Degree wheel / measure degrees with precision?

Hey guys im brand new here but I am looking for some advice.
As a machinist I'm looking to do interesting things with my lathe.

I'd like to measure the position of my lathe chuck to make degree wheels.
Their is an encoder for rpm that may be feasible already on the lathe.
I'm suspecting that 2-3 sensors would be needed at minimum to get the precision I'm looking for (1° @ 1/2"diam). Or would that compound error?
I have an internal location free of oil etc.. (where the rpm optical sensor is)

Zeroing is not necessarily required but would be very helpful.
I will be making marks by dragging a knife across the surface and turning by hand.
Having an intelligible readout on a single line display with zer/reset would be nice too. (4 digits 355.5°)
(starting point is usually non-critical or easily findable)

Any suggestions would be deeply appreciated

Thankyou for your time!

P. S. Im currently using yuri's android DRO via Bluetooth and have a spare mega & nano.

CompoundRest10DegreeSet.jpg

you can get any accuracy you want by adding gears between the axis and the rotary encoder.

think this is a possible candidate - http://nl.mouser.com/new/ams/ams-as5145-sensor/ - (never used one)
4096 steps for one rotation

in fact you can go to the extreme with tools like - Encoder legacy products -

alternative might be a digital compass ?

Thankyou for the link and information!
I will see what they recommend as machine disassembly is not possible.
Balance and alignment cannot be modified.

Im Thinking i may need to fab a 2 piece collar and in-set multiple (4) magnets to help maintain balance.

Hmmmmm

Its ooking like I need to mount an optical sensor mid shaft... Any suggestions on improving accuracy?

I need to mark 1° lines and therefore need measurement accuracy of 0.01°-0.05° to be certain that my intended markings can be used as a reference.

I will also need to be able to input my outside diameter of my part to ensure my markings are correct.

Ill be making disks up to 1" thick and diameters anywhere between 1/2" - 6.00"

Could i use multiple encoders and compare their quadrature with programming?