Design of a precise and robust linearized converter for optical encoders using a ratiometric technique

A linearization method with improved robustness for determining the displacement from sine and cosine signals generated by optical encoders is presented. The proposed scheme is based on a ratiometric technique and a dedicated compensation method. The scheme converts the sinusoidal signals into a nearly perfectly linear output signal, from which the displacement is determined precisely using a simple linear equation. Under the condition of ideal input signals, the theoretical analysis shows that the converter enables a determination of the displacement with a non-linearity error below 0.0029 µm for a linear optical encoder with a period of 20 µm. The performance of the converter with non-ideal input signals is also evaluated by establishing the relationship between the positioning errors and the parameter deviations of the input signals. Due to the robustness of the converter against the signal amplitude imbalance, a signal processing circuit is developed to convert the signal phase-shift error into the signal amplitude imbalance error. A displacement measurement experiment was carried out by applying the converter to a linear optical encoder with a period of 20 µm. A positioning accuracy of 0.2 µm over a travel length of 80 mm was achieved under laboratory conditions. The feasibility of the proposed converter has been confirmed from the experimental results.