Progressive Ophthalmic Lens Optimization via Directional Derivative Minimization

The patent applies parameter changes by modifying the optimization function to include directional derivatives of astigmatism and power gradients. This involves changing the mathematical parameters from simple power distribution to incorporating directional components (first and second directional derivatives) that account for astigmatism orientation and magnitude in different regions of the lens, thereby achieving better astigmatism control.

The patent introduces another dimension by adding directional derivative components to the optimization function. Instead of only considering scalar power values, the solution incorporates vector-like directional information (gradients in x and y directions), effectively moving from a one-dimensional power optimization to a multi-dimensional optimization that includes spatial orientation of astigmatism.

The patent applies local quality by implementing asymmetric weight distributions in the optimization function. Different regions of the lens (near zone, distance zone, intermediate zone) receive different weighting factors based on their specific optical requirements and astigmatism characteristics. This allows tailored optimization for each zone rather than applying a uniform approach across the entire lens surface.

The patent changes parameters by introducing angle-dependent weighting and prescription cylinder-based adjustments to the optimization function. The weights w1i, w2i, w3i are modified to account for local astigmatism orientation and magnitude, creating a more complex but region-specific optimization approach that adapts to local optical conditions.

The patent applies preliminary action by pre-calculating and storing the directional derivatives of astigmatism and power gradients during the lens design phase. These pre-computed values are then used in the optimization function, avoiding the need for complex real-time calculations during manufacturing or fitting. The directional information is prepared in advance to facilitate smoother optimization.

The patent introduces an intermediary optimization function that acts as a mediator between the complex optical parameters and the final lens design. This function F incorporates multiple terms (power errors, astigmatism, directional derivatives) with adjustable weights, serving as an intermediate computational layer that simplifies the overall optimization process by breaking it down into manageable components.