ABSTRACT
Interest has recently been renewed in the use of the Gerchberg-Saxton [1] and Fienup [2] iterative algorithms to solve non-periodic phase problems in microscopy. The advantage of this is that the diffraction pattern, used as input to these algorithms, can be measured to very large angles, limited only by the size of the detector. For some important types of short wavelength radiation, such as electrons, protons, X-rays, very good quality lenses are not available. Even for good quality lenses, the object may not scatter strongly, or it may only alter the phase of the transmitted wave so the that interpretation of the conventional image is difficult. However if we can record the diffracted intensity to a large angle, and then employ a suitable algorithm to solve for the phase of the diffraction pattern, there is no requirement for a lens at all. This is because the back Fourier transform of the complex-valued diffraction pattern is a perfect representation of the exit wave-field at a resolution determined only by the size (and pixel resolution) of our diffraction plane detector.
