A scale-linearization method for precise laser interferometry

The authors discuss an increase in the precision of a laser interferometer based on the phase division of the fringe using a single-frequency laser for a distance measurement in the subnanometre range. The resolution of the interferometer is extended by using four paths of the laser beam across the measurement arm of the Michelson interferometer and by subsequent electronic division to the total resolution lambda/2048. The technique fulfils the expectation that the influence of the fringe distortion caused by a phase difference of pi/2 between two quadrature signals and the difference of the intensities will be lower. A further improvement of the linearity can be achieved by using a mathematical method, which is based on the real-time measurement of parameters of the detected interferometer fringe and an optimal approximation of the quadrature signals obtained by using a conical section. The obtained parameters are transformed from the analytical form to the parametric form of the equation of the conical section and an inverse function is established. Reproducible measurements with an error of less than 0.5 nm are available now.