Fourier transform method for calculating the transmittance of inhomogeneous atmospheres

For spectral lines with combined Doppler and pressure broadening, the Fourier transform of the line shape is calculated analytically in an isothermal layer in which both the pressure and absorber concentrations vary along the line of sight. Use of the Cooley-Tukey fast Fourier transform algorithm allows efficient computation of the optical depth of such layers containing a large number of absorption lines of the same shape. The computation time is almost independent of the number of absorption lines. In many cases, this method allows increased speed and accuracy compared with conventional line-by-line methods.