Glossary

There are multiple contexts with nanopositioning where this term applies. Measurement bandwidth describes the frequency range over which a specification was acquired (this can a low pass filter cutoff frequency). For example, if a stage has 1 nm resolution, that is only half the story. Whereas describing 1 nm resolution over a 1 kHz bandwidth (for example) is a more useful description. 

The bandwidth associated with response is slightly different, though certainly coupled to the above concept. A stage can only respond so quickly. If it is driven at  a frequency that is higher than its response bandwidth, the amplitude of the motion will be attenuated. 

Piezoelectrics are not perfect capacitors. When they are charged up to a given potential, the desired motion will occur, but charge continues to migrate in the direction the electric field was most recently applied resulting in additional motion even though the potential is fixed. Note: if we quantified charge rather than voltage, piezos don't actually creep. 

Piezoelectrics exhibit a different displacement vs. voltage curve when they are driven from 0 to high voltage than vise versa, which is referred to as hysteresis. 

A nanopositioner is a piezo driven motion stage that very commonly employs the slip-stick principle. Ranges of motion are typically millimeters. While minimum step sizes can be small (single nm are achievable), these steps are fairly inconsistent from one step to another, varying by as much as 30-50%, which is why they are very rarely used for scanning application; most commonly they are used for navigation. 

Piezoelectricity was an effect discovered by Jacques and Pierre Curie in 1880. Piezoelectric materials exhibit charge transfer across their ferroelectric domains under strain. The inverse effect, where a voltage is applied to induce strain (and thus motion), is what is more commonly exploited in the nanoscale motion realm. 

Encoded stages when commanded to move to a given position will employ the slip-stick waveform to get close and then a DC voltage can be applied to arrive at, and hold, the commanded position. The amplitude of its motion while at the static position is referred to as position noise. It is a function of the drive and sensing electronics, as well as the mechanical stiffness of the stage. 

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The Q-factor for a stage or scanner is a measure of the sharpness of the resonance curve. It manifests in practice as how long a stage takes to ring down after moving to a new position. 

Repeatability is one of the more important figures-of-merit for an encoded nanopositioner. When navigating away from a fixed position and the returning to it, repeatability defines how far the new position is from the old one. According to the encoder, they are the same, but an external measurement device such as a proximity or displacement sensor may give a different number, which is how the repeatability is typically quantified.  

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The rate at which the piezo can be charged by the drive electronics is called the slew rate, dV/dt.