Physics: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

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

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 $r$ 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

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

Here, $K$ is the conic constant as measured at the vertex (where $r=0$). The coefficients ${\alpha }_i$ describe the deviation of the surface from the axially symmetric quadric surface specified by $R$ and $K$.

See also

• Versine
• Chord