Geometry-invariant gradient refractive index lens: analytical ray tracing.

Area of Science:

• Optics and Photonics
• Biomedical Optics
• Ophthalmic Lens Design

Background:

• Gradient refractive index (GRIN) lenses are crucial optical components.
• Existing GRIN lens models often lack analytical solutions for ray tracing.
• Understanding the human crystalline lens requires accurate GRIN models.

Purpose of the Study:

• Introduce a new class of GRIN lens with invariant geometry.
• Develop an analytical model for paraxial ray tracing in GRIN lenses.
• Demonstrate the application of this model for eye lens research.

Main Methods:

• Developed a GRIN lens model with iso-indicial contours mimicking external shape.
• Employed a coincoid of revolution with a higher-order aspheric term for surface representation.
• Derived closed-form expressions for ray height and angle for analytical paraxial ray tracing.

Main Results:

• Achieved invariant geometry in the GRIN structure.
• Enabled analytical calculation of optical power and third-order monochromatic aberrations.
• Demonstrated the model's suitability for studying the eye's accommodation mechanism.

Conclusions:

• The presented geometry-invariant GRIN lens offers an analytical solution for optical design.
• This model is valuable for reconstructing and analyzing the crystalline lens of the human eye.
• The analytical approach simplifies the study of GRIN lenses in biological systems.