Richard Leach - Fundamental prinsiples of engineering nanometrology (778895), страница 25
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This method is applicable ininterferometry.Figure 5.6 shows a typical optical arrangement of an interferometer set upfor angular measurements. The angular optics are used to create two parallelbeam paths between the angular interferometer and the angular reflector.The distance between the two beam paths is found by measuring the separation of the retro-reflectors in the angular reflector. This measurement ismade either directly or by calibrating a scale factor against a known angularstandard.The beam that illuminates the angular optics contains two frequencies, f1and f2 (heterodyne).
A polarizing beam-splitter in the angular interferometersplits the frequencies, f1 and f2, that travel along separate paths.At the start position the angular reflector is assumed to be approximately ata zero position (i.e. the angular measurements are relative). At this positionthe two paths have a small difference in length. As the angular reflector isFIGURE 5.6 Schema of an angular interferometer.Capacitive displacement sensorsrotated relative to the angular interferometer the relative lengths of the twopaths will change.
This rotation will cause a Doppler shifted frequency changein the beam returned from the angular interferometer to the photodetector.The photodetector measures a fringe difference given by (f1 Df1) (f2 D f2).The returned difference is compared with the reference signal, (f1 f2).This difference is related to velocity and then to distance. The distance isthen converted to an angle using the known separation of the reflectors in theangular interferometer.Other arrangements of angular interferometer are possible using plainmirrors but the basic principle is the same. Angular interferometers aregenerally used for measuring small angles (less than 10 ) and are commonlyused for measuring guideway errors in machine tools and measuringinstruments.5.3 Capacitive displacement sensorsCapacitive sensors are widely used for non-contact displacement measurement. Capacitive sensors can have very high dynamic responses (up to 50kHz), sub-nanometre resolution, ranges up to 10 mm, good thermal stabilityand very low hysteresis (mainly due to their non-contact nature).
Capacitivesensors measure the change in capacitance as a conducting target is displacedwith respect to the sensor. Figure 5.7 shows a capacitive sensor andmeasurement target. In this parallel plate capacitor arrangement, thecapacitance, C, is given byC ¼3Ad(5.20)where 3 is the permittivity of the medium between the sensor and target, A isthe effective surface area of the sensor and d is the distance between thesensor and the target surface.
This relationship is not highly dependent onthe target conductivity and hence capacitance sensors can be used withFIGURE 5.7 A typical capacitance sensor set-up.99100C H A P T ER 5 : Displacement measurementa range of materials. Note that capacitance sensors can also be used tomeasure dielectric thickness and density by varying 3 and keeping d constant.Due to the effect of stray capacitance and the need to measure very lowvalues of capacitance (typically from 0.01 pF to 1 pF), capacitance sensorsusually require the use of a guard electrode to minimise stray capacitance.Capacitance sensors are used in the semiconductor, disk drive andprecision manufacturing industries, often to control the motion of a rotatingshaft.
Modern MEMS devices also employ thin membranes and comb-likestructures to act as capacitance sensors (and actuators) for pressure, acceleration and angular rate (gyroscopic) measurement [37,38]. High-accuracycapacitance sensors are used for control of MNT motion devices [39] andform the basis for a type of near-field microscope (the scanning capacitancemicroscope) [40].The non-linear dependence of capacitance with displacement can beovercome by using a cylindrical capacitor or by moving a flat dielectric platelaterally between the plates of a parallel plate capacitor [41].
These configurations give a linear change of capacitance with displacement.The environment in which it operates will affect the performance ofa capacitance sensor. As well as thermal expansion effects, the permittivity ofthe dielectric material (including air) will change with temperature andhumidity [42]. Misalignment of the sensor and measurement surface willalso give rise to a cosine effect.Capacitance sensors are very similar to some inductive or eddy currentsensors (i.e.
sensors that use the electromagnetic as opposed to the electrostatic field). Many of the points raised above relate to both types of sensor. See[42] for a fuller account of the theory and practice behind capacitive sensors.5.4 Inductive displacement sensorsAs discussed above, inductive sensors are very similar to capacitive sensors.However, inductive sensors are not dependent upon the material in thesensor/target gap so they are well adapted to hostile environments wherefluids may be present in the gap. They are sensitive to the target material andmust be calibrated for each material that they are used with. They alsorequire a certain thickness of target material to operate (usually fractions ofa millimetre, dependent on the operating frequency). Whilst they may havenanometre resolutions, their range of operation is usually some millimetres.Their operating frequencies can be 100 kHz and above.Another form of contacting sensor, based on inductive transduction, isthe linear variable differential transformer (LVDT).
