Part 3: flat-field normalization¶

Flat-field normalization of the radios is usually the fist step of the processing chain.

1. What is Flat-field normalization¶

Flat-field is a normalization step which "corrects" for the incoming beam intensity.

Remember that in absorption tomography (in the ideal monochromatic beam setting), the beam intensity decays through the sample between positions $[x_0, x]$ as a Lambert-Beer law:

$$ I(x) = I_0 \exp \left( -\displaystyle\int_{x_0}^x \mu(l) \operatorname{d}\! l \right) $$

and we aim at "reconstructing" the linear absorption coefficient $\mu(x)$ from line integrals:

$$ -\ln\left(\dfrac{I(x)}{I_0} \right) = \displaystyle\int_{x_0}^x \mu(l) \operatorname{d}\!l $$

(the same kind of equation holds for phase-contrast tomography).

$$ -\ln\left(\dfrac{I(x)}{I_0} \right) = \displaystyle\int_{x_0}^x \mu(l) \operatorname{d}\!l $$

$I_0 = I(x=0)$ is the incoming beam intensity, which has to be recorded alongside the "projections" $I(x)$.

As detectors are not ideal, they record a background noise ("dark current") even without beam. This dark image has to be subtracted from the incoming intensity.

$$ \dfrac{I}{I_0} = \dfrac{P - D}{F - D} $$ where $P$ is the projection image recorded on detector, $D$ is the dark image, and $F$ is the flat image ($F = I_0 + D$)

2. How Flat-field normalization is done¶

The normalized intensity at index $k$, $I_n (k)$ is given by

$$ I_n (k) = \displaystyle\dfrac { I (k) - D } { F (k) - D } $$

where $I (k)$ is the raw projection number $k$, $F (k)$ is the flat corresponding to radio $k$, and $D$ is the detector dark-current.

For practical reasons, it's not possible to record one flat image (and one dark image) for every projection.
Usually there is not as many flats as radios, so $F (k)$ is obtained by linear interpolation:

     F(k1)    I(k)    F(k2)
------|--------|-------|------ ...

$$ F(k) = \dfrac{k_2 - k}{k_2 - k_1} F_{k_1} + \dfrac{k - k_1}{k_2 - k_1} F_{k_2} $$

Usually, in a tomo acquisition, the acquisition scheme is the following:

  • Darks
  • Flats
  • Projections
  • (optionally) Flats

3. "Reduced" flats and darks¶

When doing a scan, series of flats/darks are acquired.

Example sequence:

  • Acquire 50 darks
  • Acquire 100 flats
  • Acquire 10 000 projections
  • Acquire 100 flats

Each series of flats/darks is reduced to obtain one image (per sequence).
In the previous example:

  • 50 darks ------> mean ---> one dark image
  • 100 flats -----> median ---> one flat image
  • 10 000 projs
  • 100 flats -----> median ---> one flat image

In the previous acquisition/processing system (octave-fasttomo), the resulting files were called dark0000.edf, refHST<num>.edf

In nabu/tomwer, the reduced flats/darks are called <dataset_prefix>_darks.h5 and <dataset_prefix>_flats.h5

These final (reduced) frames are used for flat-field normalization.

Example (1/5)

Principle:

image.png

Example (2/5)

Bliss file layout

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Example (3/5)

Bliss file layout with data

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Example (4/5)

NXTomo file layout

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Example (5/5)

image_key_control field in NXTomo file

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In the NXTomo convention:

  • 2 = dark
  • 1 = flat
  • 0 = projection

How nabu does the flats/darks reduction¶

Before computing the mean/median of darks/flats, nabu/tomwer will first attempt to load them (to avoid re-computations).

Nabu will

  • Try to load from darks_flats_dir (in [preproc] of the configuration file), if specified
  • Try to load the <dataset>_darks.h5 and <dataset>_flats.h5 files if they are alongside the dataset
  • Try to load them from the output reconstruction directory

4. Possible flat-field modes with nabu¶

In the configuration file (section [preproc]), the paramter flatfield can have these possible values:

  • flatfield = 1 or True (default): do flat-field normalization with the frames from the dataset
  • flatfield = 0 or False: no flat-field normalization
  • flatfield = force-load: perform flatfield regardless of the dataset by attempting to load darks/flats
  • flatfield = force-compute: perform flatfield, ignore all .h5 files containing already computed darks/flats

5. Synchrotron current normalization¶

Sometimes a beam refill happens during an acquisition.
Depending on how flats are acquired, flat-fielding might not correct for the incoming beam intensity jump.
This is especially detrimental for half-tomography, as projections at $\theta$ and $\theta + 180°$ will not have the same incoming intensity.

refill_sinogram

When information on synchrotron current (SRCurrent) is available, it's possible to normalize each with this current, according to

$$ P' = \dfrac{P - D}{s/s_{Max}} + D $$

where $s$ is the synchrotron current for the current frame, $s_{Max}$ is the max current, and $D$ is the dark frame.

In nabu, the current normalization is done during flat-field:

$$ \dfrac{P' - D}{F' - D} = \dfrac{(P - D)/s_P}{(F - D)/s_F} $$

To enable it:

[preproc]
# ...
normalize_srcurrent = 1
# ...

Since version 2024.1.0, SRCurrent normalization is enabled by default.