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Radius of curvature (ROC) has specific meaning and sign convention in optical design. A spherical lens or surface has a center of curvature located either along or decentered from the system local
optical axis 300px, Optical axis (coincides with red ray) and rays symmetrical to optical axis (pair of blue and pair of green rays) propagating through different lenses. An optical axis is a line along which there is some degree of rotational symmetry in an o ...
. 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 (mathematics), 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 Lens (optics)#Types of simple lenses, biconvex lens from the side, the left surface radius of curvature is positive, and the right radius of curvature is negative. Note however that ''in areas of optics other than design'', other sign conventions are sometimes used. In particular, many undergraduate physics textbooks use the Gaussian sign convention in which convex surfaces of lenses are always positive. Care should be taken when using formulas taken from different sources.

# Aspheric surfaces

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 :$z\left(r\right)=\frac+\alpha_1 r^2+\alpha_2 r^4+\alpha_3 r^6+\cdots ,$ where the optic axis is presumed to lie in the z direction, and $z\left(r\right)$ is the ''sag''â€”the z-component of the Displacement (vector), displacement of the surface from the vertex, at distance $r$ from the axis. If $\alpha_1$ and $\alpha_2$ are zero, then $R$ is the ''radius of curvature'' and $K$ is the conic constant, as measured at the vertex (where $r=0$). The coefficients $\alpha_i$ describe the deviation of the surface from the axial symmetry, axially symmetric quadric surface specified by $R$ and $K$.