Sagitta (optics)

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}}

,

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

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\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 $K$ .[1]

References

Barbastathis, George; Sheppard, Colin. "Real and Virtual Images" (PDF). MIT OpenCourseWare. Massachusetts Institute of Technology. p. 4. Retrieved 8 August 2017.

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[MIT-1] Barbastathis, George; Sheppard, Colin. "Real and Virtual Images" (PDF). MIT OpenCourseWare. Massachusetts Institute of Technology. p. 4. Retrieved 8 August 2017.

Sagitta (optics)

Aspheric surfaces

See also

References