Data reduction for Amor
Contents
Data reduction for Amor¶
In this notebook, we will look at the reduction workflow for reflectometry data collected from the PSI Amor instrument. This is a living document and there are plans to update this as necessary with changes in the data reduction methodology and code.
We will begin by importing the modules that are necessary for this notebook and loading the data. The sample.nxs
file is the experimental data file of interest, while reference.nxs
is the reference measurement of the neutron supermirror.
[1]:
import scipp as sc
from ess import amor
import ess
[2]:
logger = ess.logging.configure_workflow('amor_reduction',
filename='amor.log')
The Amor beamline¶
Before we can load the data, we need to define the parameters of the beamline. We begin by defining the convention for naming angles in our set-up. We use the Fig. 5 from the paper by Stahn & Glavic (2016), which is reproduced below (along with its caption).
![Figure5](https://ars.els-cdn.com/content/image/1-s2.0-S0168900216300250-gr5.jpg)
The yellow area shows the incoming and reflected beam, both with the divergence \(\Delta \theta\). The inclination of the sample relative to the centre of the incoming beam (here identical to the instrument horizon) is called \(\omega\), and the respective angle of the reflected beam relative to the same axis is \(\gamma\).
In general the detector centre is located at \(\gamma_{\rm D} = 2\omega\). These are instrument coordinates and should not be confused with the situation on the sample, where the take-off angle of an individual neutron trajectory is called \(\theta\).
The amor
module provides a helper function that generates the default beamline parameters. This function requires the sample rotation angle (\(\omega\)) as an input to fully define the beamline. In the future, all these beamline parameters (including the sample rotation) will be included in the file meta data. For now, we must define this manually.
[3]:
sample_rotation = sc.scalar(0.7989, unit='deg')
amor_beamline = amor.make_beamline(sample_rotation=sample_rotation)
Loading the data¶
Using the amor.load
function, we load the sample.nxs
file and perform some early preprocessing:
The
tof
values are converted from nanoseconds to microseconds.The raw data contains events coming from two pulses, and these get folded into a single
tof
range
[4]:
sample = amor.load(amor.data.get_path("sample.nxs"),
beamline=amor_beamline)
sample
Downloading file 'sample.nxs' from 'https://public.esss.dk/groups/scipp/ess/amor/1/sample.nxs' to '/home/runner/.cache/ess/amor/1'.
[4]:
- detector_id: 9216
- tof: 1
- beam_size()float64m0.001
Values:
array(0.001) - detector_id(detector_id)int321, 2, ..., 9215, 9216
Values:
array([ 1, 2, 3, ..., 9214, 9215, 9216], dtype=int32) - detector_spatial_resolution()float64m0.0025
Values:
array(0.0025) - gravity()vector3m/s^2[ 0. -9.80665 0. ]
Values:
array([ 0. , -9.80665, 0. ]) - position(detector_id)vector3m[-0.064 0.09459759 4.12644383], [-0.05987097 0.09459759 4.12644383], ..., [0.05987097 0. 4. ], [0.064 0. 4. ]
Values:
array([[-0.064 , 0.09459759, 4.12644383], [-0.05987097, 0.09459759, 4.12644383], [-0.05574194, 0.09459759, 4.12644383], ..., [ 0.05574194, 0. , 4. ], [ 0.05987097, 0. , 4. ], [ 0.064 , 0. , 4. ]]) - sample_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - sample_rotation()float64deg0.7989
Values:
array(0.7989) - sample_size()float64m0.01
Values:
array(0.01) - source_chopper()Dataset<scipp.Dataset> Dimensions: Sizes[] Data: frequency float64 [Hz] () [6.66667] phase float64 [deg] () [-8] position vector3 [m] () [(0, 0, -15)]
Values:
<scipp.Dataset> Dimensions: Sizes[] Data: frequency float64 [Hz] () [6.66667] phase float64 [deg] () [-8] position vector3 [m] () [(0, 0, -15)] - source_position()vector3m[ 0. 0. 30.]
Values:
array([ 0., 0., 30.]) - tof(tof [bin-edge])float64µs0.0, 7.500e+04
Values:
array([ 0., 75000.])
