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].[1]

## See also

* Versine
* Chord

## References

1. ↑ Barbastathis, George; Sheppard, Colin. "Real and Virtual Images". Massachusetts Institute of Technology. p. 4. https://ocw.mit.edu/courses/mechanical-engineering/2-71-optics-spring-2009/video-lectures/lecture-4-sign-conventions-thin-lenses-real-and-virtual-images/MIT2_71S09_lec04.pdf. Retrieved 8 August 2017.

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