Sagitta (Optics)

thumb|300x300px|Deep blue ray refers the radius of curvature and the red line segment is the sagitta of the curve (black). 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.

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

${\displaystyle S(r)=\frac{r^2}{R(1+\sqrt{1-(1+K)\frac{r^2}{R^2}})}+{\alpha }_1{r}^2+{\alpha }_2{r}^4+{\alpha }_3{r}^6+\cdots .}$

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

0.00 (0 votes) Original source: https://en.wikipedia.org/wiki/Sagitta (optics). Read more