Analytical solution of an afocal two freeform mirror design problem

Area of Science:

• Optics
• Optical Design

Background:

• Afocal optical systems are crucial for various imaging applications.
• Designing systems with freeform optics presents unique challenges.
• First-order optics provides a foundational framework for analyzing optical systems.

Purpose of the Study:

• To investigate a novel afocal two freeform mirror design problem.
• To derive analytic solutions for first-order partial differential equations governing such systems.
• To present and analyze specific design examples.

Main Methods:

• Formulation of first-order partial differential equations for a two freeform mirror system.
• Derivation of analytic solutions under the condition of parallel x-y and x'-y' axes.
• Selection and presentation of two distinct design solutions.

Main Results:

• An analytic solution for the afocal two freeform mirror design problem was obtained.
• One presented solution is semiaplanatic, satisfying the aplanatic condition for x-coordinates only.
• A novel aplanatic two-mirror system lacking rotational symmetry was demonstrated.

Conclusions:

• The study provides a method for designing afocal two freeform mirror systems.
• The findings introduce new possibilities for optical system design, including non-rotationally symmetric aplanatic systems.