Howie-Whelan equation

A method for calculating the intensities of transmitted and diffracted waves at the bottom plane of a crystalline specimen when the incident electron beam interacts with the specimen. In the "Howie-Whelan equation," transmission and diffraction are dealt with in the following way. The specimen is divided into many thin layers. The transmitted and diffracted waves are given at the upper surface of a layer (on the top layer, the diffracted wave amplitudes are assumed to be 0 (zero)). These waves undergo transmission and diffraction according to the respective crystal structure factors in the layer. The new transmitted and diffracted waves are obtained at the lower surface of the layer. These waves are incident on the next layer. This process is repeated for successive planes. Finally the amplitudes of the transmitted and diffracted waves at the bottom plane of the specimen are obtained. This method (equation) is used to explain the image contrast due to lattice defects such as stacking faults and dislocations.

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