1. A system for recording an image of a scene, comprising: an image sensor that receives light representing the scene and generates image data representing a first image based on light representing the scene; a radially symmetric diffuser having a first side that receives light representing the scene and a second side and a one-dimensional thickness profile of the radially symmetric diffuser along a radial direction is random such that each ray of light passing through the radially symmetric diffuser from the first side to the second side forms a section of an annulus on the image sensor having a width w that is the difference between an inner radius and an outer radius of the annulus, such that w is larger than a width of a section of annulus that the ray of light would form in the absence of the radially symmetric diffuser, wherein width w is substantially constant regardless of where along the radial direction the ray of light passes through the radially symmetric diffuser; and a hardware processor that uses a point spread function corresponding to width w to generate a second image based on the image data representing the first image and that corresponds to a deblurred version of the first image.