Error-free phase correction of interferograms using digital all-pass filters

We present a novel method for the phase correction of FT-IR interferograms that can produce spectra free of photometric errors. It is based on the design and application of an all-pass digital filter whose phase response is the opposite to that of the interferogram. After filtering, the interferogram becomes nearly (or completely, depending on the computational effort) phase-error-free and subsequent Fourier transforming yields accurate spectra. To virtually eliminate any photometric error, this method can be followed up by the Mertz method, which given that the filtered interferogram is nearly symmetric, will generate no errors. Without the filtering, Mertz method was shown to introduce photometric error in FT-IR spectra. When stored filter coefficients are used, this method is orders of magnitude faster than the Mertz method, while still keeping the photometric error within acceptable levels. This advantage of the method could be used, for example, in hyper-spectral imaging applications where a large amount of spectra from infrared focal plane arrays needs to be collected and processed in (near) real time.The method can be easily implemented in DSP circuits. Examples of phase correction of double-sided interferograms using both the Mertz and the all-pass filter method were given and photometric accuracy compared.