Radius of curvature (optics)

Optical surfaces with non-spherical profiles, such as the surfaces of aspheric lenses, also have a radius of curvature. These surfaces are typically designed such that their profile is described by the equation

${\displaystyle z(r)={\frac {r^{2}}{R\left(1+{\sqrt {1-(1+K){\frac {r^{2}}{R^{2}}}}}\right)}}+\alpha _{1}r^{2}+\alpha _{2}r^{4}+\alpha _{3}r^{6}+\cdots ,}$ 

where the optic axis is presumed to lie in the z direction, and ${\displaystyle z(r)}$  is the sag—the z-component of the displacement of the surface from the vertex, at distance ${\displaystyle r}$  from the axis. If ${\displaystyle \alpha _{1}}$  and ${\displaystyle \alpha _{2}}$  are zero, then ${\displaystyle R}$  is the radius of curvature and ${\displaystyle K}$  is the conic constant, as measured at the vertex (where ${\displaystyle r=0}$ ). The coefficients ${\displaystyle \alpha _{i}}$  describe the deviation of the surface from the axially symmetric quadric surface specified by ${\displaystyle R}$  and ${\displaystyle K}$ .^[2]

• Radius of curvature (applications)
• Radius
• Base curve radius
• Cardinal point (optics)
• Vergence (optics)