Diodcoll shows a practical lens in which the difference between aplanatic and paraxial ray aiming is clearly visible. Paraxial ray aiming is used in many optical design programs, but it does not provide a good model for systems that have a large numerical aperture on the object side. Aplanatic ray aiming is based on the canonical coordinates introduced by H.H. Hopkins, and is generally more accurate for these systems. The optical system itself is a commercial design available from Melles Griot, used to collimate diode laser beams.�This lens is designed to take light from a laser diode and produce a collimated beam. It is a commercially available design available from Melles Griot as their part number 06GLC002. It is designed for a numerical aperture of 0.5 on the short conjugate side, and has a focal length of about 8mm.
In traditional optical design, lenses are designed with the long conjugate side on the left. There are two reasons for this convention. First, there is a maximum distance that rays can be traced without loss of numerical accuracy using ordinary ray trace equations (in OSLO, this distance is 10
8 units). Many programs are set up to take object distances greater than this as being at infinity, for which special equations are used. When the long distance is on the image side, the system must be evaluated in afocal mode. This is not a problem for OSLO, which has built-in afocal mode support. The second reason has to do with the way that rays are aimed at the lens from object space. In traditional programs, rays are aimed at a flat entrance pupil. This means that fractional coordinates of rays are proportional to their direction tangents in object space. When the object is at a great distance, this is ok, but actually fractional coordinates should be proportional to the direction cosines of rays in object space. We call this aplanatic ray aiming, as opposed to paraxial ray aiming. Aplanatic ray aiming was used in GENII for many years, and has been introduced into OSLO since the programs were merged in 1994. It has the advantage that OSLO can now be used to evaluate systems from short to long conjugate, which is not possible with a program that uses paraxial ray aiming. The laser diode collimator is a fast enough system for the differences between paraxial and aplanatic ray aiming to be readily observable. The figures below shows the two cases (the system was changed to focal mode to produce these plots).
Aplanatic ray aiming:
Paraxial ray aiming:
