Detection and quantitative assessment of image aberrations from single HRTEM lattice images

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For utilizing the full capabilities of quantitative high-resolution transmission electron microscopy in materials characterization, a precise knowledge of the various aberrations blurring the object information is essential. Here, we describe an extended approach to the detection and quantitative assessment of image aberrations from lattice images of crystal samples. The approach is based on a theoretical analysis of five-beam lattice images in the presence of all relevant optical aberrations and for partial beam coherence. Compact analytical expressions for linear and nonlinear image Fourier coefficients as explicit functions of the aberration parameters are derived. In particular, a fundamental relationship between the occurrence of erroneous image symmetries and the simultaneous presence of optical misalignments and partial beam coherence is established. An image analysis procedure is proposed which allows for the detection of even- and odd-order residual aberrations and for the quantitative determination of defocus, two-fold astigmatism and axial coma if the three-fold astigmatism is known. For coma-free images, the three-fold astigmatism can also be determined quantitatively. Moreover, the procedure allows for a reliable detection of crystal misalignment for images of wedgeshaped crystal samples.

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