New Method for the Accurate Standardization of Mechanical Oscillations of Small Amplitude

Abstract

This paper presents the theory and first experimental observations with a new method for accurately standardizing the amplitude of small mechanical oscillations in terms of an optical wavelength. A multiple beam interferometer of the Fizeau type is used in which a simple harmonic motion of known frequency is imparted to one of the surfaces of the interferometer. The oscillating multiple-beam fringe pattern is viewed with a photoelectric detector through a slit aperture arranged parallel to the fringes. The resultant photoelectric current contains harmonics of the frequency of oscillation and a strong one is selected by tuning a detector. The amplitude of the selected harmonic is shown by analysis to depend on only three variables: (1) the aperture width R relative to a fringe spacing, (2) the geometric mean reflectance r of the two silvered surfaces of the interferometer, and (3) the peak amplitude of oscillation of the fringe pattern n0 fringe spacings. A function H (R,r,n0) is calculated as a function of n0 for certain values of R and r and it is shown to have a large number of prominent turning points. With the exception of the first, these turning points form a series with a common interval of one fringe spacing. The calculated values of the positions of the turning points are independent of R and r within ranges of variation of R and r representing realistic estimates of errors likely to occur in the values of these quantities. Experiments have shown that, provided that the center of oscillation of the interferometer is stable, the form of the relationship and, more important, the positions of the turning points can be satisfactorily reproduced. The range of amplitudes that the method is potentially capable of standardizing is at present considered to be 0.25 to 10 μ, the precise values depending on the wavelength used.