Under water 3d mapping of a pool

I want to build a device that can take a 3d "image" of a pool. I don't want an "image" as in a pictorial image but rather a data representation (with the end goal of outputting it in a document that I can load into auto cad).

Obviously this is a relatively large problem domain and I don't really have anything hammered out yet. I did a quick search and it looks like 3d mapping under water isn't a simple process. A heuristic search didn't really give me any solid tutorials.

If anyone has any ideas about a project like this please let me know. I would love if a tutorial existed, but if not a list of products (daughterboards (aka shields), i/o devices, etc) and programs (open source frameworks so I don't have code program this from scratch, etc). Also maybe some of the mathematical concepts that would be necessary for a project like this.

Sonar, lasers, cameras? Should it float? Should it sink? Should it be above the pool, inside the pool, etc? Should it travel the perimeter in the water?

Not sure what the superior design concept would be. Also... waterproof.

I have a background in mathematics and some knowledge of the domain (pools) which I'm hoping will help me along this process.

Thanks in advance!

Sonar, lasers, cameras? Should it float? Should it sink? Should it be above the pool, inside the pool, etc? Should it travel the perimeter in the water?

Have you developed a bot that will map in a room? If not, then that might be a first step for you.

Not sure what the superior design concept would be.

Synthetic aperture sonar?

How large (area) and how deep is the "pool" and what accuracy do you require?