Where does the interpolation error of sine/cosine encoder discs come from? 4 signal quality metrics to check
DC offset, amplitude mismatch, phase deviation from 90° and harmonic distortion in sine/cosine signals produce a periodic interpolation error within each signal period. This article shows how to estimate each term, the factors on the disc side, and how to check the signals with a Lissajous figure.
2026-10-05 · Langfang Jingzheng Optoelectronic Technology Co., Ltd.
A sine/cosine readhead outputs two signals with a 90° phase difference. The interpolation circuit uses these two signals to calculate the phase and divides one signal period into hundreds or thousands of parts. Ideally, the two signals have equal amplitudes, no DC offset, exact quadrature and purely sinusoidal waveforms. Any deviation produces a periodic interpolation error within each signal period.
1. The four metrics and the errors they cause
| Metric | Error cycles per signal period | Error amplitude (small deviations, electrical angle) |
|---|---|---|
| DC offset (relative amplitude ε) | 1 | approx. ε rad |
| Amplitude mismatch (relative difference δ) | 2 | approx. δ/2 rad |
| Phase deviation from 90° (φ) | 2 | approx. φ/2 rad |
| Third harmonic | 4 | Increases with harmonic content |
2. Worked example: a 2048-line disc
With 2048 lines, one signal period is 360° ÷ 2048 ≈ 632.8″. An electrical angle of 1 rad corresponds to 632.8″ ÷ 2π ≈ 100.7″:
- 1% DC offset: error approx. 0.01 rad, or about 1.0″
- 2% amplitude difference: error approx. 0.01 rad, or about 1.0″
- 1° phase deviation (approx. 0.0175 rad): error approx. 0.0087 rad, or about 0.9″
The higher the interpolation factor, the more noticeable these errors become. Many interpolation chips have automatic gain and offset correction that reduces the first two, but the pattern quality of the disc itself remains the foundation.
3. Disc-side factors
- Line duty cycle and edge quality: determine how closely the waveform approaches a sine wave; affect harmonics
- Pitch uniformity: affects the graduation error over the full revolution
- Optical density or reflectance contrast: determines signal amplitude and signal-to-noise ratio; see High/low reflectance contrast of reflective encoder discs
- Eccentricity: causes a once-per-revolution angular error and also makes the signal amplitude fluctuate with rotation angle
- Disc-to-readhead gap and tilt: affect the amplitude and the matching of the two signals
4. Checking the signals with a Lissajous figure
Connect the sin and cos signals to an oscilloscope in XY mode and rotate the disc: ideal signals form a perfect circle. A center offset from the origin indicates DC offset; a horizontally or vertically elongated ellipse indicates unequal amplitudes; a tilted ellipse indicates a phase deviation from 90°; a polygonal outline indicates significant harmonics. For acceptance testing, the amplitude, offset, phase difference and harmonic content can be recorded.
In your RFQ, state the number of signal periods, the readhead or interpolation chip model, and any requirements for duty cycle and edge quality.
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.