Is it possible to get higher resolutions by using high resolution encoders and custom firmware? So I was thinking about is it possible to reach higher resolutions with encoders and DC motors? I found a cheap high-resolution magnetic encoder that can be used along with a DC motor to access higher resolutions. The encoder has 8192 PPR meaning that it can measure up to 0.04 degrees if I have correctly calculated. So if for a stepper with 0.9 step angle and no micro-stepping with 20 tooth pulley and 2mm belt, the steps/mm is 10, it means every 9 degrees with this pulley and belt setup makes 1mm and so 0.04 degree makes 0.004mm movement that is about 4 microns. Is this correct and possible? If so, why don't big companies use this method?
Link to the encoder:
RLS RMB20 rotary magnetic encoder module
The mistake in your reasoning is assuming no microstepping. Most 3D printers use 16 microsteps, and in my experience with both cheap A4988 drivers and nice TMC2209 drivers, microstepping is quite accurate. As part of an answer to a question I asked, you can see a test print showing single-microstep features. My motors have 1.8° step angle, yielding 3200 steps per rotation at 16 microsteps, or 12.5 microns of linear movement per microstep. With 0.9° step angle you could get it down to half that, and you could probably halve it again going to 32 microsteps.
Even if you can't get it as good as your 4 microns with stepper motors though, at 12.5 micron positioning resolution you're already to the point where extrusion error is going to play a much bigger role in dimensional accuracy than toolhead positioning error does. Going past that with FDM requires high resolution extruder axis movement, closed-loop control with a precise filament diameter sensor, direct drive with minimal distance between the extruder gear and nozzle, etc.