The problem of a pinhole camera is discussed using the theory of partial coherence. In particular the incoherent limit shows that the minimum object or image distances should be greater than one far field distance of the pinhole. The theoretical resolution limit is inversely proportional to the product of the pinhole size and the number of pinhole far field distances to the object plane. However, consideration of the three dimensional intensity distribution of the camera impulse response shows that the maximum resolution is achieved at one third of a far field distance. The optimum pinhole size is also discussed. In the coherent limit it is shown that the imaging system is inherently non-linear, and that the speckling deteriorates the image. Experimental results demonstrating these conclusions are shown.