Generalized formulas for ray-tracing and longitudinal spherical aberration.

Area of Science:

• Optics and Photonics
• Optical Engineering
• Computational Optics

Background:

• Traditional paraxial ray-tracing formulas are limited to small angles of incidence.
• Accurate optical design requires methods that account for nonparaxial rays and complex surfaces.
• Existing analytical ray-tracing techniques can be computationally intensive or less general.

Purpose of the Study:

• To generalize paraxial ray-tracing formulas to include nonparaxial rays.
• To develop a new, efficient analytical ray-tracing procedure for centered systems of spherical surfaces.
• To derive exact formulas for meridional rays and longitudinal spherical aberration.

Main Methods:

• Derivation of a new single meridional formula for spherical surfaces, applicable to aspheric surfaces.
• Development of a two-equation analytical ray-tracing procedure for centered spherical systems.
• Application of the procedure to derive exact formulas for thick/thin lenses and spherical aberration.

Main Results:

• A generalized meridional formula reducible to paraxial approximations and applicable to general surfaces.
• An exact, shortest-known analytical ray-tracing procedure for centered spherical systems.
• Exact formulas for meridional rays and longitudinal spherical aberration, with numerical validation.

Conclusions:

• The developed methods offer a significant advancement in optical ray tracing and lens design.
• The new procedure is highly efficient and versatile, applicable to paraxial and nonparaxial rays.
• The findings facilitate more accurate calculations of optical system performance and aberrations.