In-plane & out-of-plane integration

In-plane & out-of-plane integration#

Warning: out-of-plane integration is often not rigorous#

With a single angle of incidence, it is impossible to fully cover the range of \(q_z\) at \(q_{xy}=0\) due to the limitations of measuring the Ewald sphere with a planar 2D detector [18].

To rigorously obtain the out-of-plane region of reciprocal space at \(q_{xy}=0\), other techniques should be used, such as diffraction in specular conditions.

An approximation often made is to ignore the corrections required by the Ewald sphere, and integrate on \(q_x\) vs. \(q_z\) maps. In this case, note that comparisons between in-plane and out-of-plane integrations are mostly qualitative, particularly at high \(q_z\) values.

Definition of the integration area#

The in-plane integration will be performed within the black rectangle, while the out-of-plane integration will be performed within the red rectangle. Define the boundaries in the cell below and run it.

# Define the left and right boundaries for the in-plane integration
# -> Red rectangle
left_qx = -0.7    # Set your desired left boundary (in nm^-1)
right_qx = 0.7  # Set your desired right boundary (in nm^-1)

# Define the bottom and top boundaries for the out-of-plane integration
# -> Black rectangle
bottom_qoop = 0.3   # Bottom boundary (in nm^-1)
top_qoop = 0.7      # Top boundary (in nm^-1)

...

Performing the integration#

Once you are satisfied with the boundaries, adjust the limits of the final plot in the next cell and run it.

# Define the limits of the plot and run the cell
q_min = 2
q_max = 20

...

The in-plane and out-of-plane intensity profiles will be generated for each image individually. In the final plots, the two out-of-plane datasets will be combined to remove gaps caused by dead zones.

In your further analysis, you can choose whether to:

  • keep both datasets separate,

  • merge them, using the second image to fill the missing data.

Save parameters#

Finally, run the last cell to generate a text file with all the parameters saved.

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