Multiple harmonics suppression for optical encoders based on generalized grating imaging

In this work, we perform an investigation on the multiple harmonics suppression for optical encoders based on generalized grating imaging. We firstly analyse the formation of the harmonic distortion of the encoder signals and evaluate the interpolation errors caused by the higher harmonic signals. The result shows that the harmonic distortion of the encoder signals depends mainly on the higher harmonic components in the interference fringe. In addition, it shows that the higher harmonic signals influence the Lissajous figure of the encoder signals significantly and introduce a relatively large interpolation error. Then, conditions for eliminating the higher harmonic signals are studied, and optical filtering methods using specially designed index grating are proposed. We explain the filtering principle in detail and present three forms of index grating for multiple harmonics suppression. In particular, we show the patterns of the index grating for eliminating the dominant third and fifth harmonics, corroborating the results with numerical simulations. The results show that the amplitudes of the third and fifth harmonics are equal to zero theoretically, such that approximately ideal sinusoidal signals are obtained. Since the harmonic signals are considerably suppressed, the proposed methods will be useful for high-accuracy interpolation of encoder signals.