In optoelectronic applications or specialty lighting such as laser projection, structured light, and beam shaping, a non-imaging optical system is often required to achieve a specific light distribution design. For this purpose, a light distribution equation was established to describe the optical system. After the beam, the optical surface, and the target screen were discretized, the mapping relationship between the optical path length K of the sub-surface and the energy E at the target point was leveraged to obtain the corresponding light distribution equation under length-energy mapping. Although adjacent optical path lengths were subject to complex nonlinear competition in the length-energy mapping, K and E enjoyed a favorable monotonic mapping relationship that paved the way for introducing a deep neural network to fit the length-energy mapping. Then, deep learning was adopted to solve the light distribution equation as an inverse problem, and the required freeform optical surface was thereby obtained. With English letters and Arabic numerals in an input lattice of 28×28 as the training set, the design of optical surfaces with the corresponding character illumination distributions was achieved through multi-dimensional parameter adjustment and training of the three-layer neural network. The structural similarity of the optical simulation results reaches 99.97%, which indicates that the deep neural network can memorize (or store) the optical surfaces of each character by learning. This is equivalent to building an efficient and scalable intelligent optical character library. The basic light distribution equation established with complex media provides an elementary theoretical framework for existing light distribution methods and is conducive to the systematic expression of the theory of non-imaging optics.