Description and tolerance analysis of freeform surface figure error using specific-probability-distributed Gaussian...

Area of Science:

• Optical Engineering
• Metrology

Background:

• Freeform surfaces are crucial in advanced optical design.
• Surface figure errors in freeform imaging systems degrade system performance.
• Accurate tolerance analysis is needed for manufacturing freeform optics.

Purpose of the Study:

• To develop a practical method for representing and analyzing freeform surface figure errors.
• To incorporate manufacturing difficulty into tolerance analysis.
• To validate the method on a nonsymmetric freeform off-axis three-mirror system.

Main Methods:

• Utilized a sum of specific-probability-distributed Gaussian radial basis functions for error representation.
• Incorporated manufacturing difficulty of different surface areas.
• Performed tolerance analysis considering surface figure error and assembly error.

Main Results:

• The proposed method is easy-to-use and practical for freeform surface error analysis.
• Demonstrated the effectiveness of the method in tolerance analysis of a complex system.
• Showcased the feasibility of considering both figure and assembly errors.

Conclusions:

• The developed method provides a robust approach for freeform surface figure error representation and tolerance analysis.
• The method accounts for practical manufacturing constraints, enhancing optical system design.
• The approach is effective for complex, nonsymmetric freeform optical systems.