Freeform imaging systems: Fermat's principle unlocks "first time right" design

Area of Science:

• Optics and Photonics
• Optical Engineering
• Computational Design

Background:

• Aberration theory has evolved for over 150 years to correct optical imperfections.
• Optical systems have advanced in complexity, incorporating freeform elements with unrestricted surface shapes.
• Designing freeform optics is challenging due to the high number of surface coefficients, limiting their widespread use.

Purpose of the Study:

• To present a deterministic direct optical design method for freeform imaging systems.
• To enable precise calculation of optical surface coefficients for minimal image blurring.
• To facilitate the integration of freeform elements in next-generation high-end optics.

Main Methods:

• Utilized differential equations derived from Fermat's principle.
• Solved these equations using power series for optical surface coefficient calculation.
• Applied the method to catoptric and catadioptric design examples.

Main Results:

• Developed a systematic, deterministic, and scalable design methodology.
• Successfully calculated optical surface coefficients to minimize aberrations for each order.
• Demonstrated the method's effectiveness on various optical system designs.

Conclusions:

• Introduced a disruptive methodology for designing optical imaging systems.
• Significantly reduced the reliance on trial-and-error in optical design.
• Paved the way for faster adoption of freeform optics in advanced imaging systems.