An Interferometric Method to Measure Oscillatory Displacements, 2 nm - 255 nm

A method is described for measuring oscillatory displacements in the range 2 nm to 255 nm, using a laser interferometer. The reference mirror is moved at a constant velocity, modulating the photoelectric signal at 130 Hz. The modulated signal is digitally sampled over a prescribed interval, and a Fast Fourier Transform is taken. After correcting the harmonic amplitudes for the so-called `picket-fence error', their ratios are measured. The displacement is then calculated by reference to the ratios between Bessel functions J 2 /J 0 , J 3 /J 1 and J 4 /J 2 . An application is described for automated calibration of accelerometers at high frequencies. The latter is shown to have accuracy comparable to that of methods which establish discrete amplitudes by reference to zeros of Bessel functions.