How do you choose the line count of an encoder disc? Line count, interpolation and encoder resolution
Encoder resolution equals the disc line count multiplied by the multiplication or interpolation factor. This article gives the conversion formulas and common combinations, explains the relationship between grating pitch and reading radius and the difference between resolution and accuracy, and sets out the steps for working back from requirements to a line count.
2026-10-04 · Langfang Jingzheng Optoelectronic Technology Co., Ltd.
How many positions an encoder can resolve per revolution depends on two things: the line count of the disc, and how many parts the readhead and electronics divide each line into.
Counts per revolution = line count × multiplication or interpolation factor; angular resolution = 360° ÷ counts per revolution
For square-wave output, use ×4 A/B multiplication; for sine/cosine output, use the interpolation factor.
| Line count | Signal | Factor | Counts per revolution | Angular resolution |
|---|---|---|---|---|
| 1000 | Square wave | ×4 | 4000 | 324″ (0.09°) |
| 2500 | Square wave | ×4 | 10000 | 129.6″ |
| 5000 | Square wave | ×4 | 20000 | 64.8″ |
| 2048 | Sine/cosine | ×1024 | 2097152 (21-bit) | approx. 0.62″ |
Line count and grating pitch
For the same line count, the smaller the reading radius, the smaller the grating pitch. Grating pitch p = 2πr ÷ N: with a 20 mm reading radius and 2500 lines, the pitch is about 50 μm, and with a 1:1 duty cycle the line width is about 25 μm; 10000 lines at the same radius give a pitch of only about 12.6 μm. The smaller the pitch, the more it depends on the photolithography process, and the more tightly the gap between readhead and disc must be controlled.
Resolution is not accuracy
Resolution is the smallest step that can be distinguished; accuracy is the deviation of the reading from the true angle. Accuracy is affected mainly by three things: the graduation error of the lines themselves, disc eccentricity and interpolation error. On a disc with a 20 mm reading radius, 5 μm of eccentricity causes an error of about 52″, dozens of times larger than the resolution in the last row of the table above. For how eccentricity error is calculated, see How much angular error does 5 μm of disc eccentricity cause.
Working back from requirements to a line count
- Determine the smallest angular step the system needs and convert it to counts per revolution
- Determine the signal type: ×4 for square waves; for sine/cosine, the interpolation factor supported by the readhead or chip
- Line count = counts per revolution ÷ factor; choose a nearby common value, for example 1000, 1024, 2000, 2048, 2500 or 5000
- Estimate the reading radius from the disc outer diameter, calculate the grating pitch and confirm it is within the range supported by the readhead
- Check the allowable eccentricity and graduation error against the accuracy requirement and state them in your RFQ
This article was compiled by the engineering department of Langfang Jingzheng Optoelectronic Technology Co., Ltd. Jingzheng Optoelectronics manufactures glass encoder discs, reflective metal encoder discs, PC encoder discs and custom encoder discs. Website: www.encoderdisk.cn; phone: 0316-8933331.