Ptychography is a coherent diffractive imaging method that uses multiple diffraction patterns obtained through the scan of a localized illumination on the specimen. Until recently, reconstruction algorithms for ptychographic datasets needed the a priori knowledge of the incident illumination. A new reconstruction procedure that retrieves both the specimen's image and the illumination profile was recently demonstrated with hard X-ray data. We present here the algorithm in greater details and illustrate its practical applicability with a visible light dataset. Improvements in the quality of the reconstruction are shown and compared to previous reconstruction techniques. Implications for future applications with other types of radiation are discussed. (C) 2009 Elsevier B.V. All rights reserved.