Design considerations for the rotation of a plane premirror of a monochromator for reflecting synchrotron radiation onto the same spot of the dispersing grating of the XUV beamline.

The kinematic concept of employing a plane premirror rotated around an axis outside its surface to reflect the beam onto the same spot on the grating for three angular positions is formulated algebraically. Exact analytic solutions are found for determining the positions of the axis of rotation, the radius of the circle of rotation, and the central fixed spot on the grating in terms of the three angles and the height 2b of the grating above the incident beam. Typical numerical calculations are presented and discussed. It is generally observed that deviation of the reflected beam from the fixed spot is barely a few microns for b in centimeters.