Mark C. Abrams

High-resolution Fourier transform spectroscopy of the Meinel system of OH

The infrared spectrum of the hydroxyl radical OH, between 1850 and 9000/cm has been measured with a Fourier transform spectrometer. The source, a hydrogen-ozone diffusion flame, was designed to study the excitation of rotation-vibration levels of the OH Meinel bands under conditions similar to those in the upper atmosphere which produce the nighttime OH airglow emission. Twenty-three bands were observed: nine bands in the Delta upsilon = 1 sequence, nine bands in the Delta upsilon = 2 sequence, and five bands in the Delta upsilon = 3 sequence. A global nonlinear least-squares fit of 1696 lines yielded molecular parameters with a standard deviation of 0.003/cm. Term values are computed, and transition frequencies in the Delta upsilon = 3, 4, 5, 6 sequences in the near-infrared are predicted.

Infrared bands of the C 2 Phillips system

The spectrum of the C2 Phillips System (A1Πu → X1∑g+) was observed in the spectral region 3300–6500 cm−1 by using a high-resolution Fourier-transform spectrometer and a hollow-cathode discharge source. Three new bands were observed, the (2–3), (1–3), and (2–4) bands belonging to the Δυ = −1 and Δυ = −2 sequences. In addition, new lines were observed in the (0–2) band. These lines, combined with previous high-resolution data, are used in a linear least-squares algorithm to calculate Dunham coefficients with a standard deviation of 0.018 cm−1. These coefficients facilitate the accurate prediction of wave numbers for the vibrational levels with υ″ and υ″.between 0 and 4.

Improved molecular parameters for the Ballik-Ramsay system of diatomic carbon (b 3 Σg − → a 3 Πu)

The infrared spectrum of the C2 (b3Σg− → a3Πu) Ballik–Ramsay system was observed in a hollow-cathode discharge source by using a high-resolution Fourier-transform spectrometer. Ten bands with (υ′–υ″) equal to (0–1), (1–2), (2–3), (3–4), (0–0), (1–1), (1–0), (2–1), (3–2), and (4–3) were observed in the spectral region between 3300 and 6500 cm−1. The (3–4) and (4–3) bands were observed for the first reported time. In addition, 360 lines belonging to satellite branches were observed. A global fit of the present data combined with previous high-resolution data in an iterative nonlinear least-square algorithm yields equilibrium molecular parameters with a variance of 0.0051 cm−1. The inclusion of the satellite lines facilitates the direct improvement of the fine-structure parameters. Rotational perturbations were observed in the upper b3Σg− state and were analyzed by using deperturbation methods.

CN vibration–rotation spectrum

CN vibration–rotation bands for the sequences (1–0) through (4–3) and (2–0) through (4–2) were observed in a King furnace and measured in the spectral regions 1797–2208 and 3740–4156 cm−1 with the McMath Fourier-transform spectrometer at the National Solar Observatory. Of the 489 lines observed, the wave numbers of 454 were fitted with a linear least-squares algorithm in order to calculate equilibrium Dunham coefficients, which will reproduce the lines with a standard deviation of 0.004 cm−1.

Why chose a fourier transform spectrometer

The magnitude of information flow through a spectrometer may be thought of as the product of two quantities, one determined by the spectrometer optics and the other by the detector. Because of its axis of symmetry, the Fourier transform spectrometer (FTS) interferometer has a large entrance aperture and, consequently, a large AΩ product. Another aspect of the quantity of data obtained is the fact that the FTS records data at all frequencies simultaneously, a process called multiplexing. There is a great saving in observation time when one wants to look at many frequencies. Many problems do not require the full resolution of instruments. For these problems, it is useful to have variable resolution, because excess resolution reduces the signal-to-noise ratio. The FTS is especially flexible in this regard and has no equal in the ease of setting the instrumental resolution to the required value. If 1% line shape distortion is necessary, then an FTS with an optimum aperture will require five resolution elements across a line width. In contrast, the grating with an optimum slit width will require 30 elements across a line width. The factor of 6 in required resolving power is a large part of the practical advantage of an FTS. The FTS is the system of choice in the infrared under almost any conditions (with or without a multiplex advantage), and in the visible and UV when high accuracy is required in intensity, line shape, or wave number.

