Sagitta (optics)

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

${\displaystyle S(r)\approx {\frac {r^{2}}{2\times R}}}$,

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 ${\displaystyle r}$ from the axis.

A good explanation both of 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

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

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]

See also

• Versine
• Chord

References

1. Barbastathis, George; Sheppard, Colin. "Real and Virtual Images" (PDF). MIT OpenCourseWare. Massachusetts Institute of Technology. p. 4. Retrieved 8 August 2017.