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Ultraprecision Real-Time Displacements Calculation Algorithm for the Grating Interferometer System.

Weinan Ye1,2, Ming Zhang3,4, Yu Zhu5,6

  • 1State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China. yewn12@mails.tsinghua.edu.cn.

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Summary
This summary is machine-generated.

This study presents a fast polynomial approximation algorithm for real-time six degrees-of-freedom (DOF) displacement calculation in grating interferometry, crucial for precise wafer stage positioning.

Keywords:
algorithmgeometric errorgrating interferometerreal-timerotation–translation couplingultraprecision

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Area of Science:

  • Metrology
  • Optical Engineering
  • Semiconductor Manufacturing

Background:

  • Grating interferometry offers stable displacement measurement for wafer stage positioning.
  • Real-time calculation of six degrees-of-freedom (DOF) displacement is essential for precision manufacturing.

Purpose of the Study:

  • To develop a fast and precise algorithm for real-time six DOF displacement calculation using grating interferometry.
  • To establish a phase shift-displacement of the wafer stage (DOWS) model based on affine transformation.

Main Methods:

  • Analyzed diffraction spot displacement and optical path changes using affine transformation.
  • Developed a polynomial approximation algorithm utilizing frequency domain characteristics for model reduction.
  • Verified the algorithm through experimental testing and ZEMAX simulations.

Main Results:

  • Successfully modeled the relationship between phase shifts and DOWS.
  • Demonstrated the algorithm's capability for real-time six DOF displacement calculation.
  • Validated the algorithm's accuracy and efficiency via experiments and simulations.

Conclusions:

  • The polynomial approximation algorithm provides a fast and precise solution for real-time six DOF displacement measurement.
  • This technique enhances the positioning accuracy of wafer stages in semiconductor manufacturing.
  • Grating interferometry, coupled with this algorithm, shows significant potential for advanced metrology applications.