We present the results of a sky source based, phase diversity experiment at the W. M. Keck Observatory to retrieve the global wavefront static aberration from the telescope primary mirror to the science imager (NIRC2). The context of this study is a point spread function reconstruct (PSF-R) project for the Keck-II and Gemini- North adaptive optics systems. We demonstrate that if we select couples of in/out-of-focus PSF with identical seeing (determined with a deformable mirror based seeing monitor), retrieving the global static wavefront from AO corrected sky images is indeed possible. A sensitivity analysis shows that the reconstructed wavefront accuracy is very sensitive to errors in the knowledge of the system's optical parameters, and an accuracy of less than 1% is required. Recommendations for an accurate sky-based phase diversity static wavefront reconstruction are given, as well as our plan for the next steps of this project at the W. M. Keck Observatory.