Spatial dispersion of a single grating
Calculator of spatial dispersion for single grating
Parameter calc.
Program info
Main formulas
References

1. Laser wavelength:  nm 
2. Grating incident angle:  ° 
3. Grating groove density:  lines/mm
4. Grating width:  mm
5. Diffraction order:
6. Focusing lens focal length:  mm



 
This program is used to calculate the spatial dispersion of a laser after passing through a single grating.
Function: calculate diffraction angle, angular resolving power, linear resolving power, spectral resolving power, and the resolved linewidth (FWHM) of a single grating.
1. Grating diffraction angle:
$$\theta = \sin^{-1}(\frac{m\lambda}{d}-\sin\gamma)$$
2. Angular resolving power of a grating:
$${D_{\theta}} =\frac{\delta\theta}{\delta\lambda}=\frac{m}{dcos\theta}$$
3. Linear resolving power of a grating:
$${D_{l}} =f{D_{\theta}}$$
4. Spectral resolving power of a grating:
$$A= \frac{ \lambda}{\delta\lambda}=mN=\frac{ L}{\lambda}(sin\gamma+sin\theta)$$
5. Resolved linewidth (FWHM):
$$\delta\lambda= \frac{\lambda}{A}$$
where γ is the incident angle, θ is the diffraction angle, m is the diffraction order, λ is the wavelength, d is the grating period, f is the focal length of the focusing lens, L is the grating width, and N=L/d is the number of grooves.
[01] Cai Lüzhong et al., Optics, pp. 230-231.