Принципы нанометрологии (1027623), страница 27
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A multimodeoptical fibre cable (i.e. one that transmits a number of electromagneticmodes) has a multilayered structure including the fibre, the cladding, a bufferlayer, a hard braid and a plastic outer jacket.There are three types of reflective optical fibre sensors, known as bifurcated sensors: hemispherical, fibre pair and random [52]. These threeconfigurations refer to fibre bundles at one end of the sensor (see Figure 5.12).The bundles have one common end (for sensing) and the other end is splitevenly into two (for the source and detector) (see Figure 5.13).As the target is moved towards the sensing end the intensity of thereflected light follows the curve shown in Figure 5.14.
Close to the fibre endthe response is linear, but follows a 1/d2 curve as the distance from the fibreend increases (d is the distance from the fibre end to the target).The performance of a bifurcated fibre optic sensor is a function of thecross-sectional geometry of the bundle, the illumination exit angle and thedistance to target surface. Tilt of the target surface with respect to the fibreend significantly degrades the performance of a sensor.Optical fibre sensors are immune to electromagnetic interference, verytolerant of temperature changes and bending or vibration of the fibre does notsignificantly affect their performance.
As a consequence optical fibre sensorsare often used in difficult or hazardous environments. Note that only bifurcated fibre optic displacement sensors have been considered here. However,fibre optic sensors can be used to measure a wide range of measurands [53]and can be the basis of very environment-tolerant displacement measuringinterferometers [54], often used where there is not sufficient space for bulkFIGURE 5.12 End view of bifurcated optical fibre sensors, (a) hemispherical,(b) random and (c) fibre pair.105106C H A P T ER 5 : Displacement measurementFIGURE 5.13 Bifurcated fibre optic sensor components.FIGURE 5.14 Bifurcated fibre optic sensor response curve.optics.
Fibre sensing and delivery has been used by some surface topographymeasuring instruments [55], and fibre sensors are used to measure thedisplacement of atomic force microscope cantilevers [56].5.7 Calibration of displacement sensorsThere are many more forms of displacement sensors other than thosedescribed in this chapter (see [1,2]). Examples include sensors that use theHall effect, the piezoelectric effect, ultrasonics, electrical resistance,magnetism and the simple use of a knife-edge in a laser beam [57]. Also,some MNT devices, including MEMS and NEMS sensors, use quantummechanical effects such as tunnelling and quantum interference [58].
It isoften claimed that a sensor has a resolution below a nanometre but it is farCalibration of displacement sensorsfrom trivial to prove such a statement. Accuracies of nanometres are evenmore difficult to prove and often there are non-linear effects or sensor/targetinteractions that make the measurement result very difficult to predict orinterpret. For these reasons, traceable calibration of displacement sensors isessential, especially in the MNT regime.5.7.1 Calibration using optical interferometryIn order to characterise the performance of a displacement sensor a numberof interferometers can be used (provided the laser source has been traceablycalibrated; see section 2.9.5). A homodyne or heterodyne set-up (see sections5.2.2 and 5.2.3 respectively) can be used by rigidly attaching or kinematicallymounting an appropriate reflector so that it moves collinearly with thedisplacement sensor.
One must be careful to minimize the effects of Abbeoffset (see section 3.4) and cosine error (see section 5.2.8.3), and to reduceany external disturbances. A differential interferometer (see section 5.2.6)can also be used but over a reduced range.As displacement sensor characteristics are very sensitive over shortdistances, the limits and limiting factors of interferometric systems for verysmall displacement become critical.
For the most common interferometers itis the non-linearity within one wavelength that becomes critical. Even withthe Heydemann correction applied this can be the major error source.5.7.1.1 Calibration using a Fabry-Pérot interferometerThe Fabry-Pérot interferometer, as described in section 4.4.4, can be used foran accurate calibration at discrete positions. If one mirror in the cavity isdisplaced, parallel interference extrema appear in steps of half a wavelength.If the sensor to be calibrated at the same time measures the mirrordisplacement, a calibration can be carried out.Such a system was described by [59], where it was used to calibratea displacement generator with a capacitive feedback system with 0.2 nmuncertainty.
