Image projection through a multimode fiber (MMF) or scattering media has applications ranging from optogenetics to near eye-displays. It requires developing computer-generated holography algorithm to obtain phase pattern of spatial light modulator. In order to accurately project light, conventional methods measured the transmission matrix (TM) of the imaging system by interference. However, it is sensitive to phase instability, easily caused by thermal drift and mechanical vibration. In this work, we proposed to use the TM retrieved from intensity-only measurements and develop a nonlinear optimization algorithm to obtain the displayed phase patterns. Our method formulates the forward model with the retrieved TM, derives the analytical derivative and adopts a second-order optimization method. We validate the improved quality of the projected intensity image by an experiment setup with a MMF.
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