Algodoo

This is a different optical encoder from what I'm used to. The ones that I have used had a flat transparent disk with lines scribed or silk-screened into it. Some were incremental and some were absolute, depending on the application. Anyhow, this is a very interesting demonstration, and I'm surprised that you were able to achieve < 1 microrad resolution!

I'm familiar with rotary encoders. I've read that indexing tables can be checked with a polygon mirror. I don't know if any commercial encoders are made this way. I made the encoder as a mathematical exercise to see if I could do it.

The accuracy of this scene is good over one revolution, but you can see the error creep in over many revolutions. For example, starting at angle = 0, and then rotating exactly 10 revolutions (stopping at angle = 0) the actual and measured angles show 62.831852 which is slightly less than 2pi*10 (62.2831853). I suspect that may be caused by floating point errors in the angle calculation. What do you think?

Q: Is the 1 urad difference caused by floating point errors?

A: I don't know. The 1 urad difference is within the measurement variation. The design minimizes cumulative error. It originally had a cumulative error of 1 urad/rad which would amount to 63 urad at 20*pi. There is a problem with Algodoo. Entering 20.0 * math.pi in the console yields 62.831856 when the true value is 62.831853.

The error could be floating point error, polygon form error, polygon centering error, polygon angle offset error, target position error, target angle error, or laser angle error.

P.S. There appears to be a resolution limitation equal to 6.1E-8 * angle.