![]() Specifically, the 2D grating pitches along the X- and Y-directions should exhibit consistency to achieve uniform ☑-order 2D diffraction efficiencies for higher signal-to-noise ratios of the interference signals. Inevitably, the overall performance of the optical encoder strongly depends on the 2D crossed-grating structural parameters. Consequently, a relative displacement with a high-resolution comparable to that from laser interferometers can be obtained upon analyzing the interference signals 16. The movements of the grating with respect to the encoder’s reading head cause phase shifts of the ☑-order diffracted beams from the 2D crossed grating these are converted into interference intensity changes. In particular, two-dimensional (2D) crossed gratings with equal pitches along two orthogonal directions (the X- and Y-directions) are commonly employed in planar/surface optical encoder systems for multiaxis displacement measurements these gratings are key components that provide a measurement reference. Various types of diffraction gratings, such as blazed, ladder, planar, and concave gratings, have already been developed for application in monochromators 12, spectrometers 13, optical waveguides 14, optical encoders 8, 9, 10, 11, 15, and other optical instruments. Highly uniform, periodic micro- and nanoscale array structures are utilized in diverse applications involving photonic crystals 1, 2, 3, optical metamaterials 4, 5, photodetectors 6, 7, and diffraction gratings 8, 9, 10, 11. Moreover, our rapid and stable approach for patterning period-tunable two-dimensional-array microstructures with high uniformity could be applicable to other multibeam interference lithography techniques. The proposed system is a promising approach for fabricating high-uniformity two-dimensional crossed gratings with a relatively large grating period range of 500–1500 nm. A polarization modulation model is established considering two conditions of eliminating the unexpected interference and providing the desired identical interference intensities. Polarization states of three sub-beams, defining the uniformity of the interference fringes, are modulated at their initial-polarization states based on a strict full polarization tracing model in a three-dimensional space. The two-dimensional-pattern period can also be flexibly tuned by adjusting the interferometer spatial positioning. Orthogonal two-axis Lloyd’s mirror interference and polarization modulation produce three sub-beams, enabling the formation of two-dimensional crossed-grating patterns with wavelength-comparable periods by a single exposure. A polarized holographic lithography system is proposed for patterning high-uniformity microscale two-dimensional crossed-grating structures with periodic tunability. Periodic microscale array structures play an important role in diverse applications involving photonic crystals and diffraction gratings.
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