In optical projection lithography of all types, optimum performance depends on the design and precise alignment of the source(s) and optical components that illuminate photomasks, as well as those for the projection lens. In this paper, we illustrate the effects of abnormalities in the illumination system; these abnormalities include asymmetric nonuniformity of the light source, obscurations, aberrations of the illumination optics, and telecentric error. 'Complex' illumination describes cases wherein all or part of the field of a stepper or scanning tool is illuminated asymmetrically. The interaction of complex illumination at the photomask with defocus or aberrations generates interference effects in the same manner as phase shifting or off-axis illumination, thereby modulating the image and, in many cases, shifting the image from its intended location. We calculate, from scalar coherence theory, quantitative influences on overlay for 0.35 micrometers lithography, and we determine selected tolerances for source uniformity and symmetry as a function of wavelength and coherence parameter. The effects of complex illumination are object-dependent, and we describe the variation with mask polarity, feature size, and proximity. We will consider the use of phase masks, the use of a scanned source and projection lens, and the use of off-axis illumination as special cases and describe their interaction with complex illumination in lithography. With the use of simulation software for lithography, we demonstrate the effects of complex illumination within photoresist patterns. We show that, for expected performance of illumination in a well-characterized step and repeat or scanning tool, the effects of complex illumination are seen to be small in comparison to expected alignment tolerances. For selected cases, we demonstrate that abnormalities arising from obstructed or incorrectly positioned components cause significant errors.