Data processing: CTF and dose weighting

The preprocessing between alignment and reconstruction — estimate and correct the CTF, weight by dose, and deconvolve to lift low-frequency contrast

Intuition

Tilt-series alignment tells you which angle and position each image was taken from; reconstruction stacks those images into a 3D volume. But between the two sits a layer of preprocessing that is easy to overlook yet decides image quality: every projection is already distorted by the imaging physics of the microscope, and you have to undo that distortion before the frequencies can add up coherently instead of cancelling each other out. Two things matter most: CTF correction and dose weighting.

This page works through that preprocessing layer: what the CTF is, why skipping it leaves the image washed out, how to estimate it, how to correct it; a dose-weighting recap; why deconvolution helps and yet “adds no information”; how to keep metadata straight; and the one practical rule beginners most often break. First, the input and output:

Input: an aligned tilt series (a stack of 2D projections at known tilt angles, an .mrc / .st stack), plus metadata recording pixel size, accumulated dose per frame, and microscope parameters.
Output: the same stack, but with every image CTF-corrected and dose-weighted (optionally deconvolved as well), metadata intact and ready to hand to reconstruction.

CTF: the microscope twists the frequencies

An electron microscope is not an ideal imaging system. To make low-contrast biological specimens visible you have to defocus the objective lens a little — and the price of defocus is that different spatial frequencies get multiplied by a transfer function that oscillates with frequency. This is the contrast transfer function (CTF). Its most damaging feature is that it flips sign: contrast is positive in some frequency bands and negative in the adjacent ones, which shows up in the power spectrum as concentric light-and-dark rings (Thon rings).

Why must this be fixed before reconstruction? Because reconstruction is, at heart, an addition of the images in the frequency domain. Ignore the CTF and the sign-flipped frequencies cancel against the un-flipped ones — what should be a coherent sum becomes mutual erasure, and detail washes out. So there are two steps: estimate first, then correct.

Estimating: back out defocus from the Thon rings

Fit the spacing of those rings in each image’s spectrum and you can back out the defocus — deeper defocus, tighter rings. Common tools:

CTFFIND4 — fits the CTF of a single image and reports defocus and astigmatism; standard across cryo-EM/ET.
IMOD’s ctfplotter — built for tilt series, lets you inspect the fit interactively and handles the defocus gradient that tilting introduces.

Why do tilt series need special handling? Because the specimen is a slab with thickness: once tilted, different positions along the tilt axis sit at different distances from the focal plane, so the defocus varies with specimen height along the tilt axis. You cannot estimate a single global value; you estimate it per strip or per tilt.

Correcting: phase flipping vs Wiener / deconvolution

Once you know each image’s CTF, you can divide its effect out. Two common approaches:

Phase flipping — the simplest and most conservative. It multiplies only the flipped frequencies by $-1$ , fixing the sign and leaving amplitudes alone. It never amplifies noise, which makes it the safe default for downstream analysis like subtomogram averaging.
Wiener / deconvolution filtering — corrects the sign while weighting amplitudes by signal-to-noise, trying to lift back the frequencies the CTF suppressed. It recovers more contrast, but be careful: near the CTF zeros the signal is genuinely zero, so blind amplification only amplifies noise — hence a filter that backs off where signal-to-noise is low.

Depth

As a multiplication in the frequency domain, the observed spectrum $\hat{I}(\mathbf{k})$ is roughly the true signal spectrum $\hat{O}(\mathbf{k})$ modulated by the CTF:

\hat{I}(\mathbf{k}) = \mathrm{CTF}(\mathbf{k})\,\hat{O}(\mathbf{k}) + \hat{N}(\mathbf{k})

where $\mathrm{CTF}(\mathbf{k}) \approx -\sin\!\big(\pi(\,\tfrac{1}{2}C_s\lambda^3 k^4 - \Delta z\,\lambda k^2)\big)$ , with $\Delta z$ the defocus, $\lambda$ the electron wavelength, and $C_s$ the spherical aberration. Where the $\sin$ crosses zero the contrast vanishes, and past each zero the sign flips — exactly the origin of the Thon rings and the sign reversals. Phase flipping multiplies by $\operatorname{sgn}(\mathrm{CTF})$ ; Wiener deconvolution multiplies by $\mathrm{CTF}/(\mathrm{CTF}^2 + 1/\mathrm{SNR})$ , which backs off near the zeros so it does not amplify noise. For the Fourier background to the CTF, see the signal-processing base.

