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Sagitta (optics)

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Not to be confused with Sagitta (geometry).
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 ) ≈ r 2 2 × R {\displaystyle 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 {\displaystyle r} from the axis.

A good explanation of both 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 ) = r 2 R ( 1 + 1 − ( 1 + K ) r 2 R 2 ) + α 1 r 2 + α 2 r 4 + α 3 r 6 + ⋯ . {\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 .}

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

See also

References

  1. 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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