Necessary conditions for spatially incoherent illumination of a three-dimensional object

Spatially incoherent imaging systems are characterized by a linear-in-intensity relationship between the object and the image distributions. While strict spatial incoherence is theoretically not achievable, a particular imaging system may be made effectively linear in intensity by a choice of the appropriate illumination source location and size. The requirement for source size for effectively incoherent illumination of a two-dimensional object is well known. I extend the arguments for choosing the source size in a two-dimensional imaging system to develop necessary conditions for the source size for effectively spatially incoherent illumination of a three-dimensional object. While the conditions are necessary, they are not sufficient, since coherence in the direction of the optical axis is not addressed. (C) 2001 Optical Society of America. OCIS codes: 070.2580, 110.2990, 110.4980, 180.6900.