projector 10 as shown light is first generated by the lamp 12 having a bulb 14 located at a first focal point 16 of ellipsoid reflector 18 light is then re imaged at a second focal point 20 that is co incident with integrator rod 22 as discussed above the illumination pattern output from lamp 12 is converted within integrator rod 22 into a uniform rectangular pattern the rectangular light beam output from integrator rod 22 is then imaged onto a dmd digital micromirror device by a relay lens system not shown and is then projected to a screen the principles of the invention as set forth in detail below apply equally to other types of projectors where an integrator rod is used as discussed above the inventor has discovered that asymmetrically tapering the integrator rod 22 balances the brightness on the left and right hand sides of a projected image in situations where the projector exhibits brightness asymmetry the root cause es of which is are unknown as shown in fig2 the design of the integrator rod 22 u2032 according to an embodiment of the invention is asymmetric in the sense that only one side of it is tapered in the illustrated embodiment the input face 24 is made smaller in height than the output face 26 i e h 1 lt h 2 and l 1 lt l.