Принципы нанометрологии (1027506), страница 27
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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).
To calibratean optical interferometer (and, therefore, measure its non-linearity), theX-ray interferometer is used to make a known displacement that is comparedagainst the optical interferometer under calibration. By servo-controlling thePZT it is possible to hold lamella A in a fixed position or move it in discrete109110C H A P T ER 5 : Displacement measurementsteps equal to one fringe period [65]. Examples of the calibration of a differential plane mirror interferometer and an optical encoder can be found in [19]and [46] respectively. In both cases periodic errors with amplitudes of lessthan 0.1 nm were measured once a Heydemann correction (see section5.2.8.5) had been applied.
X-ray interferometry can also be used to calibratethe characteristics of translation stages in two orthogonal axes [66] and tomeasure nanoradian angles [67].One limitation of X-ray interferometry is its short range. To overcomethis limitation, NPL, PTB and Instituto di Metrologia ‘G. Colonetti’ (nowknown as Instituto Nazionale di Recerca Metrologica – the Italian NMI)collaborated on a project to develop the Combined Optical and X-ray Interferometer (COXI) [68] as a facility for the calibration of displacement sensorsand actuators up to 1 mm. The X-ray interferometer has an optical mirror onthe side of its moving mirror that is used in the optical interferometer(see Figure 5.16).
The optical interferometer is a double-path differentialsystem with one path measuring displacement of the moving mirror on theX-ray interferometer with respect to the two fixed mirrors above the translation stage. The other path measures the displacement of the mirror (M)FIGURE 5.16 Schema of a combined optical and X-ray interferometer.Referencesmoved by the translation stage with respect to the two fixed mirrors eitherside of the moving mirror in the X-ray interferometer. Both the optical andX-ray interferometers are servo-controlled.
The X-ray interferometer movesin discrete X-ray fringes, the servo system for the optical interferometerregisters this displacement and compensates by initiating a movement of thetranslation stage. The displacement sensor being calibrated is referenced tothe translation stage and its measured displacement is compared with theknown displacements of the optical and X-ray interferometers.5.8 References[1] Wilson J S 2005 Sensor technology handbook (Elsevier: Oxford)[2] Fraden J 2003 Handbook of modern sensors: physics, designs and applications (Springer) 3rd edition[3] Bell D J, Lu T J, Fleck N A, Spearing S M 2005 MEMS actuators and sensors:observations of their performance and selection for purpose J. Micromech.Microeng.
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