I wonder if the x4 resolution of a quadrature encoder could be doubled once again, by adding a 3rd emitter/receiver pair? Instead of quadrature it would be... octacature? Leave existing pair 'A' in its original place, adjust pair 'B' so that it rises/falls 60 degrees after pair 'A' instead of 90 degrees. Then add in the new pair 'C' 60 degrees after 'B'.I assume you already know how an incremental photo LED encoder/scale versions work?
The lines are photo etched on glass and two photo leds detect two lines 90° apart (quadrature) the resolution is increased by typically squaring up and incrementing by 4, i.e. reading all four edges.
The initial detection results in a sine wave, where this can also be used to calculate the co-tangent angles for very fine resolution and absolute encoding.
Or heck while we're at it, let's double it yet again by adding two sensor pairs. Leave the original 'A' and 'B' sensors alone physically, but rename 'B' to 'C' and add a new sensor 'B' 45 degrees between 'A' and 'C' and add a new sensor 'D' 45 degrees after 'C'.
You could maybe get 131,072 counts per rev out of a common 8192 PPR incremental encoder (8192 × 4 × 2 × 2). +/- 9.9 arc-second resolution for just a couple hundred bucks?