Phase Aberrations in Diffraction Microscopy
  In coherent X-ray diffraction microscopy the diffraction pattern generated by a sample illuminated with coherent x-rays is recorded, and a computer algorithm recovers the unmeasured phases to synthesize an image. By avoiding the use of a lens the resolution is limited, in principle, only by the largest scattering angles recorded. However, the imaging task is shifted from the experiment to the computer, and the algorithm's ability to recover meaningful images in the presence of noise and limited prior knowledge may produce aberrations in the reconstructed image. We analyze the low order aberrations produced by our phase retrieval algorithms. We present two methods to improve the accuracy and stability of reconstructions. 
S. Marchesini, H. N. Chapman, A. Barty, C. Cui, M. R. Howells, J. C.   H. Spence, U. Weierstall, and A. M. Minor