We present the results of an on-sky point spread function reconstruction (PSF-R) experiment for the Gemini North telescope adaptive optics system, Altair, in the simplest mode, bright on-axis natural guise star. We demonstrate that our PSF-R method does work for system performance diagnostic but suffers from hidden telescope and system aberrations that are not accounted for in the model, making the reconstruction unsuccessful for Altair, for now. We discuss the probable origin of the discrepancy. In the last section, we propose alternative PSF-R methods for future multiple natural and laser guide stars systems.