperature-dependent) component of this equation, n(λ), might be any one of the optical dispersion models discussed above, or it could be specified by other means. The change in refractive index as a function of temperature, Δn(λ,Τ) can be computed using a thermo-optic dispersion model.

An expression for the change in refractive index as a function of temperature, Δn(λ,T) is given in Ref. 5. It may be derived by integrating the dispersion formula for the thermo-optic coefficient (dn/dT). That is,

In the above formula T0 is the reference temperature against which the temperature difference ΔT = T - T0 is computed and D0, D1, D2, E0, E1, and λTK, are glass specific coefficients.