In this paper we describe the complex electric field reconstruction from image plane intensity measurements for high contrast coronagraphic imaging. A deformable mirror (DM) surface is modified with pairs of complementary shapes to create diversity in the image plane of the science camera where the intensity of the light is measured. Along with the Electric Field Conjugation correction algorithm, this estimation method has been used in various high contrast imaging testbeds to achieve the best contrasts to date both in narrow and in broad band light. We present the basic methodology of estimation in easy to follow list of steps, present results from HCIT and raise several open questions we are confronted with using this method.© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.