Richard Leach - Fundamental prinsiples of engineering nanometrology (778895), страница 27
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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.
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