- (detector_id, tof)DataArrayViewbinned data [len=0, len=0, ..., len=0, len=0]
Values:
[<scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] tof float64 [µs] (event) [] Data: float32 [counts] (event) [] [] , <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] tof float64 [µs] (event) [] Data: float32 [counts] (event) [] [] , ..., <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] tof float64 [µs] (event) [] Data: float32 [counts] (event) [] [] , <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] tof float64 [µs] (event) [] Data: float32 [counts] (event) [] [] ]
- base_position(detector_id)vector3m[-0.064 0.09459759 4.12644383], [-0.05987097 0.09459759 4.12644383], ..., [0.05987097 0. 4. ], [0.064 0. 4. ]
Values:
array([[-0.064 , 0.09459759, 4.12644383], [-0.05987097, 0.09459759, 4.12644383], [-0.05574194, 0.09459759, 4.12644383], ..., [ 0.05574194, 0. , 4. ], [ 0.05987097, 0. , 4. ], [ 0.064 , 0. , 4. ]]) - com()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:55.427112960] Data: float64 [None] (time, dim_1) [-1.599] - coz()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:57.533574144] Data: float64 [None] (time, dim_1) [114.52] - experiment_title()stringcommissioning
Values:
'commissioning' - horizontal()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - instrument_name()stringAMOR
Values:
'AMOR' - sample_base_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - sample_transform()Variable<scipp.Variable> () translation3 [m] [(0, 0, 0)]
Values:
<scipp.Variable> () translation3 [m] [(0, 0, 0)] - slot()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - som()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:54.339492096] Data: float64 [None] (time, dim_1) [0.799] - source_base_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - source_transform()Variable<scipp.Variable> () affine_transform3 [m] [ 1 0 0 0 0 1 0 0 0 0 1 30 0 0 0 1]
Values:
<scipp.Variable> () affine_transform3 [m] [ 1 0 0 0 0 1 0 0 0 0 1 30 0 0 0 1] - soz()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T09:04:32.611630848] Data: float64 [None] (time, dim_1) [-0.2] - start_time()string2020-11-25T16:03:10.000000000
Values:
'2020-11-25T16:03:10.000000000' - vertical()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) []
By simply plotting the data, we get a first glimpse into the data contents.
[5]:
sc.plot(sample)
Correcting the position of the detector pixels¶
Note: once new Nexus files are produced, this step should go away.
The pixel positions are wrong in the sample.nxs
file, and require an ad-hoc correction. We apply an arbitrary shift in the vertical (y
) direction. We first move the pixels down by 0.955 degrees, so that the centre of the beam goes through the centre of the top half of the detector blades (the bottom half of the detectors was turned off). Next, we move all the pixels so that the centre of the top half of the detector pixels lies at an angle of \(2 \omega\), as described in the
beamline diagram.
[6]:
logger.info("Correcting pixel positions in 'sample.nxs'")
def pixel_position_correction(data: sc.DataArray):
return data.coords['position'].fields.z * sc.tan(2.0 *
data.coords['sample_rotation'] -
(0.955 * sc.units.deg))
sample.coords['position'].fields.y += pixel_position_correction(sample)
We now check that the detector pixels are in the correct position by showing the instrument view
[7]:
amor.instrument_view(sample)
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 comprises a number of modifications.
The computation of the scattering angle \(\theta\) includes a correction for the Earth’s gravitational field which bends the flight path of the neutrons. The angle can be found using the following expression
where \(m_{\rm n}\) is the neutron mass, \(g\) is the acceleration due to gravity, and \(h\) is Planck’s constant.
For a graphical representation of the above expression, we consider once again the situation with a convergent beam onto an inclined sample.
![specular_reflection](../../_images/amor_specular_reflection.png)
The detector (in green), whose center is located at an angle \(\gamma_{\rm D}\) from the horizontal plane, has a physical extent and is measuring counts at multiple scattering angles at the same time. We consider two possible paths for neutrons. The first path (cyan) is travelling horizontally from the source to the sample and subsequently, following specular reflection, hits the detector at \(\gamma_{\rm D}\) from the horizontal plane. From the symmetry of Bragg’s law, the scattering angle for this path is \(\theta_{1} = \gamma_{\rm D} - \omega\).
The second path (red) is hitting the bottom edge of the detector. Assuming that all reflections are specular, the only way the detector can record neutron events at this location is if the neutron originated from the bottom part of the convergent beam. Using the same symmetry argument as above, the scattering angle is \(\theta_{2} = \gamma_{2} - \omega\).
This expression differs slightly from the equation found in the computation of the \(\theta\) angle in other techniques such as SANS, in that the horizontal \(x\) term is absent, because we assume a planar symmetry and only consider the vertical \(y\) component of the displacement.
