Regarding your point about the two transparent strips: they'd be 180⁰ out-of-phase and directly atop of one another? Or would they have an angular offset wrt one another instead? I'm just not sure how the light sensor and light source would be arranged with respect to those colaminated strips. I do get the point about the viewing angle limitations, though. (Super-cool sidebar: I just learned there are optical encoders that use either of the Moiré effect or the Lau effect to make optical encoders that can track position in two dimensions simultaneously.)

The operating principles of my original prototype [0] needed at least some degree of precision in the mechanical components because I had actual mechanically interfacing/interlocking parts, unlike a CNC/laser/inkjet where the head is effectively traveling "unobstructed" in free air (in the case of a CNC, creating its own void to "float" in as it goes along). There were two separate positions that needed to be tracked, the linear position (this discussion) and rotary position (for which a basic rotary optical encoder or a servo could be used).

The design of the prototype itself (machining issues aside) was sufficient for its time (late '00s) where it would have taken the place of a (then) $10-25k braille reader PC attachment, offering more characters while being available for orders of magnitude less but the world has changed so drastically in such a short time that I've had to rethink the design to be less of a PC attachment and more of a standalone "braille eReader" sort of thing, significantly complicating the mechanics and increasing the precision machining requirements. It would be a "page" composed of multiple such braille reader rows, belt-driven and either (somehow) individually drivable so one motor could drive all the rows or (preferably, if the optical encoder BOM costs could be driven down cheap enough) with a separate motor per row allowing for faster "page refreshes" (esp. important because it takes ~no time at all for a user to finish a line of text).

Here the complication becomes switching from internally actuated to externally actuated "braille discs" in a way that allows manipulating each "cell" sequentially with a drive head that moves from the start of line to the end — but also leaves the cells in an immobile position so they're not free floating and don't change when a user glides his or her finger over them to any degree in the y-axis (instead of purely in the x-axis). Additionally the size of the optical encoder element becomes an issue because there is simply not much room to cram things between each row of braille text.

My first thought to allow me to solve all these in one go was to mount each braille disc on an "electromagnetic clutch" of sorts, but I was left aghast at the price of those -- and none were miniature enough for my needs. I then tried to go old-school and use an arrangement of actual miniature magnets embedded into each braille disc so they would maintain their position until externally actuated with enough torque to overcome the magnetic inertia, but failed to prototype that with sufficient precision and couldn't find magnets that would hold strongly enough while being small enough to embed in a braille disc (and forget obtaining them within budget, at least at retail values).

Had (and still have) other ideas but the time/cost difficulties in prototyping and the limitations on mechanical tolerances of the available prototyping methods really put a damper on things.

[0]: https://patents.google.com/patent/US20130203022A1/en