Limited available elemental image array resources may be the most severe bottleneck for the promotion and application of integral-imaging-based 3D display. We propose a nonlinear mapping method for the generation of an elemental image array to get a photorealistic pseudoscopic free 3D display based on the parallel light field reconstruction nature of the integral imaging system. All the light rays emitted from the display panel are classified into a corresponding parallel light field according to its direction, and all the parallel light fields are captured as orthogonal projections of the scene before synthesizing all the orthogonal projections using a nonlinear mapping method to form the final elemental image array. Preliminary optical experiments as well as ray optical analysis are conducted to prove the feasibility and validity of the proposed method. The proposed method can exploit most of the current 3D platform. It is an effective and efficient way to generate an elemental image array.