Apodization is a mathematical tool used in Fourier transform spectrometry to reduce the spurious oscillation in the output spectrum. We investigate Norton–Beer apodizing functions and take advantage of the main series to introduce a family of new functions. They weigh the interferogram to zero continuously within the same optical path difference and, accordingly, improve the convergence property of the instrumental line shape (ILS) for the apodized spectrum. In the meantime, the range of spectral smearing is well reduced. Compared with the Norton–Beer functions, the new functions are more flexible in practice and are more applicable with regard to distinguishing the spectral lines, especially the weak lines, which are not too close to the center of a strong line but are still susceptible to the ringing of ILS.
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