A new method to compute the target photometric variables of non-imaging optical systems is presented. The method is based on the phase space representation of each surface that forms the optical system. All surfaces can be modeled as detectors of the incident light and emitters of the reflected light. Moreover, we assume that the source can only emit light and the target can only receive light. Therefore, one phase space is taken into account for the source and one for the target. For the other surfaces both the source and target phase spaces are considered. The output intensity is computed from the rays that leave the source and hit the target. We implement the method for two-dimensional optical systems, and we compare the new method with Monte Carlo (MC) ray tracing. This paper is a proof of principle. Therefore, we present the results for systems formed by straight lines which are all located in the same medium. Numerical results show that the intensity found with the ray mapping method equals the exact intensity. Accuracy and speed advantages of several orders are observed with the new method.