Propagation-based phase contrast using the transport of intensity equation (TIE) allows rapid, deterministic phase retrieval from defocused images. For weakly attenuating objects, phase can be retrieved from a single image. However, the TIE suﬀers from significant low frequency artifacts due to enhancement of noise during phase retrieval. We demonstrate that by patterning the illumination source as approximately a modified Bessel function of the 2nd kind of zero order, quantitative phase can be imaged directly at the detector within a spatial frequency band. Outside of that band, Bessel sources still improve low frequency performance in phase retrieval.