Grating Resolution

If there are two spectrum lines corresponding to two neighboring wavelengths λ and λ+Δλ, the resolution is a measure of the extent to which Δλ can be reduced while still being able to distinguish between the lines. In general, the grating's diffracted light has a limited width defined by the diffraction limit. According to the "Rayleigh criterion", it is defined to be the limit for which resolution is possible when the first diffraction minimum for wavelength λ coincides with a maximum for wavelength λ+Δλ as shown in Fig. 3. In this case, the resolution λ/Δλ for a grating width of W is given by the following:

Fig. 3 Grating Resolution

Here, N × W is the total number of grooves in the grating. When the grating is actually used together with other optical elements (e.g., when incorporated in a spectrometer), however, aberrations and imperfections in other elements (e.g., lenses and mirrors) and factors related to the light source or the size of the slits may result in even wider spectral lines. This means that the minimum wavelength difference Δλ that can be resolved will be larger, and, in general, the resolution for the optical system will be lower than that for the gratings only defined by equation (6).