Improved high resolution image processing of bright field electron micrographs

Imaging columns of the light elements carbon, nitrogen and oxygen with sub Ångstrom resolution

“…Figure 4 shows for the specific case of the dumbbell images in In these materials the chemical species nitrogen and carbon are present. Sapphire [11][12][13][14][15][16][17][18][19][20] was investigated to test if single oxygen columns can be imaged at a projected nearest The reliability of the exit wave reconstruction procedure was tested and discussed in detail 20,22 . We confirm that a reconstruction of simulated images is robust by recovering amplitude and phase from the simulated focus series of partial dislocations in silicon (Figure 9).…”

“…Alternatively, it was reported that a direct reconstruction of the phase and the amplitude of the scattered electron wave from a focal series of HRTEM images is suitable to extend the interpretable resolution of a field emission microscope down to its information limit 10 . Several approaches were published to tackle the problem of resolution extension 11,12,13,14,15,16 with an earliest contribution suggested by Schiske 17 . Subsequently, phaseretrieval electron microscopy was developed into a generally applicable tool that extended the resolution of 200 kV and 300 kV field emission electron microscopes to values around 0.14 nm 18,19,20,21 and provides the possibility to correct lens aberrations by software 22 .…”

Does a monochromator improve the precision in quantitative HRTEM?

“…It depends only on the spherical aberration constant C s and the electron wavelength l and is given by: r s ¼ 0:65 ðC s l 3 Þ 1=4 [1]. The information limit r i represents the smallest detail that can be retrieved by means of image reconstruction methods such as off-axis holography [2] and focal series reconstruction [3][4][5][6]. It is defined as the inverse of the highest spatial frequency that is transferred with sufficient intensity from the electron wave field at the exit plane of the object to the image plane.…”

Complex electron wave reconstruction using parameter estimation

“…In a first step, the leastsquares criterion (4) with described by (3) is minimized with respect to . In a second step, the least-squares estimate thus found is used as initial condition for maximizing the likelihood function (2).…”

“…Repeated experiments show that this is nearly always the case. In addition, the least-squares estimates of the Fourier coefficients have subsequently been used as initial values for maximizing the Poisson likelihood function (2). This results in slightly modified Fourier coefficient estimates having a smaller mean square error such as theory predicts.…”