Investigations into the Uncertainties of Interferometric Measurements of Linear and Circular Vibrations

Abstract

A uniform description is given of a method of measurement using a Michelson interferometer for measuring the linear motion quantities acceleration, velocity and displacement, and a diffraction grating interferometer for measuring the circular motion quantities angular acceleration, angular velocity and rotation angle. The paper focusses on an analysis of the dynamic behaviour of an interferometric measurement system based on the counting technique with regard to the measurement errors due to deterministic and stochastic disturbing quantities. The error analysis and description presented are aimed at giving some rules, mathematical expressions and graphical presentations that have proved to be helpful in recognizing the errors in interferometric measurements of motion quantities, optimizing the measurement conditions (e.g., filter settings), obtaining corrections and estimating the uncertainty of measurement.