Abbe error

A positioning or measurement error caused by parasitic rotations when a misalignment exists between the measurement axis and the point of interest. By reducing either parasitic rotations or the offset of misalignment, or both, the abbe error can be minimized. The abbe error can be estimated as: δ = ι * α where δ is positioning error, ι is the offset of misalignment between the measurement axis and the point of interest, and α is the angle of parasitic rotation.


The positioning error along one axis generated while the nanopositioner moves in other axes, such as the stage’s response in the X axis when the stage is driven in the Y axis. Occasionally, the static linear crosstalk error can also be interpreted as orthogonal error.

Orthogonality error

The angular offset of two defined motion axes from being orthogonal to each other. It can be interpreted as a part of crosstalk.

Scale factor

The displacement per unit of command. The scale factors of nPoint’s nanopostioners are calibrated with a laser interferometer.


Represents how close the actual position of a nanopositioner is to the theoretical position to which it is expected to move. It is affected (or determined) by linearity error, hysteresis, abbe error, scale factor error and positioning noise, etc.


A position change over time, which includes the effects of temperature change and other environmental effects. The drift may be introduced from both the mechanical system and electronics.

Position noise

The amplitude of the stage shaking when it is on a static command. It is usually measured and specified with RMS (1 σ) value. It is commonly used to define the resolution of the nanopositioners and is a combination of sensor noise, driver electronics noise and command noise, etc.

Settling time

The time for stage to move to a commanded position and settle to within 2% of its final value of the step size. A small signal step response reflects the dynamic characteristics of the system in more detail. Therefore, small signal settling time is normally used in the specifications of nPoint’s nanopositioning products — the settling time for the response to 1 micrometer step signal.


The motion error produced by direction reversing of the motion. It is presented as a constant hysteresis over the range and is an inherent problem in conventional motion translation mechanisms such as screw/nut, gears, trains and bearings, etc. Normally it is related to machining tolerance, wear, contact stiffness, temperature and loads, etc. nPoint’s flexure motion translation mechanism and piezo actuator designs are inherently backlash free.


The positioning error between forward scan and backward scan. A closed-loop control is an ideal solution for the problem. Capacitance sensors are normally used in nPoint’s nanopositioners to provide feedback signals. It is a non-contact displacement measurement technique, which is hysteresis free.


The maximum displacement of the nanopositioners with the performance specified.

Slew rate

The highest rate of the position change of a nanopositioner. It is measured from the response to a large step signal.


The frequency range to which the amplitude of the stage’s motion is dropped by 3dB with a small input scanning signal. It reflects how well the stage can follow the driving signal for a particular frequency range.

Linearity error

The error between the actual position and the first-order best fit line (straight line). nPoint’s nanopositioning products are calibrated with laser interferometry and the non linearity errors are compensated with a fourth order polynomial.


The minimum step size the stage can move. It is usually defined by the position noise.

Resonant frequency

The first (or the lowest) resonant frequency of a nanopositioner. The resonant frequency could be of the mode along the motion axis or in other axes including rotation and other complex modes. In general, the higher the resonant frequency of a system, the higher the stability and the wider working bandwidth the system will have. The resonant frequency of a mechanical mechanism is determined by the ratio of stiffness and mass. When selecting a nanopositioner to move large samples it is important to understand how the resonant frequency will change when the nanopositioner is loaded.

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