This probably moves it out of the realm of an "everyone can do this" thing, but there are also a couple of other approaches that the more advanced and decently funded militaries could use to deal with atmospheric correction. I first heard of tests of these in the late '70s or early '80s.
1. They made a laser that included a phase conjugate mirror such that if you hit the system with some incoming laser light it would greatly amplify it and send it back the way it came.
To use this as a weapon, you'd point it at your target, hit the target with a guide laser, some of that light reflects off the target and enters your phase conjugate laser, and your phase conjugate laser sends a much stronger beam back.
As long as your target is near enough that atmospheric conditions between your weapon and the target have not had a chance to change over the time of a speed of light round trip, all the atmospheric distortions that dispersed the guide laser's reflection to the weapon serve to concentrate the weapon's beam on the target.
2. You can make an energy weapon that uses a phased array of radiators to direct the beam. You aim it in the general direction of your target.
Then you can start varying the phase of each radiator, and you analyze the reflections from the target. If a given radiator happens to be at the right phase so that it is contributing toward producing a maximum or a minimum at the target you won't see much variation in the reflection at the frequency you are varying that radiator's phase. If the phase of the radiator is such that it is in between, you'll see more variation at that frequency in the reflection. (A graph of the radiator's contribution versus phase looks like a sine wave. When it is maximally contributing it is at the peak, when not it is near a zero. Near a peak wiggling side to side doesn't change much because a sine wave is flatter there. When near a zero the sine wave is steep so a little side to side wiggle changes a lot).
Use a different frequency for the phase variation of each radiator, feed what you see reflected into a Fourier analyzer, and use the relative strengths of what you see at the variation frequencies as feedback to adjust the radiator phases, and you can get the array to quickly adjust to by focused on and stay on the target.
They were playing around with a small one of these at Hughes Research Laboratories in the late '70s. I know because the professor [1] who taught APh 23 (Demonstration Lectures in Optics) at Caltech when I took it in the '79-80 school year was also a researcher at Hughes working on it, and one class he showed us a video of a test.
It was pretty cool. It started with a black background and a bunch of blobs of light moving around as the system has nothing to focus on. Then someone dangled a small metal model of the starship Enterprise in front of the background, and all the blobs instantly converged on it.
[1] https://en.wikipedia.org/wiki/William_B._Bridges