Analysis of Signal Distortion Caused by Opening Ratio Variation of Main Scale and Index Scale in Linear Encoder

Abstract

Linear encoder as an important displacement measurement device has been widely used in manufacturing industry. The accuracy of linear encoder is based on the precision of its scales. In this article, the manufacturing process of the scales based on photolithography process and etching process was discussed in order to explain the opening ratio variation. A mathematical model was derived to analyze the effects of opening ratio variation on the waveform of output signal. The result shows that the waveform of the signal is cut off in comparison with the ideal waveform, and the magnitude of the output signal is changed.

A theoretical investigation of generalized grating imaging and its application to optical encoders

“…(19) that the pseudoimage at the observation plane is the summation of many harmonic components. Period of the harmonic components deduced from Eq.…”

“…Then, we can truncate the summations in Eq. (19) up to first order, and the intensity distribution of the fundamental component simplifies to…”

“…(19) indicates that the amplitude and contrast of pseudoimages are determined by cos(φ 2 ). From Eqs.…”

“…According to Eq. (19), the intensity distribution at the observation plane is The contrast of the pseudoimages is obtained by substituting Eq. (26) into Eq.…”

“…The harmonic distortion of the pseudoimages would lead to the harmonic distortion of the encoder signals, which will in turn result in interpolation errors [17]. In previous works [18,19], they have designed an optical encoder based on generalized grating imaging and analyzed the metrological errors caused by harmonic signals.…”