Performance models as design aids for Fourier transform spectrometers (FTS) sensor system developments

AbstractFTS sensor systems have significant potential for a wide range of applications compared to other spectrometric systems. Absolute wavelength calibration, high spectral resolu­ tion, high throughput, two-dimensional imaging, and wide spectral range are readily achieved advantages. However, spectral fidelity and radiometric precision have been more difficult to achieve, and even to specify, than with other spectro-radiometers. The dif­ ficulty originates partly in the operation mode of the FTS sensor which requires instru­ ment errors to undergo a Fourier Transform prior to presentation in the spectral domain. We have developed and described here an FTS sensor performance model to allow evaluation of the effects of a wide range of instrument errors on the spectrum. Likewise, spectro- radiometric performance requirements can be quantitatively related to specifications for subsystems in the instrument (e.g. the scan mirror drive). We illustrate the use of our performance model through application to a contemporary measurement scenario with particu­ lar emphasis on classifying and quantifying FTS unique error sources in spectro-radio- metric applications.IntroductionThe complication with the FTS sensor system is that radiances are not directly measured and therefore the effects of error sources are not as obvious as with other spectral sen­ sors. We have developed an FTS sensor performance model which analytically describes the basic operations of the FTS sensor (i.e. encoding, recording, and decoding). Error sources can be introduced at each operation to quantify their effects on retrieved spec­ tra. Conversely, observed system performance can be interpreted in terms of subsystem er­ ror source contributions.This paper describes our performance model and illustrates its application to specific error sources for a nadir sounder mission.We do not here treat those elements of the operation of a perfect FTS sensor (e.g. sampling considerations) which are well treated elsewhere1 . Neither do we discuss the de­ sign or total performance of the nadir sounder2 used here to illustrate the performance model.FTS conceptThe basic concept for an FTS interferometer is shown in Figure 1. The radiation from the source is collimated and directed towards a beamsplitter that divides the radiation into two components. One component is reflected to a fixed arm of the interferometer and then directed back to the beamsplitter. The second component is transmitted to a mirror whose position can be translated along the line of propagation of the radiation. The re­ flected radiation recombines at the beamsplitter and is imaged as optical fringe patterns on the detector.In operation, the moving mirror is scanned at a uniform velocity. The optical fringe patterns are then modulated at the detector whereby each optical frequency component in the source radiation is encoded into a particular electrical frequency. The electrical waveform is called an interferogram. It has a characteristic center burst region of high signal. This high signal occurs when the optical paths in each arm of the interferometer are equal (i.e. at zero path difference ZPD) because the interference for all optical frequencies are in phase at ZPD. The electrical interferogram signal from the detector is sampled, digitized, and recorded as a function of the optical path difference (OPD) be­ tween the interferometer arms. Interference fringes from a reference laser which tra­ verses the same optical path are used for OPD sampling and, at the same time, provide wavelength calibration for the FTS system. Fourier Transformation of the recorded inter­ ferogram by a processor yields a spectrum which faithfully represents the optical frequen­ cies contained in the source radiation. The spectral resolution obtained in the trans­ formed spectrum is approximately equal to the reciprocal of the total (OPD) scanned by the moving mirror.21