Today I found some time to do some further tests regarding the idea of a printable optical potentiometer.
I tried to print gradients on some overhead sheets I had laying around and the result was this:
As you can see the average error is 13mm on a distance of 23 cm. That´s absolutely too much and if you calculate how much error it would be for an angular sensor then you get an average error of 21 degree.
To explain how I made the measurements: I wrote a Qt program which produced the gradient together with a millimeter raster. then I printed it out with my HP Officejet 5605z All-in-One with the maximum possible resolution and finally I used the millimeter raster to do a measurement every centimeter. The schematic of the measurement circuit
and the sensor.
As it seems the nonlinear curve that I got when I did the tests with the paper was caused by the paper, cause this time I got relatively linear values without changing the gradient.
I think if I would have access to a better printer I could improve the results but the precision is so bad that I don´t think that you could get acceptable results with this kind of sensor without using any special materials/printers. So for the use in robots it will be better to simply use the approved quadrature sensors.