The challenge in rendering integral images is to use as much information preserved by the light field as possible to reconstruct a captured scene in a three-dimensional way. We propose a rendering algorithm based on the projection of rays through a detailed simulation of the optical path, considering all the physical properties and locations of the optical elements. The rendered images contain information about the correct size of imaged objects without the need to calibrate the imaging device. Additionally, aberrations of the optical system may be corrected, depending on the setup of the integral imaging device. We show simulation data that illustrates the aberration correction ability and experimental data from our plenoptic camera, which illustrates the capability of our proposed algorithm to measure size and distance. We believe this rendering procedure will be useful in the future for three-dimensional ophthalmic imaging of the human retina.