Bidirectional Error and Hysteresis in Optical Encoders: Causes, Measurement and Limits

What hysteresis means in a non-contact encoder

In a gear or a ballscrew, backlash is lost motion: clearance that the mechanics must traverse before force is transmitted. An optical encoder has no such clearance between scanning head and scale, so its hysteresis has a different origin. The dominant mechanism is elastic: when the axis reverses, friction and inertia loads momentarily deflect the scale relative to the readhead, or the readhead relative to the carriage. Glass scales clamped only at their ends bow slightly; steel tape scales on adhesive lift marginally at the scanning zone; a readhead bracket with clearance allows the head itself to shift a few micrometres under the reversing load and return afterward.

The result is that the position signal lags the true reversal and recovers as loads settle. The encoder reports the position faithfully as it sees it, but what it sees depends on the direction of approach. This is why hysteresis cannot be calibrated away in the same way as a repeatable scale error: the offset is load- and history-dependent, so compensation works only approximately and only for stable, repeatable contributions.

Separating encoder hysteresis from machine reversal error

The axis-level symptom—different positions reported from opposite directions—is the sum of every contributor in the loop. Before ordering corrective work, isolate the feedback. The fastest component-level test requires no disassembly: command the axis to a mid-travel target, approach it unidirectionally from one side many times, then from the other, and log the raw encoder counts with the servo holding position. Mechanical loads settle within milliseconds; a signal that continues drifting toward the unidirectional mean over seconds indicates scale or bracket compliance recovering elastically.

For a definitive separation, run the reversal test twice: once with the normal mechanical loop, once with the motor decoupled so the scale can be translated by hand between two fixed readheads or against an external interferometer. The difference that remains when mechanics are removed from the loop is the encoder's own hysteresis. Machine builders who skip this step routinely spend days correcting a ballscrew that was never the problem.

Measuring encoder hysteresis properly

A meaningful measurement states four things: the target positions, the approach pattern, the settling time before the reading, and the temperature. The standard pattern is a bidirectional round-robin—approach each target from both sides, several cycles—plotted as a position-versus-direction hysteresis loop. The loop's width at each target is the local bidirectional error; the loop's shape reveals whether the cause is a simple constant offset or a position-dependent compliance, which points at scale mounting rather than bracket play.

Two practical traps distort results. First, reading too early: the elastic recovery after a reversal takes time, so a settled reading must be defined—typically holding position for hundreds of milliseconds before sampling. Second, attributing interpolation asymmetry to hysteresis: a signal imbalance that shifts the interpolated zero in a direction-dependent way looks identical at the position output. A Lissajous check of the quadrature signals distinguishes the two, and suppliers can supply subdivision error data for the configuration.

• Bidirectional round-robin over at least five positions and five cycles
• Defined settling time before each reading; log raw counts, not compensated output
• Record temperature: scale compliance is weakly temperature dependent, adhesive creep is not
• Compare loop width against the datasheet figure for the installed configuration

Designing hysteresis out of the feedback path

Most encoder hysteresis is a mounting problem, not a sensor problem. Glass scales should be clamped or bonded per the supplier's pattern so that thermal expansion is accommodated without allowing the scanning zone to move under friction loads. Tape scales need the specified adhesive system over the full length, with correct curing pressure, because a partially bonded tape acts as a leaf spring. Readhead brackets deserve the same rigor as the scale: machined faces rather than shims, fastener patterns that clamp rather than locate, and no cable routing that can pull the head against its clearance.

Where the loop cannot be stiffened further, the machine can still be made bidirectionally accurate. Three strategies cover most processes: always approach critical positions from the same direction with a defined overshoot, which converts bidirectional error into unidirectional repeatability; use bidirectional error maps in the control, effective when the hysteresis contribution is stable and the mechanical reversal error has already been compensated; and specify the encoder configuration with the lowest documented hysteresis where the process genuinely requires it, accepting that this is a component selection decision rather than a tuning exercise.

What to require from the supplier and the build

Ask for hysteresis as a configuration-specific number: the value for the ordered scale type, mounting method and readhead, together with the measurement method used to derive it. A family-level typical figure measured on a laboratory fixture tells you little about a tape scale bonded to an aluminium carrier at the far end of the machine. For rotary feedback, ask for the torque-dependent angle error of the shaft-coupling arrangement as installed.

On the build side, require the scale bonding and clamping records and a bracket inspection at incoming stage, and commission with a bidirectional round-robin whose result is archived as the axis baseline. When the axis is later re-verified, comparing loop width against the baseline detects developing compliance—adhesive creep, loose clamps—long before it becomes a dimensional problem on parts. Hysteresis handled this way stays a specified, bounded property instead of an intermittent customer complaint.