How to make affordable DIY low-res absolute rotatory optical encoders with fibers?
I don't want to have the light source and sensor in the encoder but to use optical fibers to transfer light to and from the encoder to my electronics. However, I'm being told that if there is an air gap between two ends of optical fibers, a lot of light will be lost. I want to know what is the limit? does it depend on the sensor or source or the quality of the fibers?


The limit is that you lose practically all the light.

It depends on the sensor, the source, the quality if of the fibers, how you mount them, and probably a hundred things that I don't know about.

You need to experiment on this one.  I suspect that you'll do much better if you focus the light from and to the fibers, so that it's roughly collimated as it passes through the disk.

You might want to search on "light pipe".


  I do not understand how absolute encoders work. Do they also follow the same rationale of a disk-mask plus light sources-sensors? Is their design simple enough to be built DIY?


Absolute encoders have one track per bit.  If you want "about 10 degrees" that means 5 bits (32 divisions, 11.25 degrees/LSB) or 6 bits (5.625 degrees/LSB).  In general you lay out the tracks in something called a "gray code", which is arranged so that no two bits change state at the same time -- this prevents the erroneous readings that would happen in a normal code (at, for instance, the transition from 'b111111 to 'b000000, where there would be six opportunities for errors, some of them large).


  What light source and sensor should I use to emit light into the fibers and read it back? is there some sort of off-the-shelf sensor and source connected to fibers already available which I can plug into an Arduino for example?


I can't answer this one.  I'd look for LED/lasers and sensors that are pre-mounted to fibers.