Aspheric cylindrical lens and method of fabrication

An optical lens for collimating a divergent input light, comprising:

• a substantially cylindrical and spherical back lens surface;
• a cylindrical and aspherical front lens surface defined by a plurality of coordinates, a set of said coordinates consisting of a first displacement from an optical axis of a divergent input light and a second displacement from a collimation plane, said optical axis and said collimation plane being orthogonally positioned wherein said front lens surface has been formed such that the optical path length traveled by each ray of said divergent input light from a source of said divergent input light to the collimation plane is substantially equal;
• and;
• said plurality of sets of coordinates satisfy the following conditions (1) and (2):
• H.sub.2 =H.sub.1 +(2R-(R-(R.sup.2 -H.sub.1.sup.2).sup.1/2))(tan .THETA..sub.2)-((D).sup.2 -SAG.sub.2 (H.sub.2).sup.2).sup.1/2
• SAG.sub.2 (H.sub.2)=D * cos .THETA..sub.2
• wherein reference symbol R is a radius of curvature of said spherical back lens surface, reference symbol H.sub.1 is a height above said optical axis which an off-axis diverging input light ray enters said back lens surface, reference symbol .THETA..sub.2 is an angle between an off-axis ray and a line parallel to said optical axis, and reference symbol D satisfies the following condition (3):
• D=(OPL.sub.1 +OPL.sub.2 -OPL.sub.0)/(n-cos .THETA..sub.2)
• wherein reference symbol n is a refractive index of a lens medium for said optical lens, reference symbol OPL.sub.0 is an optical length, measured along said optical axis, from the source of said diverging input light to said aspheric front lens surface, reference symbol OPL.sub.1 is an optical length, measured along an off-axis ray of input light from said source of said diverging input light to a point on said back lens surface, and reference symbol OPL.sub.2 satisfies the following condition:
• OPL.sub.2 =n(((2R-(R-(R.sup.2 -H.sub.1.sup.2).sup.1/2 -OS) * tan .THETA..sub.2).sup.2 +(2R-(R-(R.sup.2 -H.sub.1.sup.2).sup.1/2 -OS).sup.2).sup.1/2) (4)
• wherein reference symbol OS is the distance, measured along said optical axis, from said collimation plane to said aspherical front lens surface.