column approximation

"Column approximation" is an approximation method to calculate the amplitudes of transmitted and diffracted waves at the bottom of a crystal, which assumes the crystal to be composed of columns. The top specimen plane, which affects the formation of an electron wave at a point on the crystal bottom plane, is deduced by Fresnel zones. The radius of the first Fresnel zone, R, is given by √(λt), where, λ is the wavelength of the electron and t is the specimen thickness. When it is assumed that λ = 0.0026 nm and t = 100 nm, the diameter of the Fresnel zone, 2R, is ～0.5 nm. If Fresnel zones are taken up to the third zone, its diameter is ～1.5 nm. That is, when the amplitude of an electron wave at a certain point on the crystal bottom plane is calculated, it is enough to consider transmission and diffraction of the electron wave in a column of 2 nm or less. When a distorted crystal is treated, the amplitudes of the transmitted and diffracted waves are calculated inside such columns, in each of which the crystal is assumed to be a perfect, and between which the crystals are shifted each other corresponding to the distortion.