|Resolution / Bandwidth
Resolution in nanopositioning relates to the smallest change in displacement that can still be detected by the measuring devices.
For capacitive sensors, resolution is in principle unlimited, and is in practice limited by electronic noise. PI signal conditioner
electronics are optimized for high linearity, bandwidth and minimum noise, enabling sensor resolution down to the picometer range.
Electronic noise and sensor signal bandwidth are interdependent. Limiting the bandwidth reduces noise and thereby improves resolution. The working distance also influences the resolution: the smaller the working distance of the system, the lower the absolute
value of the electronic noise.
Figure 1 shows measurements of nanometer-range actuator cycles taken with a D-015, 15 ěm capacitive position sensor and a laser interferometer. The graphs clearly show the superior performance of the capacitive position sensing technique.
Figure 2 illustrates the influence of bandwidth upon resolution: the PISeca™ single electrode sensors show excellent resolution down to the sub-nanometer range, even at high bandwidths.
Linearity and Stability of PI sensors
The linearity of a measurement denotes the degree of constancy in the proportional relation between change in probe-target distance and the output signal. Usually linearity is given as linearity error in percent of the full measurement range. A linearity error of 0.1% with range of 100 µm gives a maximum error of 0.1 µm. Linearity error has no influence whatsoever upon resolution and repeatability of a measurement.
Linearity is influenced to a high degree by homogeneity of the electric field and thus by any non-parallelism of the probe
and target in the application. PI capacitive position sensor electronics incorporate a proprietary design providing superior linearity, low sensitivity to cable capacitance, low background noise and low drift. The Integrated Linearization System (ILS) compensates for nonparallelism influences.
A comparison between a conventional capacitive position sensor system and a PI ILS system is shown in Figure 3. When used with PI digital controllers (which add polynomial linearization) a positioning linearity of up to 0.003 % is achievable.
Figure 4 shows the linearity of a P-752.11C piezo flexure nanopositioning stage with integrated capacitive position sensor operated in closed-loop mode with an analog controller. All errors contributed by the mechanics, PZT drive, sensors and electronics are included
in the resulting linearity of better than 0.02 %. Even higher linearity is achievable with PI digital controllers like the E-710.
Stability of the measurement is limited mainly by thermal and electronic drift. For accuracy and repeatability reasons, it is thus necessary to maintain constant environmental conditions. The exceptional longterm stability of the PI capacitive position sensor and electronics design is shown in Figure 5.
Principle of the Measurement
When a voltage is applied to the two plates of an ideal capacitor, it creates a homogenous electric field. This principle is the basis of measuring displacement with capacitive position sensors. For small gaps, the applied voltage is proportional to the plate distance. The planes of the sensor surface (“probe”) and the target form the two capacitor plates.
The target should not be below a certain size because of boundary effects. This is important for applications with, say, a rotating drum as target. For metallic materials, the thickness of the target has no influence on the measurement.
Guard Ring Geometry/Design
The proportionality referred to is based on the homogeneity of the electric field. To eliminate boundary effects, the superior PI design uses a guard-ring electrode that surrounds the active sensor area and is actively kept at the same potential (see Fig. 7). This design shields the active sensor area and provides for excellent containment of the measurement zone. Thus optimum measuring linearity over the full range is achieved within the specified accuracy.
Calibration for Best Accuracy
PI’s nanometrology calibration laboratories offer optimum conditions for factory calibration. As references, ultra-highaccuracy incremental sensors like laser interferometers are used.
PISeca™ systems are calibrated at PI with a NEXLINE® positioning system having a closed-loop resolution better than 0.01 nm in a test stand with friction-free flexure guidance and an incremental reference sensor featuring a resolution better than 0.1 nm (Fig. 8
Special Design Eliminates Cable Influences
When measuring distance by detection of capacitance changes, fluctuations in the cable capacitance can have an adverse effect on accuracy. This is why most capacitive measurement systems only provide satisfactory results with short, well-defined cable lengths.
PI systems use a special design which eliminates cable influences, permitting use of cable lengths of up to 3 m without difficulty. For optimum results, we recommend calibration of the sensor-actuator system in the PI metrology lab. Longer distances between sensor and electronics can be spanned with special, loss-free, digital transmission protocols.
Electrode Geometry, Sensor Surface Flatness
During sensor production, great care is taken to maintain critical mechanical tolerances. Measuring surfaces are diamond machined using sophisticated process control techniques. The result is the smooth, ultra-flat, mirrored surfaces required to obtain the highest resolution commercially available.
Parallelism of Measuring Surfaces
For optimum results, target and probe plates must remain parallel to each other during measurement. For small measurement distances and small active areas, any divergence has a strong influence on the measurement results. Tilt adversely affects linearity and gain, although not resolution or repeatability (see fig. 12). Positioning systems with multilink flexure guidance reduce tip and tilt to negligable levels (see Fig. 13) and achieve outstanding accuracy.
Fig. 10: Capacitive position sensors in an
ultra-high-accuracy, six-axis nanopositioning
system designed by PI for the
German National Metrology Institute
(PTB). Application: scanning microscopy
Fig. 11: Digital sensor-signal transmission
(DST) allows a distance up to 15 m
between positioning unit and controller,
here an E-710 multi-axis digital piezo
Fig. 1: Piezo nanopositioning system making 0.3 nm steps, measured with PI capacitive sensor (lower curve) and with a highly precise laser interferometer.
The capacitive sensor provides significantly higher resolution than the interferometer
Fig. 2: Resolution significantly below 1 nm is achieved with a 20 ěm PISeca™
single-electrode sensor (D-510.020) and the E-852 signal conditioner electronics.
Left: 0.2 nm-steps under quasi-static conditions (bandwidth 10 Hz),
right: 1 nm-steps with maximum bandwidth (6.6 kHz)
Fig. 3: Linearity of conventional capacitive position sensor system vs. PI ILS
(integrated linearization system), shown before digital linearization
Fig. 4: Linearity of a P-752.11C, 15 ěm piezo nanopositioning stage operated with
E-500/E-509.C1A control electronics. The travel range is 15 ěm, the gain 1.5 ěm/V.
Linearity is better than 0.02 %; even higher linearity is achievable with PI digital
Fig. 5: Measurement stability of an E-509.C1A capacitive position sensor control module with 10 pF reference capacitor over 3.5 hours (after controller warm-up)
Fig. 6: Capacitive sensor working principle
Fig. 7: Capacitive sensors with guard ring design provide superior linearity
Fig. 8: Output linearity error of a PISeca™ single-electrode system is typically
less than 0.1% over the full measurement range
Fig. 9: Ultra-high-precision NEXLINE® positioning system with incremental sensor in a calibration and test stand for PISeca™ sensors. The resolution is significantly better than that of a laser interferometer
Fig. 12: Nonlinearity vs. tilt. Resolution and repeatability are not affected by tilt
Fig. 13. Flexure-guided nanopositioning systems like the P-752 offer submicroradian
guiding accuracy and are optimally suited for capacitive sensors