Theory of alignment monitoring by diffraction from superimposed dual gratings

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Abstract
Theoretical considerations are presented on characteristics of the optical-alignment technique using dual gratings. The general formulation of the diffraction pattern is derived for superimposition of dual amplitude-phase gratings, as functions of aperture ratios for gratings and separation gaps between dual gratings. Numerical analyses reveal characteristics for precise positioning control or alignment technique, which utilize the detection of the minimum value of the first-order diffraction beam or the detection of the zero cross point of the difference in intensities between +1- and -1- order diffraction light for dual gratings. Alignment errors due to variations in an incident light angle, displacement in detector position, and fabrication errors for the gratings are also discussed.

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