Effects of noise in its various forms

There are always various kinds of noise in the spectrum, generated either in the source or by electrical and mechanical variations in the environment or in the Fourier transform spectrometer (FTS) itself. Most often the noise is not discernable in the interferogram, but appears clearly and looks like sharp spikes in the spectrum with random positions, widths, and intensities. It is helpful to note how various sources of noise and artifacts enter into the data. Source variations in frequency and intensity during the observation multiply the envelope of the interferogram in an undesirable way. Photon statistics and thermal processes in the detector and electronics add noise to the ideal interferogram. Fortunately, the errors do not usually interact, and one can consider each of them separately. For both historical and practical reasons, it is convenient to treat the noise in terms of where in the system it arises. A two-output interferometer simplifies the analysis of noise effects. There is an FTS multiplex advantage in noise reduction because all spectral elements are recorded simultaneously. Digitizing noise is negligible for simple spectra, but the dynamic range of observable intensities for emission spectra varies inversely as the number of very strong lines.

Theory of the ideal instrument

The Fourier transform spectrometer (FTS) is a multiplex instrument. Polychromatic spectral distributions determination by measuring the interferogram produced in an amplitude-division (Michelson) interferometer, and then calculating the Fourier transform of the interferogram is the heart of Fourier transforms spectroscopy. The spectral line width determines the length of the interferogram. The smaller the line width, the longer will be the interferogram. The line shape determines the shape of the interferogram envelope. In many spectra all lines have roughly the same shapes and often the same widths. Then the envelope of the combined interferogram does show clearly the characteristic shape and width of the lines. While the spectroscopists experience is largely in the spectral domain, with some practice a considerable amount of information can be inferred from the interferograms themselves.

Discussions, interventions, digressions and obscurations

Innovation is often the product of necessity tempered with a bit of desperation. In recent years, the combination of visible and infrared focal plane arrays and Fourier transform spectrometers has opened a new perspective on imaging spectrometry. The Imaging Fourier Transform Spectrometer (IFTS) exploits the stigmatic imaging capability of the Fourier transform spectrometer (FTS) with Nyquist-sampled imaging to enable true hyper spectral imaging. Beyond the efficiency and flexibility of IFTS instruments, there is an additional compelling reason for using a multiplex spectrometer: in the dual port design, virtually every photon collected is directed toward the focal plane for detection. Other solutions are inefficient, inflexible, and wasteful of mass, power, and volume. Cameras equipped with filters admit only a restricted band pass at low spectral resolution. To compete with the spectral multiplex advantage of an IFTS, a camera system needs multiple dichroics and focal plane array (FPA). Among spectrometers, the FTS is unique in offering the opportunity to operate near minimally sampled. Not surprisingly, many users eventually run their spectrometers minimally sampled, and then find that they need yet more resolution to resolve the features in the spectrum. At this point the observed spectrum is heavily distorted by the instrumental line shape (ILS) profile.

Line positions, line profiles, and line fitting

In spectroscopy, the observer is confronted with an unknown spectrum consisting of lines, bands, and noise from which it is hoped that accurate spectroscopic line parameters can be determined. Only then can meaningful atomic and molecular structures be analyzed and parameters calculated. In line finding, the parameters to be determined are wave numbers, wavelengths, line strengths, and line shapes characteristic of the source, with accuracies limited only by the signal-to-noise ratio and photon statistics of the light. In this process, the experimenter must correct the quasi-continuous data for the limitations and faults of the spectrometer, translate the data into a set of discrete spectral lines, and then calculate the spectral line parameters. Taken all together the line parameters constitute a line list. It is from this list that atomic and molecular structure and dynamics are determined. The line position error introduced by the signal-processing algorithm in derivative methods reflects the inherent limitations of the data, and the discrepancy between the expected continuous signal profile and the observed data. The best way to prepare a line list is to choose an analytical model representative of the expected line shapes, and then to match the model to the features in the spectrum by means of a least square fit.

The inductively coupled plasma spectrum of OD in the infrared

To gain more information about the highly excited rotational states of the Δv = 1 sequence of OD vibration-rotation bands, the spectrum has been produced in an inductively coupled plasma discharge and measured with a Fourier transform spectrometer between 1670 and 5768 cm−1. Along with the extension of 1–0 band, we have been successful in recording the 2–1 band for the first time. A nonlinear least square fit of these bands yielded equilibrium molecular parameters forv = 0, 1 and 2 levels with a standard deviation of 0·0032 cm−1. The centrifugal distortion parameters show a systematic vibrational dependence.