Light Fields capturing all light rays at every point in space and in all directions contain very rich information about the scene. This rich description of the scene enables advanced image creation capabilities, such as re-focusing or extended depth of field from a single capture. But, it yields a very high volume of data which needs compression. This paper studies the impact of Light Fields compression on two key functionalities: refocusing and extended focus. The sub-aperture images forming the Light Field are compressed as a video sequence with HEVC. A focus stack and the scene depth map are computed from the compressed light field and are used to render an image with an extended depth of field (called the extended focus image). It has been first observed that the Light Field could be compressed with a factor up to 700 without significantly affecting the visual quality of both refocused and extended focus images. To further analyze the compression effect, a dedicated quality evaluation method based on contrast and gradient measurements is considered to differentiate the natural geometrical blur from the blur resulting from compression. As a second part of the experiments, it is shown that the texture distortion of the in-focus regions in the focus stacks is the main cause of the quality degradation in the extended focus and that the depth errors do not impact the extended focus quality unless the light field is significantly distorted with a compression ratio of around 2000:1