Diffraction-limited grating

This function is shown in Figure 2.7. As we saw from the discussion of the Rayleigh criterion of resolution, this is also the shape of the ILS function of a diffraction-limited grating monochromator. It can be seen that the amplitude of the sidelobes has been considerably reduced from that of the sidelobes for the sine function. Suppression of the magnitude of these oscillations is known as apodization, and functions such as Ai(S), which weight the interferogram for this purpose, are known as apodization functions. 

The geometrical condition for a grating to serve as a neat polarizer imposes the following requirement the grating line spacing must lie under the diffraction limit for the shortest wavelength Aj/, of the used spectral range. This could easily be seen from the diffraction equation (Schroder, 1987), compare Eq. 3.1-13,... 

Figure 13.32 The diffraction orders associated with coherent illumination of a grating mask, illustrating the condition for minimum diffraction-limited resolution. (Reprinted...

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... 

The analogy of a crystal surface as a diffraction grating also suggests how surface defects can be probed. Recall that for a diffraction grating the width of a diffracted peak will decrease as the number of lines in the grating is increased. This observation can be used in interpreting the shape of RHEED spots. Defects on a crystal surfr.ee can limit the number of atomic rows that scatter coherendy, thereby broadening RHEED features. 

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