Equations to design an aplanatic catadioptric freeform optical system

Area of Science:

• Optical Engineering
• Freeform Optics Design

Background:

• Designing complex optical systems like catadioptric freeform systems presents significant challenges.
• Existing methods may lack the flexibility to handle arbitrary surface shapes and orientations.

Purpose of the Study:

• To introduce a novel set of equations for designing aplanatic catadioptric freeform optical systems.
• To provide a foundational methodology for creating initial designs of complex optical systems.

Main Methods:

• Developed a partial differential equation system to define optical surfaces.
• Employed numerical solutions to determine the first and last surfaces of the system.
• Applied the method to freeform optical systems with arbitrary reflective/refractive surfaces.

Main Results:

• A set of equations for designing aplanatic catadioptric freeform optical systems was successfully formulated.
• The numerical solution provides a defined starting point for the first and last surfaces.
• Demonstrated the methodology with an illustrative example.

Conclusions:

• The presented equations offer a systematic approach to initiating the design of complex freeform optical systems.
• The methodology facilitates the creation of initial setups for further optimization in optical design.
• This work contributes a valuable tool for engineers designing advanced catadioptric systems.