As a point of interest, all optical encoders and scales of this type, TTL included, start off with an optically detected signal that is sine wave in nature,
All optical encoders?! Of what type? Those I see typically have lines on the disk.
In these Heidenhain and similar scales or encoders, the arc tangent function is used to produce a high resolution absolute encoder count from the sine/cosine signal.
Don't think "absolute" is applicable to scales. In a rotary encoder I could see how they could possibly do this by matching a full sin/cos cycle to a single rotation, although I have never seen this. Usually a sine/cos encoder is just treated as an incremental encoder. I am not familiar with Heidenhain encoders in particular though.