spherocylindrical
Having one spheric and one cylindric surface.
spherocylindrical: sphere and cylinder ground into one lens
A spherocylindrical lens has two different radii of curvature: one surface curves like a portion of a sphere, the other like a cylinder. This combination means light converges differently along two perpendicular meridians, making the lens correct astigmatism, where the eye or optical system focuses light unequally in different planes. The lens behaves as a sphere in one axis and a cylinder in the perpendicular axis.
These lenses are ground on special machines that cut both a spherical base and a cylindrical surface into the same piece of glass or plastic. The spherical component might have a power of, say, +2.00 diopters, while the cylindrical component adds another +1.50 diopters at 90 degrees to it. The resulting lens is notated as a prescription pair: base sphere power and cylinder power with an axis angle in degrees.
Prescription and Manufacturing
In eyeglass making, spherocylindrical lenses are the standard correction for astigmatism in humans. An optometrist's prescription like +2.00 +1.50 x 180 means a +2.00 diopter sphere with +1.50 cylinder at the 180-degree meridian. Manufacturing these to tolerance requires precision grinding and polishing; the cylinder axis must be accurate to within a degree or two, and the power to within 0.12 diopters for most eyeglasses.
Industrial imaging systems, cameras, and projection optics also use spherocylindrical elements to correct for barrel or pincushion distortion in single meridians, or to reshape beam cross sections in laser applications. A cylindrical component can compress a round beam into an ellipse without affecting focus in the perpendicular direction, useful in beam shaping for fiber coupling.
The term spherocylindrical distinguishes this lens type from purely spherical (single radius), toric (two different sphere radii), or plano-cylindrical (flat in one axis, curved in the other). Confusion sometimes arises because toric lenses, which have two different sphere radii in different meridians, are occasionally called spherocylindrical in older or looser usage, but the strict definition requires one axis to be truly cylindrical (zero curvature) and the other spherical.