James W. Brault

New studies of the visible and near‐infrared absorption by water vapour and some problems with the HITRAN database

New laboratory measurements and theoretical calculations of integrated line intensities for water vapour bands in the near-infrared and visible (8500–15800 cm−1) are summarised. Band intensities derived from the new measured data show a systematic 6 to 26% increase compared to calculations using the HITRAN-96 database. The recent corrections to the HITRAN database [Giver et al., J. Quant. Spectrosc. Radiat. Transfer, 66, 101–105, 2000] do not remove these discrepancies and the differences change to 6 to 38%. The new data is expected to substantially increase the calculated absorption of solar energy due to water vapour in climate models based on the HITRAN database.

Spectrum and term system of neutral nickel, Ni I

Spectra of nickel, emitted from hollow cathode discharges, have been recorded in the region 1700-55 000 A (58 800-1800 cm−1). Fourier transform spectrometers were used above 1800 A, yielding very high accuracy and resolution. The number of classified Ni I lines has increased from 1071 to 1996. 289 of the lines have been resolved in 2-4 isotope components. The term system derived from the observations comprises 286 energy levels. The term structure and the coupling conditions have been studied by means of ab initio and parametric theory.

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.

Laboratory spectroscopy of molecular oxygen in the visible and near-infrared

The spectrum of molecular oxygen goes from the pure rotational system in the sub-millimetre region to the K edge at 2.3 nm.

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.

Processing of spectral data

The spectral data collected needs to be reduced to numbers and plots that are useful to astronomers, physicists, chemists, and scientists in general. Atlas plots of the spectrum of the radiation at both low and high dispersions are important. The former gives an overview of the intensity distribution, and the latter shows details such as line shapes and widths. Another need is for a line list that includes all lines evident on the high resolution atlas, and which incorporates accurate fitted line parameters, including frequency and wavelength, intensity, width, area, and damping, or an equivalent set of line parameters. The chapter discusses making of atlases and line lists. The examples are based on data taken on the McMath–Pierce Fourier transform spectrometer at the National Solar Observatory, Kitt Peak. With the “linelist” command and subsequent least square fitting, one can make a list of lines and their fitting parameters directly from an emission spectrum or an absorbance spectrum.

Working with digital interferograms, fourier transforms, and spectra

The precision required in calculating the Fourier transform, that is at the heart of high-resolution Fourier transform spectrometer (FTS), is far too great for any kind of analog technique. The development of the modem digital computer and algorithms, such as the fast Fourier transform (FFT), is absolutely essential for high-resolution Fourier spectroscopy. But digital invariably implies discrete, and so one must understand the constraints imposed by the operation of sampling the interferogram. To avoid aliasing in an extended spectrum, the spectrum often must be limited with an anti-aliasing low-pass filter that attenuates the undesirable frequencies. If a higher order alias is used, it is essential that both the optical bandwidth for the spectrum and the electronic bandwidth for the noise be limited to that single order, because all aliases contribute to the final spectrum, including the noise. The best way to start interpolation is to increase the number of points in the spectrum. One can do this by increasing the number of points in the interferogram before transforming it. When finding line positions, the application of simple peak-finding algorithms to relatively complex spectra usually benefits from some lighter apodization, so that only the strongest lines are accompanied by a few sidelobes. An apodized spectrum should not be used for finding line. One should always fit the data with a model, even if one needs only line positions.