Sinusoidal signals to quadrature signal calcs?

Picked up a RSF MSA 6701 470mm linear encoder the other day for 20 bucks for placing a encoder on the knee of the Bridgeport boss5. I believe the knee will be W axis. I was hoping I could use the encoder as is but no the case. The unit output a sinusoidal signals 7-16 µApp which needs to be converted to Quadrature signals for the Mesa 7i77.

Linear encoder specs (Part number changes to MSA 670.13 in new number system)
Encoder MSA 670.13
grating pitch 20 µm
accuracy ±5 µm/m
RI K3: 105 mm from left and 455 mm from left
supply: +5 V
output: sinusoidal signals 7-16 µApp
CC 691: K1, 0,49 m uhf-cable, connector LD9
pin out acc. to Z: 43.981 (Attached)
measuring length 470 mm

Purchased a HEIDENHAIN EXE 602 B/5 unit off ebay for $33 delivered.


Guessing
.020 um = .02 mm
.02 mm /25.4(mm/in) = .000787401575 inches grating

5 fold divisions
.000787401575 inches grating/5 = .000157480315

encoder steps per inch
1/(.000157480315) = 6350 steps per inch



metric calcs are a little cleaner

20 um = .02 mm
.02mm / 5 = .004 mm
1/.004mm = 250 steps per mm
250 steps per mm * 25.4 (mm/in) = 6350 steps per inch


Any thoughts.....