SANS2D: I(Q) for sample and background¶

In this notebook, we will be reducing a sample and a background measurements to a one-dimensional \(I(Q)\).

It assumes the detector data has been recorded in event mode, while the monitor data has been histogrammed.

The data used in this notebook has been published in Manasi et al. (2021), and we kindly thank the authors for allowing us to use their data.

Outline:

We will begin by loading the data files containing the sample, direct, and background measurements.
We will then apply some corrections to beamline components specific to the SANS2D beamline.
This will be followed by some masking of some saturated or defect detector pixels
Finally, the sample and background measurement will be converted to the \(Q\) dimension

[1]:

import matplotlib.pyplot as plt
import scipp as sc
from ess import loki, sans
import scippneutron as scn

Define reduction workflow parameters¶

We define here whether to include the effects of gravity, as well as common time-of-flight, wavelength and \(Q\) bins for all the measurements.

We also define a range of wavelengths for the monitors that are considered to not be part of the background.

[2]:

# Include effects of gravity?
gravity = True

tof_bins = sc.linspace(dim='tof', start=0, stop=100000, num=2, unit='us')

wavelength_bins = sc.linspace(dim='wavelength', start=2.0, stop=16.0, num=141,
                              unit='angstrom')

q_bins = sc.linspace(dim='Q', start=0.01, stop=0.6, num=141, unit='1/angstrom')

# Define the range of wavelengths for the monitors that are considered
# to not be part of the background
monitor_non_background_range = sc.array(dims=['wavelength'],
                                        values=[0.7, 17.1], unit='angstrom')

Apply corrections to pixel positions¶

We apply some corrections to the detector pixel and monitor positions, as the geometry stored in the file is inaccurate.

[4]:

# Custom SANS2D position offsets
sample_pos_z_offset = 0.053 * sc.units.m
bench_pos_y_offset = 0.001 * sc.units.m
# There is some uncertainity here
monitor4_pos_z_offset = -6.719 * sc.units.m

# Geometry transformation
x_offset = -0.09288 * sc.units.m
y_offset = 0.08195 * sc.units.m

[5]:

ds.coords["pixel_width"] = 0.0035 * sc.units.m
ds.coords["pixel_height"] = 0.002033984375 * sc.units.m

# Change sample position
ds.coords["sample_position"].fields.z += sample_pos_z_offset
# Apply bench offset to pixel positions
ds.coords["position"].fields.y += bench_pos_y_offset

for key in ds:
    ds[key].attrs["monitor4"].value.coords["position"].fields.z += monitor4_pos_z_offset

# Now shift pixels positions to get the correct beam center
ds.coords['position'].fields.x += x_offset
ds.coords['position'].fields.y += y_offset

Use to_I_of_Q workflow¶

We now reduce the sample and the background measurements to Q using the sans.to_I_of_Q workflow.

In that process, the intensity as a function of Q is normalized using the direct measurement and direct beam function.

The workflow needs monitor data from the sample, background, and direct runs to compute the normalization. It accepts those in the form of a dictionaries:

[9]:

sample_monitors = {'incident': binned['sample'].attrs["monitor2"].value,
                   'transmission': binned['sample'].attrs["monitor4"].value}

direct_monitors = {'incident': binned['direct'].attrs["monitor2"].value,
                   'transmission': binned['direct'].attrs["monitor4"].value}

background_monitors = {'incident': binned['background'].attrs["monitor2"].value,
                       'transmission': binned['background'].attrs["monitor4"].value}

We then call the workflow on the sample and direct runs:

[10]:

sample_q = sans.to_I_of_Q(data=binned['sample'],
    data_monitors=sample_monitors,
    direct_monitors=direct_monitors,
    direct_beam=direct_beam,
    wavelength_bins=wavelength_bins,
    q_bins=q_bins,
    gravity=gravity,
    monitor_non_background_range=monitor_non_background_range)
sample_q.plot()

An interpolation was performed on the direct_beam function. The variances in the direct_beam function have been dropped.

[11]:

background_q = sans.to_I_of_Q(data=binned['background'],
    data_monitors=background_monitors,
    direct_monitors=direct_monitors,
    direct_beam=direct_beam,
    wavelength_bins=wavelength_bins,
    q_bins=q_bins,
    gravity=gravity,
    monitor_non_background_range=monitor_non_background_range)
background_q.plot()

An interpolation was performed on the direct_beam function. The variances in the direct_beam function have been dropped.

We are now in a position to subtract the background from the sample measurement:

[12]:

result = sample_q.bins.sum() - background_q.bins.sum()
result

[13]:

fig1, ax1 = plt.subplots(1, 2, figsize=(10, 4))
sc.plot(result, ax=ax1[0])
sc.plot(result, norm='log', ax=ax1[1])
fig1

[13]:

../../_images/instruments_loki_sans2d_reduction_22_0.png

Note

Instead of .bins.sum(), one could use sc.histogram() above to define different Q bins compared to the ones defined at the top of the notebook. This can be done in event mode, see here.

There may be performance advantages to first use a coarse Q binning when the computing I(Q) numerator, and use finer binning for the final results.

References¶

Manasi I., Andalibi M. R., Atri R. S., Hooton J., King S. M., Edler K. J., 2021, Self-assembly of ionic and non-ionic surfactants in type IV cerium nitrate and urea based deep eutectic solvent, J. Chem. Phys. 155, 084902

SANS2D: I(Q) for sample and background

Contents

SANS2D: I(Q) for sample and background¶

Define reduction workflow parameters¶

Loading data files¶

Apply corrections to pixel positions¶

Masking¶

Mask bad pixels¶

Mask Bragg peaks in time-of-flight¶

Use to_I_of_Q workflow¶

Wavelength bands¶

References¶