Free Spectral Range

It can be seen from the grating equation (2)' that when light of wavelength λ enters a grating, it is diffracted in many different directions corresponding to different values of m. As m only takes integral values, the diffraction angle β will take discrete values. For this reason, as shown in Fig. 4, when light with a wide range of wavelengths is directed at a grating, neighboring orders of spectra may partially overlap.
The range for which there is no overlapping is called the grating's "free spectral range." If the following equation is satisfied, mth-order light with wavelengths in the range λ1 to λ2 can be used without overlapping:

Fig. 4 Grating's Free Spectral Range

Fig. 4 Grating's Free Spectral Range

 

 For example, when using first-order light with wavelengths greater than or equal to 350 nm, wavelengths up to 700 nm can be used without overlapping. The range 350 to 700 nm is the free spectral range. When using second-order light, the free spectral range is from 350 to 525 nm. As briefly described in the section on grating equations, however, it is necessary to use an appropriate groove density for light of wavelength λ2 at long-wavelength side, in this case 700 nm, to be obtained as diffracted one.
If the applied wavelength region is wider than the free spectral range, spectra corresponding to the unrequired orders must be removed from the overlapping region. For example, when using first-order light with wavelengths in the range 350 to 800 nm, a filter is used to cut the overlapping second-order light with wavelengths in the range 350 nm to 400 nm, in other words, to cut light with wavelengths of 400 nm or less. It is also possible to deal with overlapping by changing detectors.