Calibrating the Latitudinal Angle.

The scanning mirror controls the latitudinal angle ($\phi$), and we read its position from the attached 4096-position shaft encoder. Since we are typically taking 5,000-10,000 samples per revolution, it is clear that we must interpolate the shaft position, since subsequent readings may report identical shaft positions.

To do this, we assume constant motor speed over the time required to collect a 1K buffer of samples. It is not possible to know exactly when the encoder moves from one position to the next, but since we have a large number of samples, we can estimate where the transitions occur by performing a least-squares line fit using the points around the transitions.