Light field cameras allow us to digitally refocus a photograph after the time of capture. However, recording a light field requires either a significant loss in spatial resolution [11, 21, 10] or a large number of images to be captured [12]. In this paper, we propose incoherent holography for digital refocusing without loss of spatial resolution from only 3 captured images. The main idea is to capture 2D coherent holograms of the scene instead of the 4D light fields. The key properties of coherent light propagation are that the coherent spread function (hologram of a single point source) encodes scene depths and has a broadband spatial frequency response. These properties enable digital refocusing with 2D coherent holograms, which can be captured on sensors without loss of spatial resolution. Incoherent holography does not require illuminating the scene with high power coherent laser, making it possible to acquire holograms even for passively illuminated scenes. We provide an in-depth performance comparison between light field and incoherent holographic cameras in terms of the signal-to-noise-ratio (SNR). We show that given the same sensing resources, an incoherent holography camera outperforms light field cameras in most real world settings. We demonstrate a prototype incoherent holography camera capable of performing digital refocusing from only 3 acquired images. We show results on a variety of scenes that verify the accuracy of our theoretical analysis.