Centration is defined as the maximum allowable deviation between the optical and mechanical axes for a spherical lens. The optical axis is defined as the line connecting the centers of curvatures of both lens surfaces (as shown below). The mechanical axis is the centerline of the outer cylindrical edge of the lens or simply its geometrical axis. The mechanical axis coincides with the rotating axis of the centering machine that edges the lens to its final diameter. This centering process also, in turn, defines the diameter tolerance, which is typically +0, given mounting considerations.
If a ray of light is coincident with the mechanical axis, then a lens will deviate the ray so that it passes the optical axis at the focal plane (as shown below). The separation of the two axes at the focal plane is then defined as the decentration, or axial displacement centering error. The centering accuracy value used in optical fabrication is actually twice this value and is often called the Total Indicator Runout or TIR. The deviation is then the angle equal to the decentration divided by the focal length of the lens. The concentricity or centration of a lens is typically specified by the deviation angle, however it is typically tested at double the value while the lens is rotated. An angular deviation of 1 to 3 arc minutes is common for precision components.
