Flexible design of progressive addition lenses for effective sizing of viewing zones using ellipse, hyperbola, parabola, and circle parametric equations

This study addresses the critical issue of optical power distribution in progressive addition lenses (PALs). We introduce a novel approach by defining the addition vertex power curve along the meridian line as a trigonometric function. Four distinct conic equations (ellipse, hyperbola, parabola, and circle) are proposed to extend power distribution evenly across the lens surface. An offset parameter is introduced for controlling viewing area widths. The elliptical equations offer the best results for larger fixed focus areas, while circular equations excel for smaller areas. This personalized method caters to individual patient needs, providing optimized PAL designs.