Values for the refractive index at arbitrary temperatures and pressures may be related to values of the index at the reference temperature and pressure through the absolute (vacuum referenced)  refractive index of air (n_air). Again, in ZEMAX the refractive index of air is always equal to 1.0 at the system temperature (T_s) and pressure (P_s).

The following formulas are used to calculate absolute values for n_air at T_s and P_s, as well as at other temperatures and pressures such as T₀ and P₀ (the reference temperature and pressure):



In these equations l refers to the input wavelength (at the system temperature and pressure), P is the pressure in atmospheres, and T is the temperature in degrees C. More information about these formulas may be found in the chapter of the ZEMAX manual entitled “Thermal Analysis”.

To calculate index data at arbitrary T and P, we first calculate n_air(P₀,T₀) and n_air(P_s,T_s). Both of these quantities are calculated at the input wavelength. These values are then used to determine the “relative” wavelength, which is simply the input wavelength scaled to the reference temperature and pressure, using the formula:

l_rel = l_input*n_air(P_s,T_s)/n_air(P₀,T₀)

The relative index of refraction at the reference temperature and pressure is then calculated from the appropriate dispersion formula using the relative wavelength:

n_rel(P₀,T₀) = f(l_rel;c₀)

where f represents the functional form of the appropriate dispersion formula and the vector c₀ represents the dispersion coefficients for the glass. This relative index value is converted to an absolute index value using the formula:

n_abs(P₀,T₀) = n_rel(P₀,T₀)/n_air(P₀,T₀)

Since the relative index was calculated at the reference temperature and pressure, the absolute index is calculated using the absolute index of air at this same temperature and pressure. The absolute index of the glass at the glass temperature and “pressure” (= system pressure) is determined from:

n_abs(P,T) = n_abs(P₀,T₀) + Dn_abs

where Dn_abs is calculated using the following formula (see the chapter of the ZEMAX manual entitled “Thermal Analysis” for details):



In the above formula, n is the relative index of the glass at the reference temperature and pressure, DT is the difference between the glass temperature and the reference temperature, and the variables D₀, D₁, … represent the thermal dispersion coefficients for the glass. Finally, the relative index at the glass temperature and pressure is obtained from:

n_rel(P,T) = n_abs(P,T)*n_air(P_s,T_s)

It is this value that ZEMAX uses for the refractive index of the glass during ray trace calculations.