Dose weighting: frequencies that died first get low weight

This step is covered in detail in motion correction and dose weighting; here we only recap how it relates to the CTF. The electron beam records signal and destroys the specimen at the same time. High-resolution (high-frequency) information is the most sensitive to accumulated dose and is often gone by the middle of the series; low-frequency information is far more tolerant.

Dose weighting assigns each frequency a weight according to how much signal it still has at a given accumulated dose: low-dose, low-frequency components get high weight, while high-frequency components the dose has already destroyed get suppressed, so you do not stack pure noise into the reconstruction as if it were signal. It is complementary to CTF correction — the CTF fixes signs the imaging system twisted, dose weighting suppresses bands the beam destroyed — and both usually happen during motion correction (e.g. MotionCor2) or just before reconstruction. Both need the accumulated electron dose per frame, which is why recording dose metadata from the start matters.

Deconvolution: adds no information, but makes structure legible

After CTF correction and dose weighting, the low-frequency contrast of a tomogram is often still weak — it looks gray and hazy. Deconvolution — found in tools like Warp and IsoNet — lifts that low-frequency contrast further, so membranes and organelles and other large-scale structure pop out.

The key point: deconvolution adds no new information; it only reweights the frequencies you already have so that an eye or an algorithm can latch onto structure more easily. But that is exactly what helps visualization and particle picking — both humans and picking algorithms lean heavily on the low-frequency outline. In other words, a deconvolved volume is good for looking and picking, but for quantitative analysis and subtomogram averaging it is safer to return to the phase-flipped-only volume.

Depth: train and predict on the same data

This raises the trap beginners fall into most: train and predict on the same data type. If a model (denoising, missing-wedge completion, segmentation…) was trained on deconvolved tomograms, you must also feed it deconvolved tomograms at prediction time; train on raw (non-deconvolved) volumes and you can only predict on raw volumes. Deconvolution, dose weighting, and filtering all change the spectral distribution of the data, and the model has learned the statistics of that distribution — switch the preprocessing and you have switched the input domain, so results quietly degrade without raising an error. Prior-learning methods like CryoGEN / CryoWGEN are especially strict about this: from preparing the training data through inference, keep the preprocessing chain identical down to the last step.

Metadata: keep the information from scattering

Every step above depends on a set of parameters that runs through the whole pipeline: pixel size (which converts frequency to resolution), tilt angles (needed for reconstruction), per-image defocus (needed for CTF correction), and accumulated dose per frame (needed for dose weighting). These usually live together in star files — a plain-text table, one object per row, one parameter per column — acting as the contract passed between alignment, CTF estimation, and reconstruction.

Mismatched metadata — a wrong pixel size, a flipped sign convention on the defocus, a tilt-angle order that no longer matches the images in the stack — is more often the reason a reconstruction fails than the algorithm itself, and it usually fails silently, just giving an inexplicably bad result. Build the habit: every time you switch tools, first check its conventions for pixel-size units (Å/px), defocus sign, and angle order.

A checklist you can follow

Walk through this in order and the preprocessing layer is done:

Check the metadata: do the pixel size (Å/px), accumulated dose per frame (e⁻/Å²), microscope voltage and $C_s$ , and per-image tilt angles all match the raw data?
Estimate the CTF: run CTFFIND4 or IMOD ctfplotter on each tilt image to get per-image defocus; for a tilt series, let the tool handle the defocus gradient along the tilt axis.
Check the fit: glance at how well the Thon rings are fit — the modeled rings should line up with the measured ones. The larger the tilt and the weaker the signal, the shakier the fit; adjust by hand where needed.
Dose weighting: confirm that motion correction already weighted by accumulated dose per frame (see the frames page).
CTF correction: choose phase flipping (conservative, safe, good for quantitative work and subtomogram averaging) or Wiener/deconvolution (more contrast, good for looking and picking).
(Optional) deconvolution: if it is mainly for visualization or particle picking, generate a deconvolved volume too — but store it separately and label it, and do not mix it with the non-deconvolved volume.
Lock the data type: decide which volume the downstream steps (reconstruction, training, analysis) will use, and stick to it from then on — training and prediction must be the same type.

For the Fourier background to the CTF and frequency-domain modulation, see the signal-processing base and the Fourier transform; for how the preprocessed images stack into a 3D volume, see From tilt series to tomogram.

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