An LVDT probe consistsInductive displacement sensorsof three coils wound on a tubular former. A centre-tapped primary coil isexcited by an oscillating signal of between 50 Hz and 30 kHz and a nonmagnetic rod, usually with an iron core, moves in and out of the tube.Figure 5.8 illustrates this design. As the rod moves the mutual inductancebetween the primary and two other, secondary, coils changes. A voltageopposition circuit gives an output potential difference that is directlyproportional to the difference in mutual inductance of the two secondarycoils that is in turn proportional to the displacement of the rod within thetube.
When the core is central between the two secondary coils, the LVDTprobe is at its null position and the output potential difference is zero.LVDTs have a wide variety of ranges, typically 100 mm to 500 mmand linearities of 0.5 % or better. LVDTs have a number of attractive features.First, there is no physical contact between the movable core and the coilstructure, which results in frictionless measurement. The zero output at itsnull position means that the signal can be amplified by an unlimited amount,and this essentially gives an LVDT probe infinite resolution, the only limitation being caused by the external signal-conditioning electronics. There iscomplete isolation between the input and output, which eliminates the needfor buffering when interfacing to signal-conditioning electronics.
Therepeatability of the null position is inherently very stable, making an LVDTFIGURE 5.8 Schematic of an LVDT probe.101102C H A P T ER 5 : Displacement measurementFIGURE 5.9 Error characteristic of an LVDT probe.probe a good null-position indicator. Insensitivity to radial core motionallows an LVDT probe to be used in applications where the core does notmove in an exactly straight line. Lastly, an LVDT probe is extremely ruggedand can be used in relatively harsh industrial environments (although theyare sensitive to magnetic fields).Figure 5.9 shows the ‘bow-tie’ error characteristic of a typical LVDT probeover its linear or measuring range. Probes are usually operated around thenull position, for obvious reasons, although, depending on the displacementaccuracy required, a much larger region of the probe’s range can be used.LVDTs find uses in advanced machine tools, robotics, construction,avionics and computerised manufacturing.
Air-bearing LVDTs are nowavailable with improved linearities and less damping. Modern LVDTs canhave multiple axes [43] and use digital signal processing [44] to correct fornon-linearities and to compensate for environmental conditions and fluctuations in the control electronics [45].5.5 Optical encodersOptical encoders operate by counting scale lines with the use of a light sourceand a photodetector. They usually transform the light distribution into twosinusoidal electrical signals that are used to determine the relative positionbetween a scanning head and a linear scale. The grating pitch (resolution) ofthe scales varies from less than 1 mm to several hundred micrometres. Aswith interferometers, electronic interpolation of the signals can be used toOptical encodersproduce sub-nanometre resolution [5] and some of the more advanced opticalencoders can have accuracies at this level [46–48].The most common configuration of an optical encoder is based upona double grating system; one grating acts as the scale and the other is placedin the reading head.
The grating pair produces a fringe pattern at a certaindistance from the second grating (usually a Lau or moiré pattern). Thereading head has a photodetector that transforms the optical signal into anelectrical signal. When a relative displacement between the reading head andthe scale is produced, the total light intensity at the photodetector variesperiodically.
The electronic signals from the photodetector are analysed inthe same manner as the quadrature signals from an interferometer (seesection 5.2.4). Figure 5.10 is a schema of a commercial optical encodersystem capable of sub-nanometre resolution. The period of the grating is512 nm. The reading head contains a laser diode, collimating optics and anindex grating with a period of 1024 nm (i.e. twice the period of the scale). Thesignals collected by the detectors are transformed into quadrature signalswith a period of 128 nm (i.e.
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