The conversion graph is defined in the reflectometry module, and can be obtained via
[8]:
graph = amor.conversions.specular_reflection()
sc.show_graph(graph, simplified=True)
[8]:
Computing the wavelength¶
To compute the wavelength of the neutrons, we request the wavelength
coordinate from the transform_coords
method by supplying our graph defined above (see here for more information about using transform_coords
).
We also exclude all neutrons with a wavelength lower than 2.4 Å.
[9]:
sample_wav = sample.transform_coords(["wavelength"], graph=graph)
wavelength_edges = sc.array(dims=['wavelength'], values=[2.4, 16.0], unit='angstrom')
sample_wav = sc.bin(sample_wav, edges=[wavelength_edges])
sample_wav
[9]:
- detector_id: 9216
- wavelength: 1
- beam_size()float64m0.001
Values:
array(0.001) - detector_id(detector_id)int321, 2, ..., 9215, 9216
Values:
array([ 1, 2, 3, ..., 9214, 9215, 9216], dtype=int32) - detector_spatial_resolution()float64m0.0025
Values:
array(0.0025) - gravity()vector3m/s^2[ 0. -9.80665 0. ]
Values:
array([ 0. , -9.80665, 0. ]) - sample_rotation()float64deg0.7989
Values:
array(0.7989) - sample_size()float64m0.01
Values:
array(0.01) - source_position()vector3m[ 0. 0. 30.]
Values:
array([ 0., 0., 30.]) - wavelength(wavelength [bin-edge])float64Å2.4, 16.0
Values:
array([ 2.4, 16. ])
- (detector_id, wavelength)DataArrayViewbinned data [len=0, len=0, ..., len=0, len=0]
Values:
[<scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] wavelength float64 [Å] (event) [] Data: float32 [counts] (event) [] [] Attributes: tof float64 [µs] (event) [] , <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] wavelength float64 [Å] (event) [] Data: float32 [counts] (event) [] [] Attributes: tof float64 [µs] (event) [] , ..., <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] wavelength float64 [Å] (event) [] Data: float32 [counts] (event) [] [] Attributes: tof float64 [µs] (event) [] , <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] wavelength float64 [Å] (event) [] Data: float32 [counts] (event) [] [] Attributes: tof float64 [µs] (event) [] ]
- L1()float64m15.0
Values:
array(15.) - L2(detector_id)float64m4.129, 4.129, ..., 4.001, 4.001
Values:
array([4.12934447, 4.12928254, 4.12922474, ..., 4.0006401 , 4.00069976, 4.00076368]) - Ltotal(detector_id)float64m19.129, 19.129, ..., 19.001, 19.001
Values:
array([19.12934447, 19.12928254, 19.12922474, ..., 19.0006401 , 19.00069976, 19.00076368]) - base_position(detector_id)vector3m[-0.064 0.09459759 4.12644383], [-0.05987097 0.09459759 4.12644383], ..., [0.05987097 0. 4. ], [0.064 0. 4. ]
Values:
array([[-0.064 , 0.09459759, 4.12644383], [-0.05987097, 0.09459759, 4.12644383], [-0.05574194, 0.09459759, 4.12644383], ..., [ 0.05574194, 0. , 4. ], [ 0.05987097, 0. , 4. ], [ 0.064 , 0. , 4. ]]) - com()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:55.427112960] Data: float64 [None] (time, dim_1) [-1.599] - coz()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:57.533574144] Data: float64 [None] (time, dim_1) [114.52] - experiment_title()stringcommissioning
Values:
'commissioning' - horizontal()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - incident_beam()vector3m[ 0. 0. 15.]
