300x300px, Deep blue ray refers the radius of curvature and the red line segment is the sagitta of the curve (black). In

optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...

and especially

telescope making ''Amateur Telescope Making'' (''ATM'') is a series of three books edited by Albert G. Ingalls between 1926 and 1953 while he was an associate editor at ''Scientific American''. The books cover various aspects of telescope construction and obser ...

, 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

, where is the

radius of curvature In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius o ...

of the optical surface. The sag is the

displacement Displacement may refer to: Physical sciences Mathematics and Physics * Displacement (geometry), is the difference between the final and initial position of a point trajectory (for instance, the center of mass of a moving object). The actual path ...

along the

optic axis An optical axis is a line along which there is some degree of rotational symmetry in an optical system such as a camera lens, microscope or telescopic sight. The optical axis is an imaginary line that defines the path along which light propagat ...

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 foun
here

Aspheric surfaces

Optical surfaces with non-spherical profiles, such as the surfaces of

aspheric lens An aspheric lens or asphere (often labeled ''ASPH'' on eye pieces) is a lens (optics), lens whose surface profiles are not portions of a sphere or Cylinder (geometry), cylinder. In photography, a camera lens, lens assembly that includes an aspheri ...

es, are typically designed such that their sag is described by the equation :

S(r)=\frac+\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 In geometry, circular symmetry is a type of continuous symmetry for a Plane (geometry), planar object that can be rotational symmetry, rotated by any arbitrary angle and map onto itself. Rotational circular symmetry is isomorphic with the circl ...

quadric surface specified by

R

and

K

References

{{optics-stub Optics

Aspheric surfaces

See also

References