Generalization and analysis of the fringe-counting method for interferometric measurement of motion quantities

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 article focuses 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. Special means allowing the quantization error lo be suppressed are theoretically derived and experimentally verified. By using these means, a modified version of the fringe-counting method has been developed with which the characteristics of the conventional fringe-counting method (minimum displacement amplitude of 5 (mu)m, maximum frequency of 800 Hz) have been greatly improved (minimum displacement amplitude of 5 nm, maximum frequency of 20 kHz). © 1999 Elsevier Science Ltd. All rights reserved.