A photon sieve, modification of a Fresnel zone plate, has been recently proposed to achieve higher resolution imaging and spectroscopy at UV and x-ray wavelengths. In this paper, we present Fresnel imaging formulas that relate the output of a photon sieve imaging system to its input, originating from either a coherent or incoherent extended source. By using a well-known model for the zone plate, we also provide approximations to these imaging formulas, which are more efficient to compute. These imaging relations for both photon sieve and the approximate model are crucial for effectively analyzing and solving the inverse problems that arise from the new imaging modalities enabled by photon sieves. We illustrate this by formulating the forward model of the image formation process for an application in polychromatic imaging.