Diffraction-limited grating spectrometer

This is the well-known formula that states that the resolution of a diffraction grating increases (and Jv decreases) with increasing order n of diffraction and number N of lines in the grating >. For the case of three lines, or for any other spectrum, the intensity is measured with a grating spectrometer as fimction of yd (for several orders of diffraction) (see Fig. 5). The data obtained in this way are then easily converted to / (A) or I ( ) and the problem of determining the spectral distribution I ( ) is solved. It should be noted that the linewidth obtained (see Fig. 5) is influenced by the limited resolution of the instrument and that the line-widths of the three laser lines are assumed to be actually much smaller. In other words, we have been discussing the properties of the instrument line-shape function of a diffraction grating. 

In order for a grating spectrometer to achieve its ultimate resolution it must be used at the diffraction limit set by Euj. (5.7.8). This requires that the range of incidence angles at the grating be very small, which in turn limits the width of the entrance slit and, consequently, the angular size of the object that can be observed. Because planets and many other objects are extended sources, it is often necessary to observe fields-of-view that are larger than the diffraction limit. Under these conditions the resolution is degraded by the ratio of the size of the actual field-of-view or slit width to the diffraction limit... 

In contrast, diode array based instruments, popular as relatively low cost spectrometers, have a reverse arrangement by having the dispersion of wavelengths post-sample by a dispersive optic (e.g. a diffraction grating) which irradiates the diode array detector with the spectrum across its elements. Whilst commercially available diode array instruments are invariably of lower optical quality than the best scanning instruments, and are limited by their spectral resolution through the number of elements in their array, they do offer the advantage of rapid spectral acquisition as the complete... 

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