The focus path of a laser beam deflected by a prismatic polygon mirror was calculated. It is shown that the larger the focal distance of the objective or the polygon radius, the closer the focus path approaches a straight scanning line. Especially in the case of small pattern scanning, a remarkably small deviation between actual focus path and straight scanning line can be achieved by suitable sizing and arrangement of the optical elements.
U. Bergmann, K. Klose, and L. Spiess, "Focus path of a laser beam deflected by a prismatic polygon mirror: its calculation and optimization," Appl. Opt. 15, 3084-3088 (1976)