MTE5881 Chap.8 Restoring and Preparing CBED Data
Restoring and Preparing CBED Data
Detector preparation converts a visually useful CBED pattern into a quantitative dataset. Diffraction focus is separated from symmetric point-spread blur, the PSF is measured from aperture images and deconvolution restores resolution while amplifying noise. Signal-dependent variance is measured rather than assumed.
Reflection masks, disc centres, reciprocal vectors and the zone-axis origin then define pattern coordinates and inverse-variance weights for dynamical fitting. A sharper image is a resolution claim, not proof of reduced uncertainty. Restoration can introduce ringing, boundary loss and correlated noise, so the post-restoration variance and excluded pixels must be documented.
Indexing errors are equally dangerous: attaching an unchanged sub-image to the wrong reciprocal vector makes the dynamical comparison physically wrong. Overlays, independent centre predictions and normalised residuals provide checks before computational refinement begins.
What this chapter covers
- 01
Diffraction focus
- 02
Point-spread function
- 03
Deconvolution
- 04
Noise versus signal
- 05
Reflection masks
- 06
Inverse-variance weighting
Worked example · free
Audit a detector-restoration decision
- +1Separate improved spatial resolution from statistical precision.
- +2Propagate or remeasure variance after restoration and inspect edge ringing.
- +2Use inverse measured variance for reliable pixels and mask saturation or unstable regions.
Key terms
- Diffraction focus
- The alignment condition checked before interpreting symmetric blur as detector PSF.
- Deconvolution
- A restoration process that reverses blur while potentially amplifying high-frequency noise.
- Inverse-variance weight
- A fit weight that reduces the influence of observations with larger measured uncertainty.
- Point-spread function
- The detector response that distributes intensity from an ideally sharp input across neighbouring pixels.
- Regularisation
- A stabilising constraint that limits noise amplification and artefacts during an inverse restoration.
- Reciprocal basis
- Two non-collinear indexed vectors used to predict disc-centre positions across a diffraction pattern.
- Normalised residual
- A model-data difference scaled by estimated uncertainty so discrepancies are judged relative to expected noise.
- Aperture edge
- A nominally sharp calibration feature used to separate focus error and detector point-spread blur experimentally.
- Pixel mask
- A recorded selection excluding saturation, overlap, damage or unstable restoration from quantitative fitting.
- Variance function
- An empirical relationship between signal level and detector uncertainty used to construct defensible inverse-variance weights after restoration and masking.
Restoring and Preparing CBED Data FAQ
Why is focus checked before the PSF?
Defocus can produce a directional taper at an aperture edge, while the remaining symmetric blur after focus correction is attributed to the detector PSF. Combining them would make the restoration kernel absorb an alignment error.
Why is noise not assumed equal to intensity?
Detector noise can include several signal-dependent and signal-independent contributions. Quantitative fitting therefore measures variance as a function of signal and builds weights from that empirical relationship rather than a convenient automatic rule.
Why do disc labels matter?
Each sub-image must be matched to the correct reciprocal reflection in the dynamical calculation. Swapped labels preserve the picture but attach intensity to the wrong scattering vector, corrupting excitation and coupling relationships.
Exam move
Memorise the preparation dependency chain rather than isolated software actions: correct focus, measure PSF, deconvolve, measure post-restoration noise, mask invalid pixels, locate centres, define reciprocal coordinates and compute weights. For every step, name the observable and the failure it prevents. Inspect both raw and variance-scaled residuals.
Save overlays of indexed disc centres because geometry catches silent file errors before HPC refinement. When a result changes strongly with modest PSF or mask choices, report that sensitivity instead of hiding it. Practise distinguishing directional defocus from symmetric detector blur on an aperture edge before constructing a PSF.
Validate deconvolution with a known synthetic edge and an unused measured edge; compare regularisation choices for ringing, noise amplification and boundary behaviour. Measure variance against signal after restoration rather than assigning greater confidence because edges look sharper.
Build the reciprocal basis from two non-collinear vectors, predict centres not used in the fit and inspect whether displacement grows with radius. Confirm the transmitted disc and reflection order before allowing a distortion model to move anything. Create a mask ledger listing saturation, overlap, damage and unstable restoration as explicit exclusion reasons.
Finally, read raw and variance-scaled residuals together: brightness-dominated error and statistically unusual error answer different questions. Freeze the PSF, noise function, coordinates and mask as one versioned preparation record. Perform a swap test in which two reflection labels are exchanged while pixels remain unchanged, and explain why the dynamical calculation then uses the wrong scattering vectors.
Compare coordinate residuals near the centre and edge to distinguish random picking error from radial distortion. Inspect the normalised-residual distribution for bright and dim pixels separately; systematic imbalance indicates a deficient signal-dependent noise model. Repeat one refinement with a modestly altered mask and PSF setting, treating output movement as sensitivity rather than a new best value.
Record acquisition conditions beside the aperture calibration, because a kernel measured under different detector settings may not transfer. The final dataset should be reproducible from saved observations and preparation decisions, not merely from a corrected image.
