Exit-plane Wave Function Research Articles

Determination of experimental imaging conditions for off-axis transmission electron holography

A new iterative method is proposed for the accurate determination of the experimental imaging conditions (defocus, spherical aberration coefficient) necessary for the restoration of the object wave function in transmission off-axis electron holography for thin crystalline specimens on the basis of criteria related to the local intensities of the image of the specimen itself. The optimum region for which a functional is minimized with respect to defocus and aberration coefficient is found on the basis of simulations for a model structure. The procedure is shown to be effective for a maximum phase shift in the exit plane wave function, σ v( r) t, up to 5.6 or more: this covers most of the experimental conditions commonly used in high-resolution imaging. It is shown that some special methods for the accurate determination of the size of the hologram in the direction of beam overlapping should be worked out; otherwise a sampling interval as small as 10 -3 Å is required for digitization of a hologram.

On the iterative restoration of the exit plane wave function from defocus series in HREM

The accuracy and the convergence rate of the maximum likelihood method of the electron wave function restoration from defocus series has been analyzed assuming that the imaging conditions are known. The procedure is found unstable near the exact solution if some other parameters are refined along with the wave function. The effects of the random noise in defocus series and of the dynamical scattering are discussed. The noise control offered by the MIMAP approach is found not effective under the common imaging conditions used in HREM. The wave function can be restored with reasonable accuracy from the noisy defocus series with the spatial resolution equal to the “information” limit of the electron microscope.

On the iterative restoration of exit plane wave function from defocus series in HREM

The validity domain of a Multiple Image MAximum Posteriori (MIMAP) approach has been estimated on UMo5O16 complex oxide structure (Fig.1). Model defocus series (both noise-free and with an additive random noise) have been prepared by multislice method with no objective aperture imposed. Defocus values Δfn=((8n+3)Csλ/2)05 (n=0,...,4) corresponded to plateaus of JEOL-4000EX microscope transfer function operated under U=400kV. The following problems are considered:Self-consistency. Apart from a wave function MIMAP aims at refinement of translational misalignment, difference in defocus values within series and a “fog” level c0. The latter represents an additive constant to image intensity arising by image recording and manipulation. We assumed that defocus values were known exactly and images were perfectly aligned. If one sets c01 to its exact value c0=0 and starts restoration from noise-free defocus series of a t=12 thin crystal the procedure will diverge (Fig.2).