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

[math]\displaystyle{ S(r) \approx \frac{r^2}{2 \times R} }[/math],

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 [math]\displaystyle{ r }[/math] 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

[math]\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 . }[/math]

Here, [math]\displaystyle{ K }[/math] is the conic constant as measured at the vertex (where [math]\displaystyle{ r=0 }[/math]). The coefficients [math]\displaystyle{ \alpha_i }[/math] describe the deviation of the surface from the axially symmetric quadric surface specified by [math]\displaystyle{ R }[/math] and [math]\displaystyle{ K }[/math].

See also

• Versine
• Chord