This page contains a Flash digital edition of a book.
Tomography for HAADF-STEM


The CTFS method is an alternative to tilt-series STEM tomography, but with improved resolution in the axial direction for a given tilt range.


Materials and Methods Image acquisition . To record


a CTFS, the objective aperture semi- angle α is chosen as high as possible in order to achieve the smallest possible DOF, typically up to about 49 mrad (≈2.8°). T e available tilt range is then covered in tilt increments of at most 2α , that is, the tilt increment is set to ≤5.6°. T e reason for this condition is that the Fourier transform of a focal series is nonzero in a set that has the shape of an inverted double cone of the opening angle 2α [ 17 ]. As long as this condition is fulfi lled, the volume


Figure 2 : Two images of the CTFS dataset taken at the same tilt angle (-40°) but at different focal values. The difference between the focus planes was 780 nm, which corresponds to 13 images. The orange arrows indicate sections of the images that are in focus. Image adapted from [ 15 ].


corresponding to the tilt step is covered in reciprocal space. For every tilt angle, a focal series is recorded. T e distance from one focal plane to the next is selected such that an object perfectly in focus in one focal plane appears blurred by a disc fi lter of not more than one pixel radius on the next focal plane. This condition ensures that the interpolation error in the backprojection remains small and holds if the distance between consecutive focal planes is ≤1/sin(α )·pixelsize. In the case of α = 49 mrad, this condition corresponds to a vertical distance of ≈20 pixels.


Data Processing – Alignment . As it is with TEM tilt series, CTFS data need to be aligned to compensate for sample movements during image acquisition. In-plane alignment is initially suffi cient between images recorded at the same tilt angle, that is, within a focal stack. If necessary, an additional alignment step can be added to align the images within each focal stack. However, the sample shiſt s do not only consist of in-plane movements like translation and rotation, but also of an axial shiſt . T e exact focal positions of the images are, thus, unknown.


Lateral alignment errors can be corrected by averaging the images in a focal series and aligning the resulting conventional tilt series using a standard method [ 18 ]. In order to compensate for the axial shiſt s, particles are detected in the tilt series. T e particles are tracked through the tilt series, that is, the same particle is identifi ed in several frames of the series [ 19 ]. T e 3D position of each particle is then computed using triangulation from its position in the different images. In the next step, it is determined in which image of the series the particle is best in focus. T e image with the highest intensity at the particle’s position is defi ned as the best focus for this particle and has to be searched in the focal stack. By combining both relations, a given image in a focal series can be assigned a focal depth, and the accuracy of this estimate is improved by averaging over many values gained by repeating this procedure for many particles.


Data Processing – Tomographic Reconstruction . The reconstruction of a 3D volume from CTFS data is based on an iterative Kaczmarz-type method [ 20 ]. It is related to the


Figure 3 : Results of the tomographic reconstruction. (a) A 3D rendering (perspective projection). (b) Sliced view in xy. (c) Sliced view in xz and yz directions. The largest nanoparticle is marked with an orange arrow in all views. All images are coded with false color for better visibility. The slice in yz direction was rotated by 90°.


28 www.microscopy-today.com • 2016 May


Page 1  |  Page 2  |  Page 3  |  Page 4  |  Page 5  |  Page 6  |  Page 7  |  Page 8  |  Page 9  |  Page 10  |  Page 11  |  Page 12  |  Page 13  |  Page 14  |  Page 15  |  Page 16  |  Page 17  |  Page 18  |  Page 19  |  Page 20  |  Page 21  |  Page 22  |  Page 23  |  Page 24  |  Page 25  |  Page 26  |  Page 27  |  Page 28  |  Page 29  |  Page 30  |  Page 31  |  Page 32  |  Page 33  |  Page 34  |  Page 35  |  Page 36  |  Page 37  |  Page 38  |  Page 39  |  Page 40  |  Page 41  |  Page 42  |  Page 43  |  Page 44  |  Page 45  |  Page 46  |  Page 47  |  Page 48  |  Page 49  |  Page 50  |  Page 51  |  Page 52  |  Page 53  |  Page 54  |  Page 55  |  Page 56  |  Page 57  |  Page 58  |  Page 59  |  Page 60  |  Page 61  |  Page 62  |  Page 63  |  Page 64  |  Page 65  |  Page 66  |  Page 67  |  Page 68  |  Page 69  |  Page 70  |  Page 71  |  Page 72  |  Page 73  |  Page 74  |  Page 75  |  Page 76