Two major classes of instrument use interferometry not for spatial resolution, but for spectral discrimination. These are the Fabry-Perot interferometer and the Fourier-Transform Spectrometer. Both rely on interference between parallel partially reflecting plates to modulate the source spectrum (as opposed to the spatial modulation discussed earlier).
A Fabry-Perot etalon consists of two optically flat plates with variable (and accurately commandable) spacing. Reflection from the inner faces gives opportunities for interference between radiation on various numbers of reflections. The radiation passes through the etalon only for a set of narrow wavelength bands satisfying λ = (2 t μ cos θ) / m where the plate spacing is t, μ the refractive index of the material between the plates (i.e. close to 1 for air), and m is an integer. The number of reflections depends on the reflectivity of the plates; the wavelength range narrows for higher reflectivity since m grows. This is shown in fig. 4.1.17 of the text. So far we have an expensive (and completely tunable) narrow-band filter. However, spectroscopy can be used with a slit and a cross-disperser, an element of small angular dispersion that separates the various spectral orders m perpendicular to their dispersions. Overlap of orders can be a problem. The most frequent use of a Fabry-Perot etalon is in imaging spectroscopy; the spacing between plates (and thus the transmitted wavelength) is varied systematically, yielding a data cube of two spatial and one spectral dimension. A blocking filter or second coarser etalon must be used to prevent light from entering in more than one peak. The separation of peak wavelengths is known as the free spectral range, the range over which the device is useful, and the ratio of this range to the FWHM of the transmitted peaks is the finesse, a measure of spectral resolution. The advantage of such etalons is that a very high wavelength resolution, as high as λ / Δ λ ~ 107, can be reached in a reasonably compact way. Also, they are excellent for mapping velocity fields, combining the spatial coverage of narrow-band imaging with spectrometer-like spectral resolution.
Data reduction for these systems can be complicated by the fact that constructive interference occurs at a different wavelength for various incident angles, giving a mapping of monochromatic light into a paraboloid within the data cube. Rebinning the data cube can be so time-consuming that it is just as frequent to either use only the small region at the apex, where the mapping is nearly constant, or to model the results and then to distort the model appropriately. These devices receive more astronomical use than the text suggests.
The Fourier-transform spectrometer has been described by one of its proponents (Jim Brault, whose brain functioned in the Fourier domain) as the literal expression in glass and steel of the Fourier equation. Instead of spatial information, it seeks to recover spectral information integrated over the entrance aperture. A parallel beam enters an etalon, and the transmitted light is measured. But this time, the transmitted intensity is continuously measured while the etalon spacing is swept back and forth over a wide range. The incident spectrum may be obtained by an inverse Fourier transform. This technique has found wide use in the infrared, where a single detector can work faster than with a narrow-band filter and single measurements because the whole spectrum is being measured at once, albeit in a complicated way. This offers a multiplex advantage, though the noise and background effects are not trivial to evaluate, and for years was the only way to obtain high spectral resolution in the infrared.
We also encounter interference, in the form of diffraction patterns, in analyzing the results of occultation measurements. Our planet is thoughtfully provided with a large satellite in a rather slow orbit, which at one time or another covers objects over more than 10% of the celestial sphere (though surprisingly little at a given time). Its limb is an adequate knife-edge covering and uncovering bits of sky, which we may use to look for close double stars and measure stellar diameters. This works because, of course, the action takes place beyond the atmosphere and we only need measure an intensity at a given time; we don't need spatial information. Considering a star as a point source shining past the lunar knife-edge, its illumination pattern on the Earth's surface will be described by Fresnel diffraction, giving a progressively damped pattern of fringes as we move into the lunar shadow. From a given point, this translates into a time series of fringes as the combined lunar and terrestrial motions sweep the lunar limb across the star. Double or resolved structure will reveal itself as attenuation of the fringe pattern, when observed with a telescope small compared to the fringe spacing (about 12 meters for visible light at the lunar distance).
The practical problems of observing lunar occultations are significant - you need clear whether at a specific time and place in order to have any result at all, one needs high time resolution, there is moonlight to contend with, and for reappearances you have to be looking in exactly the right place beforehand. Thus occultations at the dark limb are greatly to be treasured.
In reducing an occultation data stream, the diffraction pattern can be compared with that of a point source (in this case, smaller than 0.002 arcsecond). A mismatch indicates resolved structure. Double objects will often give beat patterns, while a resolved star damps out the oscillations as different parts of the stellar surface sit in different phases of the fringe pattern. One then fits a model varying diameter and, for example, limb darkening, to fit the data. Multiple occultations with different directions of lunar motion can yield crude 2-dimensional models.
Planetary occultations are also observed widely, though now the aim is to study the foregound body using a background point source as probe. Since the distances are much larger, diffraction is seldom important. This has been used to probe the atmospheres of Mars, Jupiter, and Uranus, study fine structure in the rings of Saturn, seek sizes and shapes of minor planets, and discover rings around Uranus and Neptune. Extension to radio wavelengths is a free by-product of many planetary probes, since we may use the probe's transmitter as a well-defined background source to measure propagation through successively deeper lines of sight in an atmosphere. Occultations have given significant information on minor planets, providing direct size and shape indications as a crucial check on radiometric techniques.
Occultations have been valuable in other wavelength regimes. This is how the first accurate position and radio structure were measured for the bright quasar 3C 273, and how X-ray emission from the Crab Nebula was confirmed. The EXOSAT X-ray satellite was placed in a highly elongated orbit so as to be able to engineer occultations over much of the sky (though ironically more interesting things were found, and the technique was seldom used). Strong gamma-ray source can be identified from orbit even using detectors with no spatial resolution at all, by noting when there are step functions in the total count rate indicating rising or setting of sources across the Earth's limb.
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