Diffraction grating For a given optical bench and array detector, the diffraction grating can be selected to provide additional flexibility on spectral coverage, spectral resolution, and etc. of the spectrometer. The three important parameters that determine the dispersion property of a diffraction grating include groove density (g), grating width (Wg), and blaze wavelength (lB). Based on the grating equation, the angular dispersion of a diffraction grating can be expressed as:           db/dl = 10-6×k×g/cos(b)          (Equation 4-1) where db/dl is the angular dispersion in rad/nm; g is the groove density in grooves/mm; b is the diffraction angle in rad; k is the diffraction order. For a given optical bench, the linear dispersion will be:          dl/dx = 106× cos(b)/(k×g×F)          (Equation 4-2) where dl/dx is the linear dispersion in nm/mm; F is the focal length of the focusing mirror in mm (see Figure 4-1). When the spectral coverage range (Dl) and the detector width, Wd (detector width) = n (pixel number) * Wp (pixel width), are determined based on the design specifications, the required linear dispersion of the optical bench can be estimated as:           dl/dx = Dl/Wd          (Equation 4-3) Thus the groove density (g) of the diffraction grating and the focal length (F) of the optical bench can be designed according to equations 4-2 and 4-3. It should be noted that the longest wavelength that will be diffracted by a grating is 2×d, where d is the period of the grating, d = 1/g. This places a long wavelength limit on the spectral range of the grating. For NIR applications, this long wavelength limit may restrict the maximum allowed groove density for the grating. The minimum wavelength difference that can be resolved by the diffraction grating is given by:           dl = l/(k×g×Wg) =  l/(k×N) where N is the total number of grooves on the diffraction grating. Generally, the resolving power of the grating is much higher than the spectral resolution requirement of the spectrometer (dl << dl), where dl  is set by the pixel number of the array detector (see equation 3-1). When the required wavelength coverage is broad, i.e. lmax > 2×lmin, optical signals in wavelengths from different diffraction orders may end up at the same spatial position on the detector plane which can be evident from the described grating equation. In this case, a linear variable filter (LVF) option is provided for the spectrometer in light path to filter out the unwanted order contributions, or perform “order sorting”. As we discussed before, there are two types of diffraction gratings, i.e. ruled and holographic gratings. The ruled grating exhibits much more stray light due to surface imperfections and other errors in the groove period.  Thus for spectroscopic applications (such as UV spectroscopy) where the detector response is poorer and optics are suffering more loss, holographic gratings are generally selected to improve the stray light performance of the spectrometer. Gratings can be blazed to provide high diffraction efficiency (>85%) at a specific wavelength, i.e. a blaze wavelength (lB). As a rule of thumb, the grating efficiency will decrease by 50% at 0.6×lB and 1.8×lB.  This sets a limit on the spectral coverage of the spectrometer. Generally, the blaze wavelength of the diffraction grating is biased toward the weak side of the spectral range to improve the overall SNR of the spectrometer. Return to Econic Product page