Non-Circular-Arc Lens Curved-Surface Design for Display Optimization

The patent applies parameter changes by transitioning from a fixed circular-arc shape to variable curve shapes (hyperbola, ellipse, parabola) based on the refractive index characteristics of the lens. The curve shape parameters (a, b) are determined by the variance between lens refractive index and medium refractive index, allowing the lens to adapt to different optical properties while maintaining manufacturability through systematic parameter determination.

The lens curved-surface shape is made dynamic rather than static. Instead of a fixed circular-arc design, the curve shape changes according to the refractive index characteristics of the lens material and its interaction with the surrounding medium. This dynamic adaptation allows optimization of light manipulation for different display applications.

The patent provides systematic parameter determination methods for non-circular-arc curves (hyperbola, ellipse, parabola) based on refractive index variance. By establishing clear mathematical relationships between optical parameters and curve geometry, the design guides manufacturing processes, reducing the complexity of producing non-standard lens shapes.

The patent replaces complex mechanical trial-and-error lens design with optical parameter-based design. Instead of adjusting lens shapes through mechanical processes, the optimal shapes are determined through optical calculations involving refractive indices, allowing direct translation to manufacturing specifications.