Integration ghosts in interferograms: origin and correction

Abstract

We report on an error source and a possible correction which occurs with Fourier Transform Spectrometers due to the use of an integrating detector. The new class of imaging Fourier-Transform-Spectrometers (FTS) is in many cases best realised using continuously moving mirrors and an integrating array detector with fixed frame rate. In case of not perfectly constant optical path difference (OPD) speed, this corresponds to an irregular OPD sampling, resulting in radiometric errors. This effect is well-known and can be solved by resampling, i.e. interpolation on a regular OPD grid. A less known effect is caused by the detector integrating over constant time intervals, which – like the sampling steps - are also of varying length in the OPD domain due to the non-constant OPD speed. The resulting error is discussed in the presented paper, where also an elegant correction method is proposed. Constant-width integration in the OPD domain acts as a spatial low-pass filter on the interferogram. If the integration width varies, a modulation is applied to the interferogram’s envelope. This modulation results in a radiometric error in the spectrum. The presented correction is a finite impulse response filter with only three taps, to be applied to the measured time-sampled interferogram before resampling. In case the interpolation is done with filters, these filters and the new 3-tap filter can be combined to reduce processing overhead.