Quantitative determination of defocus,thickness and composition from high-resolution transmission electron microscopy lattice images

A quantitative method for the direct determination of defocusf, local thickness t and local compositionx from high-resolution transmission electron microscopy lattice images of wedge-shaped crystal samples is proposed. The method relies on the analytically derived relation between the first-order linear and nonlinear image Fourier coefficientsJ ₁ andJ ₂ onf,t andx. By plotting J1 VSJ ₂ for varying t, ellipses with defocus- and composition-specific geometry are obtained. By reconstructing the appropriate ellipse for image regions of homogeneous composition, f and t can be determined independently. At interfaces, local compositionsx can be determined within the full range 0 x 1 by utilizing systematic variations of the ellipse's geometry with varyingx.