The requirement for calibrating transducers having subnanometre displacement sensitivities stimulated the development of an instrument in which the displacement is measured by a combination of optical and X-ray interferometry. The need to combine both types of interferometry arises from the fact that optical interferometry enables displacements corresponding to whole numbers of optical fringes to be measured very precisely, but subdivision of an optical fringe may give rise to errors that are significant at the subnanometre level. The X-ray interferometer is used to subdivide the optical fringes. Traceability to the meter is achieved via traceable calibrations of the lattice parameter of silicon and of the laser frequency. Polarization encoding and phase modulation allow the optical interferometer to be precisely set on a specific position of the interference fringe-the null point setting. The null point settings in the interference fringe field correspond to dark or bright hinges. Null measurement ensures maximum possible noise rejection. However, polarization encoding makes the interferometer nonlinear, but all nonlinearity effects are effectively zero at the fringe set point. The X-ray interferometer provides the means for linear subdivision of optical fringes. Each X-ray fringe corresponds to a displacement that is equal to the lattice parameter of silicon, which is ca. 0.19 nm for the (220) lattice planes. For displacements up to 1 mu m the measurement uncertainties at 95% confidence level are +/-30 pm, and for displacements up to 100 mu m and 1 mm the uncertainties are +/-35 and +/-170 pm, respectively. Important features of the instrument, which is located at the National Physical Laboratory, are the silicon monolith interferometer that both diffracts X-rays and forms part of the optical interferometer, a totally reflecting parabolic collimator for enhancing the usable X-ray flux and the servo-control for the interferometers
The article illustrates the use of Fourier optics to describe the operation of two-beam scanning laser interferometers. It deals with the effect of diffraction on the spatial periodicity of a monochromatic and coherent beam. Particular attention is given to the analysis of systematic errors in high-accuracy laser metrology. The article reviews the special case of plane wave and Gaussian illuminations, examines how beam truncation affects the period of traveling fringes and presents a general relation between the relative wavelength deviation and the impulse standard deviation of the photons
The position and angle measurements discussed in the paper are carried out by application of a displacement-angle interferometer which employs a single laser and is capable of resolutions better than 1 pm and 1 nrad. Angle and displacement values are simultaneously obtained by measuring the phase shifts between four points of the interference pattern with the use of a position-sensitive detector. Though the instrument resembles an optical lever, it is largely insensitive to beam movements, since angle values are obtained by phase rather than position measurements. The interferometer design and performance are discussed, emphasis being given to applications in x-ray/optical interferometry.
The measurement of nanometre displacements with picometre resolution has been made possible by a phase-modulation recovery scheme applied to an optical Michelson interferometer using polarization encoding. In contrast to conventional schemes, phase modulation is carried out before the interferometer optics. In this way, the low-frequency components of the phase shift between the two interfering beams are locked at zero (within limits set only by shot noise) before beam splitting by a feedback loop driving the modulator. An interferometer prototype, illuminated by a beam thus modulated, was constructed and coupled to an X-ray interferometer to compare the optical and X-ray interferometric measurement values of sub-nanometre displacements. A resolution better than 1 pm over a 100 Hz bandwidth was obtained.
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