Values:
array([ 0., 0., 15.]) - instrument_name()stringAMOR
Values:
'AMOR' - position(detector_id)vector3m[-0.064 0.14089401 4.12644383], [-0.05987097 0.14089401 4.12644383], ..., [0.05987097 0.04487779 4. ], [0.064 0.04487779 4. ]
Values:
array([[-0.064 , 0.14089401, 4.12644383], [-0.05987097, 0.14089401, 4.12644383], [-0.05574194, 0.14089401, 4.12644383], ..., [ 0.05574194, 0.04487779, 4. ], [ 0.05987097, 0.04487779, 4. ], [ 0.064 , 0.04487779, 4. ]]) - sample_base_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - sample_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - sample_transform()Variable<scipp.Variable> () translation3 [m] [(0, 0, 0)]
Values:
<scipp.Variable> () translation3 [m] [(0, 0, 0)] - scattered_beam(detector_id)vector3m[-0.064 0.14089401 4.12644383], [-0.05987097 0.14089401 4.12644383], ..., [0.05987097 0.04487779 4. ], [0.064 0.04487779 4. ]
Values:
array([[-0.064 , 0.14089401, 4.12644383], [-0.05987097, 0.14089401, 4.12644383], [-0.05574194, 0.14089401, 4.12644383], ..., [ 0.05574194, 0.04487779, 4. ], [ 0.05987097, 0.04487779, 4. ], [ 0.064 , 0.04487779, 4. ]]) - slot()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - som()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:54.339492096] Data: float64 [None] (time, dim_1) [0.799] - source_base_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - source_chopper()Dataset<scipp.Dataset> Dimensions: Sizes[] Data: frequency float64 [Hz] () [6.66667] phase float64 [deg] () [-8] position vector3 [m] () [(0, 0, -15)]
Values:
<scipp.Dataset> Dimensions: Sizes[] Data: frequency float64 [Hz] () [6.66667] phase float64 [deg] () [-8] position vector3 [m] () [(0, 0, -15)] - source_transform()Variable<scipp.Variable> () affine_transform3 [m] [ 1 0 0 0 0 1 0 0 0 0 1 30 0 0 0 1]
Values:
<scipp.Variable> () affine_transform3 [m] [ 1 0 0 0 0 1 0 0 0 0 1 30 0 0 0 1] - soz()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T09:04:32.611630848] Data: float64 [None] (time, dim_1) [-0.2] - start_time()string2020-11-25T16:03:10.000000000
Values:
'2020-11-25T16:03:10.000000000' - vertical()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) []
[10]:
sample_wav.bins.concatenate('detector_id').plot()
Compute the Q vector¶
Using the same method, we can compute the \(Q\) vector, which now depends on both detector position (id) and wavelength
[11]:
sample_q = sample_wav.transform_coords(["Q"], graph=graph)
sample_q
[11]:
- detector_id: 9216
- Q: 1
- Q(Q [bin-edge], detector_id)float641/Å0.106, 0.106, ..., -0.002, -0.002
Values:
array([[ 0.1056337 , 0.10563638, 0.10563888, ..., -0.01430872, -0.0143096 , -0.01431054], [ 0.01559069, 0.01559109, 0.01559147, ..., -0.00239267, -0.0023928 , -0.00239295]]) - beam_size()float64m0.001
Values:
array(0.001) - detector_id(detector_id)int321, 2, ..., 9215, 9216
Values:
array([ 1, 2, 3, ..., 9214, 9215, 9216], dtype=int32) - detector_spatial_resolution()float64m0.0025
Values:
array(0.0025) - sample_size()float64m0.01
Values:
array(0.01) - source_position()vector3m[ 0. 0. 30.]
Values:
array([ 0., 0., 30.])
- (detector_id, Q)DataArrayViewbinned data [len=0, len=0, ..., len=0, len=0]
Values:
[<scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: Q float64 [1/Å] (event) [] pulse_time datetime64 [ns] (event) [] Data: float32 [counts] (event) [] [] Attributes: theta float64 [rad] (event) [] tof float64 [µs] (event) [] wavelength float64 [Å] (event) [] , <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: Q float64 [1/Å] (event) [] pulse_time datetime64 [ns] (event) [] Data: float32 [counts] (event) [] [] Attributes: theta float64 [rad] (event) [] tof float64 [µs] (event) [] wavelength float64 [Å] (event) [] , ..., <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: Q float64 [1/Å] (event) [] pulse_time datetime64 [ns] (event) [] Data: float32 [counts] (event) [] [] Attributes: theta float64 [rad] (event) [] tof float64 [µs] (event) [] wavelength float64 [Å] (event) [] , <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: Q float64 [1/Å] (event) [] pulse_time datetime64 [ns] (event) [] Data: float32 [counts] (event) [] [] Attributes: theta float64 [rad] (event) [] tof float64 [µs] (event) [] wavelength float64 [Å] (event) [] ]
- L1()float64m15.0
Values:
array(15.) - L2(detector_id)float64m4.129, 4.129, ..., 4.001, 4.001
Values:
array([4.12934447, 4.12928254, 4.12922474, ..., 4.0006401 , 4.00069976, 4.00076368]) - Ltotal(detector_id)float64m19.129, 19.129, ..., 19.001, 19.001
Values:
array([19.12934447, 19.12928254, 19.12922474, ..., 19.0006401 , 19.00069976, 19.00076368]) - base_position(detector_id)vector3m[-0.064 0.09459759 4.12644383], [-0.05987097 0.09459759 4.12644383], ..., [0.05987097 0. 4. ], [0.064 0. 4. ]
Values:
array([[-0.064 , 0.09459759, 4.12644383], [-0.05987097, 0.09459759, 4.12644383], [-0.05574194, 0.09459759, 4.12644383], ..., [ 0.05574194, 0. , 4. ], [ 0.05987097, 0. , 4. ], [ 0.064 , 0. , 4. ]]) - com()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:55.427112960] Data: float64 [None] (time, dim_1) [-1.599] - coz()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:57.533574144] Data: float64 [None] (time, dim_1) [114.52] - experiment_title()stringcommissioning
Values:
'commissioning' - gravity()vector3m/s^2[ 0. -9.80665 0. ]
Values:
array([ 0. , -9.80665, 0. ]) - horizontal()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - incident_beam()vector3m[ 0. 0. 15.]
