Faithful reconstruction, which is a key phenomenon in optical data storage, is significant in polarization holography and has attracted much attention. It is defined as the reconstructed wave being identical to the signal wave. We design an experiment to observe the faithful reconstruction of elliptical polarization holography in which the two orthogonal elliptical polarization waves are applied in the recording stage. In the experiment, phenanthrenequinone-doped poly methyl methacrylate is used as the recording material, and the angle between the signal and reference waves is ∼56  deg. We control the exposure time of recording material to observe the faithful reconstruction of orthogonal elliptical polarization holography. How to obtain the faithful reconstruction is interesting work; therefore, we propose a prerequisite for faithful reconstruction. Although the prerequisite is derived from orthogonal elliptical polarization holography, it could also be applied in orthogonal linear and circular polarization holography. The result may be helpful for understanding the faithful reconstruction of orthogonal polarization holography.