Absolute measurement method for a spherical surface by random off-axis rotation based on Zernike polynomials.

Area of Science:

• Metrology
• Optical Engineering
• Surface Metrology

Background:

• Accurate surface profile measurement is crucial in various scientific and industrial applications.
• Traditional methods often require high-precision positioning systems, limiting efficiency and accessibility.
• Addressing limitations in current surface measurement techniques is an ongoing challenge.

Purpose of the Study:

• To propose a novel off-axis rotation absolute measurement method for surface profiling.
• To enhance measurement efficiency and accuracy by treating random movements as off-axis rotations.
• To reduce reliance on high-precision positioning equipment.

Main Methods:

• Calculating the off-axis rotation center through feature point matching on the measured surface.
• Utilizing Zernike polynomial fitting for surface profile calculation.
• Implementing multiple rotations to mitigate symmetrical and environmental errors, collecting N(N-1)/2 results from N rotations.

Main Results:

• The proposed method achieves accurate surface profile results.
• High measurement efficiency is demonstrated compared to traditional techniques.
• The method eliminates the need for high-precision positioning systems.

Conclusions:

• The off-axis rotation absolute measurement method offers a highly efficient and accurate solution for surface profiling.
• This technique overcomes the limitations of traditional methods by not requiring precise positioning.
• The approach is suitable for various applications demanding precise surface metrology.