Quadrature decoder ideas for glass scales and rotary encoders on Arduino and AVR

Ever wonder how the Heidenhain glass scales, can measure at increments of 0,5 µm? if the graduation on the scale is only 20um? If you come from the digital world, there are four transitions so the minimum should be 4um.

This mystery made me read up on the Heidenhain signals 1VPP or 11 µAPP ( 1VSS, 11 µASS ) These are analog signals, if you read the older literature it becomes clear that photo sensitive devices are used to generate the current, the 1Vpp signals are probably pre-loaded with a 90ohm resistor. 

Vernier scales are similar, so are modulation techniques like QAM, QPSK. With glass scales there is no amplitude or phase modulation on top of the carrier, only two orthogonal signals, the rotational relationship between the two base-band signals (I/Q) translates to position, speed and velocity. 

So what advantages do analog signals have over digital? The states are infinite, limited only by noise. But how to extract infinite states from two orthogonal signals? Run them through an AD converter and calculate the angle., this will work but the system response is limited by conversion rate and calculation performance.

Investigating further I stumbled on CORDIC https://en.wikipedia.org/wiki/CORDIC

With a search for CORDIC Quardrature decoder, I found various other methods of Sine/Cosine to Digital Conversion
http://www.ichaus.de/upload/pdf/WP7en_High-Precision_Interpolation_140124.pdf

  Flash Conversion

 Vector -Tracking Conversion

 SAR Conversion with Sample-and- Hold Stage

 Continuous -Sampling A/D Conversion

Out of pure curiosity, I will implement the continuous sampling conversion with CORDIS lookup on the Arduino, and perhaps try the vector tracking conversion on the Attiny2313

Should this work, I will try to convert my Sino Digital scales to analog and see what accuracy I can achieve. Perhaps even build a Heidenhain scale interface for the Touch DRO Project.

Resources 

CORDIC

1. pico-bootrom
2. /bootrom

/

mufplib.S

https://eprints.soton.ac.uk/267873/1/tcas1_cordic_review.pdf

https://www.mikrocontroller.net/articles/AVR-CORDIC

Linear interpolation

https://www.mikrocontroller.net/articles/AVR_Arithmetik/Sinus_und_Cosinus_(Lineare_Interpolation) 

Fast Sampling on AVR
http://yaab-arduino.blogspot.com/2015/02/fast-sampling-from-analog-input.html

http://wiki.linuxcnc.org/cgi-bin/wiki.pl?ResolverToQuadratureConverter