A profilometer (I have one made by Mitutoyo) is what is normally used to measure deviations in surface finish. It operated somewhat like a phonograph needle and traces the surface and the electronic signals are graphed and measured in different terms, depending on the specifications.
As John and Bill said, they are rather expensive, but a sample plate with various standard specified finish examples (16, 32, 63, 125, 250, 500 etc.) can be had pretty reasonably. Some also give examples of various machining methods. Turning doesn't "look" or feel the same as milling or grinding, so you can get a fingernail and eye comparison with what you need.
Edit to add:
An old timer's trick that might or might not help. I know you are looking for a 32 finish, but rarely is a better finish objectionable. I have a story about that, sometime though. A 16 finish will barely, if at all, pick up a #2b pencil lead if you try to draw a line perpendicular to the lay of the cut, whatever cutting method is employed. So if you can't get a line on it with a pencil, it's probably better than you need at a 32. I suppose experiments could be done with harder and softer leads, like with hardness files, to get a close idea, but at least this is better than just a guess.