Freeform geometrical optics I: principles.

Area of Science:

• Optics and Photonics
• Computational Physics

Background:

• Classical lens design relies on established ray-tracing rules to calculate optical system parameters.
• Existing methods can be computationally intensive and may not universally accommodate all optical element types.

Purpose of the Study:

• To present a new theoretical foundation for lens design based on vector analytical solutions.
• To demonstrate a method that accounts for refractive, reflective, and catadioptric elements.
• To show how this approach enhances aberration control and reduces computational time.

Main Methods:

• Development of a reduced vector analytical solution set of equations.
• Application of the new theoretical framework to lens design calculations.
• Integration of aberration budget control at each optical surface.

Main Results:

• The vector analytical approach successfully incorporates all optical elements (refractive, reflective, catadioptric).
• Precise control over the system's aberration budget is maintained at every surface.
• Significant reduction in computation time compared to classical methods was achieved.

Conclusions:

• The proposed vector analytical method offers a versatile and efficient alternative to classical lens design.
• This approach provides enhanced control over optical system aberrations.
• The methodology enables faster and more comprehensive lens design for complex optical systems.