Define the physical period before counting edges
Let N be the number of complete optical periods around the active track. One period contains a clear region and its neighbouring opaque region. Angular pitch is 360°/N. PPR may mean single-channel pulses and CPR may mean decoded counts, but both abbreviations are used inconsistently across suppliers. Write the physical period count and the decoding rule explicitly.
Quadrature decoding and nominal increments
When A and B are valid quadrature signals with N cycles per revolution, counting both edges of both channels gives 4N counts. Counting a single rising edge gives N; counting both edges of one channel gives 2N. The nominal increment is 360°/C or 1,296,000/C arcseconds for C counts per revolution. An index is a reference event and is not an extra position count.
| Decoding | Counts per revolution | Nominal increment |
|---|---|---|
| Single-channel rising edge | 2,500 | 0.144° |
| Both edges of one channel | 5,000 | 0.072° |
| Both edges of A and B | 10,000 | 0.036° = 129.6 arcsec |
Calculate pitch at the active reading radius
At track radius r, tangential pitch is p = 2πr/N. For an ideal 50% clear fraction, clear width and opaque width are each p/2 at that radius. Radial-sector widths change with radius, so a line-width requirement needs its measurement radius. The outside diameter of the glass is not automatically the active track diameter. Closure also matters: the last-to-first period must follow the same spacing rule.
Check frequency at the required shaft speed
For N signal cycles per revolution and speed n in rpm, single-channel frequency f = Nn/60 Hz. A four-edge decoder receives 4f count events per second. Check the analogue reader bandwidth, output transition rate, receiver and controller limit separately. Interpolated output can have a higher count rate than the base optical signal. Index pulse duration and receiver timing also need to remain valid at maximum speed.
Linear pitch and subdivision
For a linear scale with physical pitch p and travel speed v, the base signal frequency is v/p using consistent length units. If the complete decoder supplies K subdivisions per period, the nominal increment is p/K and the output count rate is Kv/p. Define K as the total subdivision, including any quadrature factor, so it is not multiplied by four twice.
Keep resolution, accuracy and repeatability separate
Subdivision changes the reported increment. Accuracy compares reported position with a reference over a stated angle or travel, while repeatability describes repeated readings under defined conditions. State approach direction, speed, temperature and mounting when assessing them. A smaller increment does not remove pattern error, eccentricity, noise or thermal drift, and there is no fixed repeatability-to-accuracy ratio that applies to every encoder.