Two methods, one based on non-linear least squares and one based on an approximation, are described for determining the rotational temperature of diatomic molecules from absorption spectra measured with moderate resolution. Experimental tests with CO and CO/air mixtures gave good results. The importance of line widths and instrumental distortions is emphasized.

Determination of rotational temperatures of diatomic molecules from absorption spectra measured at moderate resolution

Nonlinear interferometers allow for mid-infrared spectroscopy with near-infrared detection using correlated photons. Previous implementations have demonstrated a spectral resolution limited by spectrally selective detection. In our work, we demonstrate mid-infrared transmission spectroscopy in a nonlinear interferometer using single-pixel near-infrared detection and Fourier-transform analysis. A sub-wavenumber spectral resolution allows for rotational-line-resolving spectroscopy of gaseous samples in a spectral bandwidth of over 700$\,$cm$^{-1}$. We use methane transmission spectra around 3.3$\,\mu$m wavelength to characterize the spectral resolution, noise limitations and transmission accuracy of our device. The combination of nonlinear interferometry and Fourier-transform analysis paves the way towards performant and efficient mid-infrared spectroscopy with near-infrared detection.

A nonlinear interferometer for Fourier-transform mid-infrared gas spectroscopy using near-infrared detection

In this paper we study the effect of material dispersion on the performance of a moving-optical-wedge Fourier transform spectrometer. The spectrum is thus evaluated numerically using a test spectrum source. The obtained numerical results show that the classical technique for numerical dispersion compensation, usually used with a Michelson interferometer, cannot be efficiently used with wedge interferometers as it is limited to the cases of weak dispersion. The error in this technique is thus evaluated in different cases and a new numerical technique is proposed to overcome this error. We also notice shrinkage in the interferogram spread in the spatial domain in contradiction with the normal dispersion effect in a Michelson interferometer.

Dispersion compensation in moving-optical-wedge Fourier transform spectrometer.

The nature of the systematic radiometric error in the MGS TES spectra

Phase correction is a critical procedure for most space-borne Fourier transform spectrometers (FTSs) whose accuracy (owing to often poor signal-to-noise ratio, SNR) can be jeopardized from many uncontrollable environmental conditions. This work considers the phase correction in an FTS working under significant temperature change during the measurement and affected by mechanical disturbances. The implemented method is based on the identification of an instrumental phase that is dependent on the interferometer temperature and on the extraction of a linear phase component through a least-squares approach. The use of an instrumental phase parameterized with the interferometer temperature eases the determination of the linear phase that can be extracted using only a narrow spectral region selected to be immune from disturbances. The procedure, in this way, is made robust against phase errors arising from instrumental effects, a key feature to reduce the disturbances through spectra averaging. The method was specifically developed for the Mars IR Mapper spectrometer, that was designed for operation onboard a rover on the Mars surface; the validation was performed using ground and in-flight measurements of the Fourier transform IR spectrometer planetary Fourier spectrometer, onboard the MarsExpress mission. The symmetrization has been exploited also for the spectra calibration, highlighting the issues deriving from the cases of relevant beamsplitter emission. The applicability of this procedure to other instruments is conditional to the presence in the spectra of at least one spectral region with a large SNR along with a negligible (or known) beamsplitter emission. For the PFS instrument, the processing of data with relevant beamsplitter emission has been performed exploiting the absorption carbon dioxide bands present in Martian spectra.

Instrumental phase-based method for Fourier transform spectrometer measurements processing.

Chirping is the deliberate dispersion of the frequencies in a signal to remove a strong central peak. In a Fourier spectrometer, chirping improves dynamic range. For typical applications, the improvement is equivalent to about 16 dB in SNR. A very large nonlinear phase correction is required, but this is shown to be surprisingly simple to achieve in practice.

Chirped Fourier Spectroscopy. 1:Dynamic Range Improvement and Phase Correction

Chirping introduced into a Michelson interferometer permits correction for nonlinearities, distortion, and intermodulation in the final spectrum. This is because the false harmonics of each frequency carry the characteristic phase of the original frequency, whereas true spectral components at higher frequencies have their own characteristic phase. In an unchirped interferogram, there is no such distinguishing phase. This paper explains how the distinguishing phase occurs, presents two algorithms for carrying out the distortion correction when the form of the distortion is known, and displays results of correcting selected distorted experimental interferograms. This capability is a new advantage of chirping in Fourier spectroscopy.

Use of chirping to compensate for nonlinearities in Fourier spectroscopy

When applied to a Fourier spectrometer, chirping raises questions about the resolution and contrast of the device A theory is presented to show how the nonlinear phase affects the instrument profile and resolution; the penalty for chirping a high resolution interferometer is much smaller than had been believed An algorithm is presented for recovering contrast; it is shown that the fast Fourier transform is still usable, allowing realization of full contrast Systems bearing a residual nonlinear phase dispersion (accidental chirping) can take advantage of this theory

Chirped fourier spectroscopy. 2: theory of resolution and contrast.

The possibility of overcoming the dynamic range problem in Fourier spectroscopy by the use of chirping has long been recognized in principle. Only recently has chirping been shown to be free of other difficulties and thus worthy of use under normal circumstances. This letter cites a novel advantage that accrues from chirping a Michelson interferometer used for infrared spectroscopy.

Thomas P. Sheahen

Papers

Chirped Fourier Spectroscopy. 1:Dynamic Range Improvement and Phase Correction

Use of chirping to compensate for nonlinearities in Fourier spectroscopy

Chirped fourier spectroscopy. 2: theory of resolution and contrast.

Use of Chirping to Distinguish Good from Bad Interferograms and Spectra

Observation of C3O2 during atmospheric reentry