I am trying to figure out how to approximate the spot size of a laser beam that is focused using a microscope objective where the size of the laser beam is smaller than the diameter of the objective. I have tried googling and reading various other questions online but still haven't been able to cobble a coherent plan together. From this excellent response I've been able to cobble together an understanding that the working distance and the focal length of a lens are different. But I'm still at sea as to how I convert the information I'm given about an objective, e.g. magnification, NA and focal length to spot size. Would it be sufficient to simply treat an objective as a simple optic with the focal length given by the manufacturer and then use something like this spot size calculator to figure out the focused size? If not, would someone mind walking me through the steps to approximate (doesn't need to be exact, back of an envelope is great) spot size for a $5 \;\text{mm}$ well-collimated beam that is focused using this objective?
[Physics] How to calculate spot size of a laser focused through a microscope objective
laserlensesmicroscopyopticsreflection
Best Answer
The spot size calculator is just what you need. Assuming your laser has a TEM$00$ Gaussian beam (the most common and desirable beam cross section), the math behind it is very simple. $w = 4\lambda f/\pi D$.
The calculator gives the spot diameter assuming your optics are perfect. A lens as expensive as the one you picked should be pretty good. You might investigate cheaper alternatives. You only need one wavelength. Is that lens optimized over the visible wavelengths? You don't need to worry about off axis aberrations. Spherical aberration is your primary concern.
See Cross-sectional area of a Gaussian beam of particles for more about the nature of Gaussian beams. There is a discussion of lasers.
Also see Best collimation at focal point of lens?.