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In interference linear optical displacement sensors, precise position information is provided by the pair of quadrature sine and cosine signals while measuring scales moves along each other. One of these scales is a transmission diffraction grating that combines beam splitter function with phase retardation element. Precalculated parameters of that gratings based not only on diffraction efficiency analysis but phase relations in orders as well, helps to stabilize quadrature signals in the displacement sensor. This paper set the optimization condition in terms of phase shifts of light in diffraction orders influencing phase imbalance. To simulate the conversions of optical radiation by diffraction gratings, a rigorous coupled waves analysis was used. The phase imbalance of the obtained quadrature signals is estimated depending on the uncertainties of influencing parameters.
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M. V. Shishova, M. S. Kovalev, S. B. Odinokov, A. Y. Zherdev, D. S. Lushnikov, "Relief phase diffraction gratings providing quadrature phase shift for optical encoder," Proc. SPIE 11367, Photosensitive Materials and their Applications, 1136717 (1 April 2020); https://doi.org/10.1117/12.2555389