Centered optical systems are relatively easy to design and align but when decentered and tilted surfaces are used alignment becomes difficult unless you have a plan. To illustrate this we use the modified Yolo telescope in the Zemax samples folder:

This "simple" telescope was thought so difficult to align that its inventor, Art Leonard, claims never to have built one. However, it is really quite simple using the COC Point option in the Prescription menu, a simple fixture and an autostigmatic microscope.

Although the paraxial lens data is very simple, the three mirrors are tilted about both the x and y axes. If one could locate the centers of curvatures of the mirrors relative to a reference location the alignment would be straightforward. This information is available in the COC Point option in the Prescription Data Window as shown below. This is found under Reports -> Prescription Data, in the 'COC Point' section. This gives the x, y, z locations of the centers of curvature of the three mirrors relative to whichever surface is chosen as the Global Reference, which is surface 1 in this case.

Then, a fixture can be made of a plate in the x-z plane with holes in x-z for posts and bearing balls establishing the heights in the y direction for each center of curvature. Similar holes and posts can be used to locate the mirror vertices. Each mirror is aligned separately by locating the global vertex in x-y-z with the concave mirror surface facing the ball at its center of curvature. An autostigmatic microscope is centered on the ball, the ball removed and the mirror aligned to the microscope. The finished telescope is shown below in two views where the lines from each mirror’s vertex to its respective center of curvature extend far off the drawing and are not fully shown:



 The upper view is the y-z plane and the lower is the x-z plane.

This simple report gives the data needed to align complex three-dimensional geometries.