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Spectrometer Resolution

Rayleigh criterion

The spectral resolution or resolving power of a spectrograph is a measure of its ability to resolve features in the electromagnetic spectrum. The resolving power is understood as the inverse relative spectral resolution, e.g. the wavelength divided by the smallest wavelength difference that can be distinguished by the spectrograph. When relating to spectrometry, the term chromatic resolving power is often used.

The image a distant point source forms at the focal plane of an optical telescope lens or camera lens is actually a Fraunhofer diffraction pattern. The lens opening plays the role of the aperture. The image formed by an extended composite source is therefore a superposition of many airy disks. The resolution of a detail in the image therefore depends on the size of the individual Airy disks. If D is the diameter of the lens opening, then the angular radius of an Airy disk is approximately 1.22 l/D. This is also the approximate minimum angular seperation between two equal point sources such that they can be just barely resolved, because at this angular separation the central maximum of the image of one source falls on the first minimum of the other. This condition for optical resolution is known as the Rayleigh criterion.

In the case of a rectangular aperture, of width b, such as the entrance and exit slits or a spectrograph, the minimum angular separation according to the Rayleigh criterion is just l/b. The intensity of the saddle point is 8/p2=0.81 times the maximum intensity.

For instruments based on multiple beam interferences, such as the Fabry-Perot interferometer, the Taylor criterion is more convenient to use, because there are no fringes used for the definition of the local minimum. According to this convention, two equal lines are considered resolved if the individual curves cross at the half intensity, point or either line alone.

The two conventions are often not clearly distinguished, and many people use the Taylor criterion still referring to Lord Raleigh. In real life, the capability of distinguishing between to separate spectral feature depends not only on their separation, but also on the signal to noise ratio. For noisy signals, the "real" resolution may be much worse then the Rayleigh or Taylor criteria would predict. If the signal to noise ratio is high, data processing technique may allow separating two spectral features much closer than their Full Width at Half Maximum (FWHM). The latter statement is particularly true more information on the expected line shapes is available than just the experimental results.