Abstract
The demand for ultrahigh resolution in positioning and alignment is increasing in the field of precision engineering. By superimposing a pair of specially coded two-dimensional (2D) gratings, the correct alignment position of the two gratings can be detected with high resolution and accuracy. Due to the small dimensions of the grating, the diffraction effect is strong and it cannot be ignored. In this article, design considerations for such 2D zero-reference gratings are presented and the behavior of the diffraction of the zero-reference gratings is analyzed theoretically. The transmission function obtained by diffraction analysis agrees with the result from the autocorrelation method by neglecting the diffraction effect. The alignment is independent of the small variation in the gap between two gratings.
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