Technical Notes

ROTATION SEQUENCES AND EULER ANGLES

                   ROTATION SEQUENCES AND EULER ANGLES
                        (c) 1993, 2009  M.Lampton
                             STELLAR SOFTWARE

     The orientation of an object in three dimensions can be
     described an a variety of ways.  One such description as
     follows: take an arbitrary point P that is not the origin, and
     write its coordinates (x,y,z) in a frame of reference fixed in
     the object.  Also, write its coordinates (X,Y,Z) in a lab frame
     of coordinates having the same center.  The matrix M that

HOW TO SET UP AN AUXILIARY OPTICAL AXIS

               HOW TO SET UP AN AUXILIARY OPTICAL AXIS
                      (c) 1992, 2003, 2009 M.Lampton
                           STELLAR SOFTWARE
 

     Suppose a group of optical elements is to be lined up along
     some axis that is neither the lab X, Y, or Z directions.  How
     does one express the positions and orientations of its elements
     in the lab frame to enter them into a BEAM optics table?

     This auxiliary axis will have its origin somewhere in space,
     say (Xa Ya Za).  It will also have some direction along which