Radius of curvature (ROC) has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located in (x, y, z) 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.