Phase Object Approximation (POA)
- Practical Electron Microscopy and Database -
- An Online Book -

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 This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers. ================================================================================= The TEM sample is usually described by a projected potential model where the atomic potentials will modify the phase (and only the phase) of the wave of the incident electrons as the electrons passes through the material, which is represented by the phase object approximation (POA). Based on the expression of Fraunhofer diffraction one can derive the phase-object approximation (POA) that gives the TEM-specimen transmission function, qe(r) as,           ------------------------------ [3702a] where,          σ -- The interaction constant,          ϕp(r) -- The projection of the electrostatic potential of the specimen along the direction of the electron beam. As its name implies, the phase-object approximation assumes that only the phase of the complex electron wave is affected when they are penetrating through the specimen. In the POA, one can have,                                     ψex(r) = qe(r)ψ0(r) ------------------------------ [3702b] where,           ψ0(r) -- The incident electron wave,           ψex(r) -- The exit-surface wave. When the specimen is thin and thus the phase change is small, this model can be further simplified by the weak phase object approximation (WPOA), which is a linear approximation. All the purpose of the methods of the electron image series reconstructions with TEM is to find an object wave function, ψo,s. The reconstruction methods can be basically categorized by two groups: i) weak phase object approximation (WPOA) and more generally ii) phase object approximation (POA). In principle, the methods based on the POA give a better estimation of the object wave function, but they don’t have closed form solutions and have to be computed iteratively and thus is very time consuming. [1] On the other hand, the reconstruction methods based on WPOA are fast but the TEM imaging requires much thinner samples.                                   [1] A. I. Kirkland and R. R. Meyer, Indirect high resolution transmission electron microscopy: Aberration measurement and wavefunction reconstruction, Microscopy and Microanalysis, vol. 10, pp. 401–413, 2004.
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