1. A prediction system for predicting solar irradiance based on cloud characteristics, the system comprising: a sky imager comprising a customized lens configured to capture one or more substantially planar images of the sky, wherein the customized lens has a projection map given by the equation: R ⁡ ( θ ) = 2 × f × sin ⁡ ( θ 2 ) cos ⁡ ( θ 2 ) γ or approximations thereof, wherein R is a position of an image point on an image sensor, f is the focal length of the customized lens, θ is an angle of observation, and γ is a constant, having a value between 0 and 1; an image processor coupled to the sky imager and configured to process the one or more substantially planar images; a computing system coupled to the image processor and configured to: detect cloud characteristics based on the one or more substantially planar images; and predict the solar irradiance based on the cloud characteristics.