When the rectangular slit of an optical encoder projects an image, the containment of higher-order components in the projected image depends on the gap distance. Therefore, we performed the Fourier series expansion of the function describing Fresnel diffraction pattern to obtain a simple relational expression that can show the relation between the gap distance and the containment of each order component and then carried out an experiment to verify the obtained expression. Using this expression, we found that certain orders of the wave components disappear depending on the slit opening ratio and also that the use of a slit with an opening ratio smaller than 0.5 results in lesser distortion of the waveform over a wide range of gap values. Reduction of waveform distortion over such a wide range can prevent increment of errors caused by shaft displacement in the axial direction and assembly errors. Thus, robust performance of the encoder can be achieved. The results of this study are expected to be useful in the design of robust optical encoders.
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