ptychoscopy

Table of Contents

Formulas

Reconstruction probe window
Maximal usable defocus
Pixel size in the reconstructed image
Scattering angle to real space spacing

Tested packages

Formulas

Several restrictions and limitations described are based on comparison of set values with calculated limits. These are based on following formulas.

Reconstruction probe window

Electron probe shape can be reconstructed during iterative reconstruction, but its size (probe window) is limited by

w_{full} = \frac{\lambda \cdot CL_{eff}}{d_{eff}} [ref]

where \lambda is electron wavelength, CL_{eff} the effective detector camera length and d_{eff} the effective real space pixel size (including binning).

Maximal usable defocus

Electron probe grows in size with induced defocus accordingly to the probe semi-angle. For proper reconstruction, the probe has to fit into probe window with some safety margins (recommended is to use half of the window). Maximum defocus is so given by

\Delta f_{max} = \frac{w_{full}/4}{\tan \alpha_{corr}}

where w_{full} is probe window and \alpha_{corr} the real probe semi-angle.

Pixel size in the reconstructed image

Pixel size in reconstructed image made by iterative methods is not given by real space electron probe sampling density, but by maximal angular cover of the detector. It can be calculated by

pix_{ptycho} = \frac{\lambda CL_{eff}}{d_{eff} N_{eff}/2} [ref]

where \lambda is electron wavelength, CL_{eff} the effective detector camera length, N_{eff} the number of detector's effective pixels (considering binning) and d_{eff} the effective real space pixel size (considering binning).

Scattering angle to real space spacing

As we know CTF in angle units, we have to recalculate its shape to real space spacing in a sample. It can be calculated by

d = \frac{2 \lambda}{\sin \theta} [ref]

where \lambda is electron wavelength and \theta is the scattering angle

Tested packages

Proper widgets layout was tested in JupyterLab 4.0.8 and Python 3.11.5. The code was tested with packages:

Numpy version 1.26.2
Scipy version 1.11.4
Plotly version 5.18.0
Pandas version 2.1.1
IPython version 7.31.1
Ipywidgets version 8.0.4