sagitta (optics)

file:Sagitta_(optics).jpg

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 {{mvar|R}} is the radius of curvature of the optical surface. The sag {{math|S(r)}} is the displacement along the optic axis of the surface from the vertex, at distance $r$ from the axis.

A good explanation of both this approximate formula and the exact formula can be found [https://web.archive.org/web/20160308214806/http://www.opticampus.com/popcourse.php?url=high_powered%2F 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

: $S(r)=\frac{r^2}{R\left (1+\sqrt{1-(1+K)\frac{r^2}{R^2}}\right )}+\alpha_1 r^2+\alpha_2 r^4+\alpha_3 r^6+\cdots .$

Here, $K$ 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 $K$ .{{cite web|last1=Barbastathis|first1=George|last2=Sheppard|first2=Colin|title=Real and Virtual Images|url=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|website=MIT OpenCourseWare|publisher=Massachusetts Institute of Technology|accessdate=8 August 2017|page=4 }}

References

Category:Optics

sagitta (optics)

Aspheric surfaces

See also

References