Sagitta (optics)

Optical surfaces with non-spherical profiles, such as the surfaces of aspheric lenses, are typically designed such that their sag is described by the equation

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

Here, ${\displaystyle K}$ 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 ${\displaystyle K}$.[1]

• Versine
• Chord