I think you forgot a factor of two again -- the spot should move 1.13 inches if the mirror rotates 1/10,000 of a revolution. No problem seeing that with a 1.5 inch spot.
I like the spotting scope idea too -- tape a scale to the side of a spotting scope which has a reticle and view the scale through the rotating mirror, and you've got a cheap autoreflection alignment scope. But to get a clear bright image with the scope, you need a good mirror that is about the size of the scope objective. The laser method has lower resolution but can use a much smaller mirror.
Ummmmmm.... well, I'm no physics major here, but if I'm not mistaken, it is the "angle of incidence" that "doubles". So every time the mirror rotates at all, one "step" or more, unless the laser position goes "with it" (so that angle DOES NOT change), then the angle the laser beam strikes the mirrored surface the will change, and it is THAT angle that "doubles" the laser-beam deflection. That would mean some relatively complicated method of figuring the amount the angular change of the mirror, and how much the "spot" should move at the 132 feet distant surface. Wow!!
Try it quickly, just for fun....mount the mirror fixed to something, and fasten the laser to a moveable/swingable "radius bar" with the "centre" of that radius at the mirror, and with the laser aligned down the radius bar to strike the mirror. Create a surface at approx the same distance as the radius of the laser, and starting at a point roughly perpendicular to the mirror/ turn on the laser and note the point it strikes the "wall". Move/swing the radius bar a certain distance, and note the position it intersects the wall. Move the radius bar again the exact same distance, and I believe you will find that the point of intersection distance "doubled" the distance of the first move, and the next move would double the second.
Even just thinking about this.... imagine that you shone a light at a mirrored surface directly in front of you and perpendicular to you. The reflected light would come right back at you. Rotate the mirror only 45 degrees, and the light will reflect a right angle. Rotate further to almost 90 degrees, and the light will be reflected to almost dead away from you, or near 180 degrees. Pool ball off the cushion idea.
Brian, I just drew the setup. With the laser hitting the center of the mirror. I drew it with the laser origin the same and just rotated the mirror. So the laser is stationary but the mirror was drawn at two angles. The difference beteween the laser included angles appears to be twice the angular rotation of the mirror. Try it and see if you get the same thing. Since the laser is shining on a flat target there will be some error because the radius will be changing with rotation. But since the measurement is only going to be, at the most, 1/1000 of a full rotation, or .36 degrees, it won't matter much. Eric
It is almost impossible to get a belt or friction drive to work with ZERO backlash. Reversal of rotation generates an an error of twice the compressibility of the drive system and this may well be enough to account for your error.
Try bolting a rigid arm to your encoder a few inches long and spring loading this against a solidly anchored stop. Insertion and removal of feeler gauges between the arm and the stop will soon show whether your .0009 error is inherent in the encoder or your friction drive.
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