Practical methods for rapid and accurate computation of interferometric spectra for remote sensing applications

The apodization of an interferogram corresponds to a linear transformation in spectral space between unapodized and apodized radiances. Many apodization functions have well-behaved numerical inverse transformations, and we show an analytic inverse for the Hamming apodization function. The inverse transformation has many practical uses for remote sensing applications and can also be used theoretically to show the equivalence between unapodized spectra and properly apodized spectra. The inverse transformation, which is a representation of the discrete convolution theorem, can be used to readily convert computed apodized spectra to spectra computed for other symmetric apodization functions (including unapodized), which may have poorer characteristics with regard to calculating channel-transmittance parameters or radiances. We also show a quantitative method for comparing apodization functions of different mathematical forms.