Grating Resolving Power of Laser Beams with Gaussian Distribution

[mikey1234]

TL;DR Summary

Grating resolving power for Gaussian Beams vs Uniform incidence

All resources I’ve found for grating resolving power assume uniform distribution on the grating and produce airy disks. Resolvance is determined by the Rayleigh criterion where the peak of one wavelength is at the minima of the adjacent one. This definition doesn’t seem applicable for Gaussian laser beams.

How does the grating resolving power of Lamda/(delta Lambda) = mN, where m is the order (assume 1) and N is the number of slits illuminated change for a diffraction limited laser beam with a Gaussian distribution? Let’s say our criterion for resolvance is separating the peaks by wo (1/e^2 width) diameter.

 

[Charles Link]

The resolution formula is used to estimate the resolution of a diffraction grating spectrometer, and there is very little to be gained by trying to do the calculation for a beam with a Gaussian distribution. The resolving power $R=\frac{\lambda}{ \Delta \lambda}=N m$ is a nice simple one, and it would unnecessarily complicate matters to have some function of $w_o$ in this formula.

 

[Gleb1964]

The resolution power for truncated Gaussian beam would only decrease compare to the uniform beam.