Unlike NET, NEAT has significance only in terms of viewing a specific source, and is a function of source temperature, Ts. If the target has an emissivity of ev at wave number v cm-1 then
It follows that, in principle, the NET and the NEAT have the same value at Ts = 0 K, for a blackbody source with ev = 1.
FlG. 9.13. Conceptual grating spectrometer layout, showing entrance and exit optics and associated optics.
In summary, in much the same way that NEP describes the performance of a particular detector and D* describes a detector type or family (§9.2), NET describes the performance of an instrument or system, while SNR and NEAT both characterize the quality of a specific measurement made using that system.
Many of the instruments used for climate measurements are essentially infra-red radiometers with the properties described above. Most of them have refinements of one kind or another, which will be described when we discuss specific sensors and measurement programmes in the next chapter. For high spectral resolution work, however, spectrometers using gratings or prisms and interferometers, usually of the Fabry-Perot or Michelson type, are required. These are more complex devices in general than radiometers, and, although the same principles apply, performance limitations are more acute, especially in geophysical applications, including climate studies, where distant observations of relatively cool sources are often involved.
Spectrometers are categorized by the wavelength-selective element and the means by which it is tuned or scanned over a range of wavelengths. The most familiar examples are those employing slits in conjunction with gratings or prisms, which disperse the radiation and then select the desired region geometrically. These are generally simpler and more robust than slitless interferometric devices such as the Michelson interferometer and its derivatives, although the latter offer a significantly higher throughput of energy and are capable of higher spectral resolution. The main elements of a simple slit-plus-grating spectrometer are shown in Fig. 9.13. The dispersive element is represented as working in transmission, as some gratings and all prisms do, but in reality it is more likely to be a reflecting grating as these have fewer intrinsic losses and a wider wavelength response. For the same reason, the lenses used to collimate the beam before incidence on the grating, and to focus it onto the output slit in front of the detector, are often in reality conic-section mirrors. The arrangement most commonly used in laboratory infra-red spectrometers has a single detector, and the grating tilts to scan in wavelength. These systems may have uncooled detectors for convenience and cheapness.
A commercial device of this type, developed for field research and applications by the oil and mineral exploration industry, uses a dual-beam approach in which the target is continuously compared to a reference source, using the same optical system, with a 200-Hz tuning-fork chopper and a sophisticated control and data-logging system. Three gratings and two thermoelectrically cooled detectors, silicon for the short wavelengths and lead sulphide for the longer, give a spectral range from 0.35 to 3.0 ¡m. The gratings and order-sorting filters are switched automatically by stepper motors under microprocessor control, to give a smooth scan over the range, while the operator trains the field of view onto the target of interest using a telescopic gunsight type of arrangement. The whole device weighs less than 16 kg including batteries for one day of operation.
Optimum performance of a dispersive spectrometer, in terms of signal-to-noise ratio for a given resolving power AA/A, is obtained when the entrance and exit slit widths are equal. If the design is free of effects due to diffraction or aberrations, then the instrumental transmission function e(A) is a triangle of width (meaning full width at the half-maximum power points) AA.
The origin of the triangular shape can be understood by imagining the passage of quasi-monochromatic radiation through an infinitely narrow entrance slit. This produces a uniform response across the finite exit slit, corresponding to a rectangular instrument function. If the actual entrance slit is now seen as being made up of the sum of a large number of narrow slits, the sum of the transmission functions is triangular.
The flux passing through the exit slit is given by
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