Phased array feeds offer the possibility of more efficient use of large radio astronomy reflector antennas by providing more closely spaced beams over a wide field of view and higher aperture efficiency in each beam than have been realized with horn feeds. This paper examines the array design constraints imposed by complete sampling of the fields near the reflector focus. In particular, array element spacing must be less than 1 (lambda) for large F/D reflectors and less than about 0.7 (lambda) for F/D < 0.5. This rules out conventional horns as array elements and sets a limit on the array bandwidth. The receive-only case of radio astronomy permits the use of number of signal combining techniques that do not degrade system sensitivity. Because practical arrays are of finite extent, and unwanted noise from the antenna surroundings is largely coherent between the elements, neither field conjugate nor maximal-ratio diversity methods of array weight optimization can be used. A modified form of field matching is a good starting approximation, however. Correction of reflector errors is examined briefly.