Sagitta (optics) explained

Sagitta (optics) should not be confused with Sagitta (geometry).

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

S(r) ≈ (r ^{2})/(2 x R) ,

where is the radius of curvature of the optical surface. The sag 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) = (r ^{2})/(R\left ( 1+ \sqrt{ 1- ( 1+ K) (r ^{2})/(R ^{2})) \right )} + \alpha _{1} r ^{2+ \alpha} _{2} r ^{4+ \alpha} _{3} r ^{6+ …} . 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]

See also

• Versine
• Chord

Notes and References

1. Web site: Barbastathis. George. Sheppard. Colin. Real and Virtual Images. MIT OpenCourseWare. Massachusetts Institute of Technology. 8 August 2017. 4 .