In optics and especially telescope making, sagitta or sag is a measure of the glass removed to yield an optical curve. It is approximated by the formula
S ( r ) ≈ r 2 2 × R {\displaystyle S(r)\approx {\frac {r^{2}}{2\times R}}} , where R is the radius of curvature of the optical surface. The sag S(r) is the displacement along the optic axis of the surface from the vertex, at distance r {\displaystyle r} from the axis. A good explanation of both this approximate formula and the exact formula can be found here.
Aspheric surfaces 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
S ( r ) = r 2 R ( 1 + 1 − ( 1 + K ) r 2 R 2 ) + α 1 r 2 + α 2 r 4 + α 3 r 6 + ⋯ . {\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, K {\displaystyle K} is the conic constant as measured at the vertex (where r = 0 {\displaystyle r=0} ). The coefficients α i {\displaystyle \alpha _{i}} describe the deviation of the surface from the axially symmetric quadric surface specified by R {\displaystyle R} and K {\displaystyle K} .
See also Versine Chord
References