As a capacitive system can be assumed to have a smoothlyvarying non-linear behaviour, discrete steps can be feasibly used. However,fringe periodic deviations as they may appear in interferometric systemscannot be detected. A continuous calibration system is possible if thewavelength can be tuned and accurately measured simultaneously (seesection 2.9.5).5.7.1.2 Calibration using a measuring laserThe stability of an iodine-stabilized He-Ne laser is considered to be one partin 1011 (see section 2.9.3).
Relating this stability to the typical length of107108C H A P T ER 5 : Displacement measurementa laser cavity (a Fabry-Pérot cavity) of, say, 15 cm one could conclude that thecavity length is fixed with an uncertainty of 1.5 pm. Of course there are manydisturbing factors, such as temperature effects in the air, that make sucha small uncertainty in a true displacement measurement hard to achieve.
Inthe set-up described in [60], the iodine-standard is stabilized on its successiveiodine peaks, and a sensor can be calibrated at a number of discrete points.Thermal drift effects mainly determine the uncertainty; the frequencystability itself contributes only 1.5 pm to the uncertainty. This is probablyone of the most obvious traceable displacement measurements possible,although difficult to realize in practice.Separate measuring lasers can be used to give a continuous measurement[61,62].
Here the laser frequency can be tuned by displacing one of itsmirrors, while the laser frequency is continuously monitored by a beatmeasurement. Mounting the laser outside the cavity removes the majorthermal (error) source, but further complicates the set-up. In [63] a piezoelectric controller accounts for a displacement that is applied to a mirror andis measured by both a sensor and a Fabry-Pérot system. The slave laser isstabilized to the Fabry-Pérot cavity, i.e.
its frequency is tuned such that itgives a maximum when transmitted through the cavity. At the same time theslave laser frequency is calibrated by a beat measurement against the iodinestabilized laser. Also here the uncertainties from the frequency measurementare in the picometre range, and still thermal and drift effects dominate [63].Design considerations are in the cavity length, the tuning range of theslave laser, the demand that the slave laser has a single-mode operation andthe range that the frequency counter can measure.
Typical values are 100 mmcavity length and 1 GHz for both the tuning range of the slave laser and thedetection range of the photodiode and frequency counter. For a largerfrequency range the cavity length can be reduced, but this increases thedemands on the ability to measure a larger frequency range. With tuneablediode lasers the cavity length can be reduced to the millimetre level, but thisrequires different wavelength measurement methods [59].5.7.2 Calibration using X-ray interferometryThe fringe spacing for a single pass two-beam optical interferometer is equalto half the wavelength of the source radiation and this is its basic resolutionbefore fringe sub-division is necessary.
The fringe spacing in an X-rayinterferometer is independent of the wavelength of the source; it is determined by the spacing of diffraction planes in the crystal from which X-raysare diffracted [64]. Due to its ready availability and purity, silicon is the mostcommon material used for X-ray interferometers. The atomic latticeCalibration of displacement sensorsFIGURE 5.15 Schema of an X-ray interferometer.parameter of silicon can be accurately measured (by diffraction) and isregarded as a traceable standard of length.
Therefore, X-ray interferometryallows a traceable measurement of displacement with a basic resolution ofapproximately 0.2 nm (0.192 nm for the (220) planes in silicon).Figure 5.15 shows a schema of a monolithically manufactured X-rayinterferometer made from a single crystal of silicon. Three, thin, vertical andequally spaced lamella are machined with a flexure stage around the thirdlamella (A). The flexure stage has a range of a few micrometres and is drivenby a piezoelectric actuator (PZT). X-rays are incident at the Bragg angle [10]on lamella B and two diffracted beams are transmitted. Lamella A is analogous to a beam-splitter in an optical interferometer.
The transmitted beamsare incident on lamella M that is analogous to the mirrors in a Michelsoninterferometer. Two more pairs of diffracted beams are transmitted and onebeam from each pair is incident on lamella A, giving rise to a fringe pattern.This fringe pattern is too small to resolve individual fringes, but whenlamella A is translated parallel to B and M, a moiré fringe pattern between thecoincident beams and lamella A is produced. Consequently the intensity ofthe beams transmitted through lamella A varies sinusoidally as lamella A istranslated.The displacements measured by an X-ray interferometer are free from thenon-linearity in an optical interferometer (see section 5.2.8.4).
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