Transmission functions are derived that are valid in the nonparaxial case for a class of lenses that will image a continuum of points along an optical axis to a single image point. This lens, which we call a logarithmic asphere, is then used in a digital camera. The resolution of the camera is limited by the pixel size of the CCD; i.e., it is not diffraction limited. Digital processing is used to recover the image, and image-plane processing is used for speed. We find a tenfold increase in the depth of field over that for the diffraction-limited case.