Radius of curvature
has specific meaning and sign convention in optical design
. A spherical lens
surface has a center of curvature
located in (x
) either along or decentered from the system local optical axis
. The vertex
of the lens surface is located on the local optical axis. The distance from the vertex to the center of curvature is the radius of curvature
of the surface. The sign convention for the optical radius of curvature is as follows:
- If the vertex lies to the left of the center of curvature, the radius of curvature is positive.
- If the vertex lies to the right of the center of curvature, the radius of curvature is negative.
Thus when viewing a biconvex lens from the side, the left surface radius of curvature is positive, and the right surface has a negative radius of curvature.
Note however that in areas of optics other than design, other sign conventions are sometimes used. In particular, many undergraduate physics textbooks use an alternate sign convention in which convex surfaces of lenses are always positive. Care should be taken when using formulas taken from different sources.
Optical surfaces with non-spherical profiles, such as the surfaces of aspheric lenses
, also have a radius of curvature. These surfaces are typically designed such that their profile is described by the equation
where the optic axis
is presumed to lie in the z
is the sag
—the z-component of the displacement
of the surface from the vertex, at distance
from the axis.
is then defined to be the radius of curvature
of the surface. The constant
is the conic constant
, and the coefficients
describe the deviation of the surface from a conic surface
(a surface that is a portion of a spheroid
, or hyperboloid