SANS2D: I(Q) workflow for a single run (sample)¶

This notebook describes in detail the steps that are undertaken in the sans.to_I_of_Q workflow.

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.

Note: It uses sample run for simplicity and it is not intended to describe complete data reduction pipeline. The complete pipeline is described in SANS2D reduction.

Outline:

We will begin by loading the data files containing the sample and the direct (empty sample holder) 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
Both sample and direct measurement, as well as their monitors, will then be converted to wavelength
From the direct run, and the direct beam function, the normalization term will be computed
Both sample measurement and normalization term will be converted to \(Q\)
Finally, the sample counts (as a function of \(Q\)) will be divided by the normalization term (as a function of \(Q\))

[1]:

import scipp as sc
from ess import loki, sans
import scippneutron as scn

Define reduction parameters¶

We define here whether to include the effects of gravity, and the binning in wavelength and in \(Q\) to be used.

[2]:

# Include effects of gravity?
gravity = True

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

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

Extract monitors¶

From these two runs, we extract the data from the incident and transmission monitors, and place them in their own dict, as this will be useful further down.

[4]:

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

Apply offsets to pixel positions¶

Note: for production ESS Nexus files are produced, this step should go away.

Note: The corrections also include adjusting the beam center position, which in the future will be determined using helpers in the ess.sans package.

Various positions for the sample holder, detector pixels, and monitors are incorrect in the Nexus files. The step below corrects this. We also add the shape of the pixels, which is missing from the geometry information, and is required to compute the solid angle for each detector pixel.

[5]:

# 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 based on the found beam center position
x_offset = -0.09288 * sc.units.m
y_offset = 0.08195 * sc.units.m

[6]:

# Add pixel shapes
sample.coords["pixel_width"] = 0.0035 * sc.units.m
sample.coords["pixel_height"] = 0.002033984375 * sc.units.m

# Change sample position
sample.coords["sample_position"].fields.z += sample_pos_z_offset
# Apply bench offset to pixel positions
sample.coords["position"].fields.y += bench_pos_y_offset
# Now shift pixels positions to get the correct beam center
sample.coords['position'].fields.x += x_offset
sample.coords['position'].fields.y += y_offset

# Change transmission monitor position
monitors['sample']['transmission'].coords["position"].fields.z += monitor4_pos_z_offset
monitors['direct']['transmission'].coords["position"].fields.z += monitor4_pos_z_offset

Coordinate transformation graph¶

To compute the wavelength \(\lambda\), the scattering angle \(\theta\), and the \(Q\) vector for our data, we construct a coordinate transformation graph.

It is based on classical conversions from tof and pixel position to \(\lambda\) (wavelength), \(\theta\) (theta) and \(Q\) (Q), but takes into account the Earth’s gravitational field, which bends the flight path of the neutrons, to compute the scattering angle \(\theta\).

The angle can be found using the following expression (Seeger & Hjelm 1991)

\[\theta = \frac{1}{2}\sin^{-1}\left(\frac{\sqrt{ x^{2} + \left( y + \frac{g m_{\rm n}}{2 h^{2}} \lambda^{2} L_{2}^{2} \right)^{2} } }{L_{2}}\right)\]

where \(x\) and \(y\) are the spatial coordinates of the pixels in the horizontal and vertical directions, respectively, \(m_{\rm n}\) is the neutron mass, \(L_{2}\) is the distance between the sample and a detector pixel, \(g\) is the acceleration due to gravity, and \(h\) is Planck’s constant.

The monitors require a slightly different conversion graph, as the flight path of the neutrons hitting them does not scatter through the sample, it links the source to the monitor with a straight line.

The conversion graphs for the detectors and the monitors are defined in the sans module, and can be obtained via

[11]:

data_graph, monitor_graph = sans.i_of_q.make_coordinate_transform_graphs(gravity=gravity)
sc.show_graph(data_graph, simplified=True)

[11]:

../../_images/instruments_loki_sans2d_to_I_of_Q_19_0.svg

Convert the data to wavelength¶

To compute the wavelength of the neutrons, we use Scipp’s transform_coords method by supplying our graph defined above (see here for more information about using transform_coords) to a helper conversion function.

[12]:

sample, monitors = sans.i_of_q.convert_to_wavelength(
    data=sample,
    monitors=monitors,
    data_graph=data_graph,
    monitor_graph=monitor_graph)

Convert to Q¶

Using the coordinate transformation graph as above, we can compute the momentum vector \(Q\), and then merge all the events in the detector pixel bins, so as to obtain an intensity that depends only on \(Q\).

This is done with the convert_to_q_and_merge_spectra helper.

[22]:

wavelength_bands = sc.concat(
            [wavelength_bins.min(), wavelength_bins.max()], dim='wavelength')

[23]:

sample_q = sans.i_of_q.convert_to_q_and_merge_spectra(
    data=sample,
    graph=data_graph,
    wavelength_bands=wavelength_bands,
    q_bins=q_bins,
    gravity=gravity)

[24]:

sc.plot(sample_q, norm='log')

Convert denominator to Q¶

Converting the denominator to \(Q\) is achieved in the same way

[25]:

denominator_q = sans.i_of_q.convert_to_q_and_merge_spectra(
    data=denominator,
    graph=data_graph,
    wavelength_bands=wavelength_bands,
    q_bins=q_bins,
    gravity=True)

sc.plot(denominator_q, norm='log')

References¶

Heenan R. K., Penfold J., King S. M., 1997, SANS at Pulsed Neutron Sources: Present and Future Prospects, J. Appl. Cryst., 30, 1140-1147

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

Seeger P. A., Hjelm R. P. Jnr, 1991, Small-angle neutron scattering at pulsed spallation sources, J. Appl. Cryst., 24, 467-478

SANS2D: I(Q) workflow for a single run (sample)

Contents

SANS2D: I(Q) workflow for a single run (sample)¶

Define reduction parameters¶

Loading data files¶

Extract monitors¶

Apply offsets to pixel positions¶

Masking¶

Mask bad pixels¶

Mask Bragg peaks in time-of-flight¶

Coordinate transformation graph¶

Convert the data to wavelength¶

Compute normalization term¶

Transmission fraction¶

Remove background noise and rebin monitors¶

Direct beam function¶

Solid Angle¶

The denominator term¶

Convert to Q¶

Convert denominator to Q¶

Normalize the sample¶

References¶