Values:
array([ 0., 0., 15.]) - instrument_name()stringAMOR
Values:
'AMOR' - position(detector_id)vector3m[-0.064 0.14089401 4.12644383], [-0.05987097 0.14089401 4.12644383], ..., [0.05987097 0.04487779 4. ], [0.064 0.04487779 4. ]
Values:
array([[-0.064 , 0.14089401, 4.12644383], [-0.05987097, 0.14089401, 4.12644383], [-0.05574194, 0.14089401, 4.12644383], ..., [ 0.05574194, 0.04487779, 4. ], [ 0.05987097, 0.04487779, 4. ], [ 0.064 , 0.04487779, 4. ]]) - sample_base_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - sample_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - sample_rotation()float64deg0.7989
Values:
array(0.7989) - sample_transform()Variable<scipp.Variable> () translation3 [m] [(0, 0, 0)]
Values:
<scipp.Variable> () translation3 [m] [(0, 0, 0)] - scattered_beam(detector_id)vector3m[-0.064 0.14089401 4.12644383], [-0.05987097 0.14089401 4.12644383], ..., [0.05987097 0.04487779 4. ], [0.064 0.04487779 4. ]
Values:
array([[-0.064 , 0.14089401, 4.12644383], [-0.05987097, 0.14089401, 4.12644383], [-0.05574194, 0.14089401, 4.12644383], ..., [ 0.05574194, 0.04487779, 4. ], [ 0.05987097, 0.04487779, 4. ], [ 0.064 , 0.04487779, 4. ]]) - slot()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - som()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:54.339492096] Data: float64 [None] (time, dim_1) [0.799] - source_base_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - source_chopper()Dataset<scipp.Dataset> Dimensions: Sizes[] Data: frequency float64 [Hz] () [6.66667] phase float64 [deg] () [-8] position vector3 [m] () [(0, 0, -15)]
Values:
<scipp.Dataset> Dimensions: Sizes[] Data: frequency float64 [Hz] () [6.66667] phase float64 [deg] () [-8] position vector3 [m] () [(0, 0, -15)] - source_transform()Variable<scipp.Variable> () affine_transform3 [m] [ 1 0 0 0 0 1 0 0 0 0 1 30 0 0 0 1]
Values:
<scipp.Variable> () affine_transform3 [m] [ 1 0 0 0 0 1 0 0 0 0 1 30 0 0 0 1] - soz()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T09:04:32.611630848] Data: float64 [None] (time, dim_1) [-0.2] - start_time()string2020-11-25T16:03:10.000000000
Values:
'2020-11-25T16:03:10.000000000' - theta(Q [bin-edge], detector_id)float64rad0.020, 0.020, ..., -0.003, -0.003
Values:
array([[ 0.02017592, 0.02017643, 0.02017691, ..., -0.00273277, -0.00273294, -0.00273312], [ 0.01985198, 0.0198525 , 0.01985298, ..., -0.00304645, -0.00304662, -0.0030468 ]]) - vertical()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - wavelength(Q [bin-edge])float64Å2.4, 16.0
Values:
array([ 2.4, 16. ])
[12]:
q_edges = sc.geomspace(dim='Q', start=0.008, stop=0.08, num=201, unit='1/angstrom')
sample_q_binned = sc.bin(sample_q, edges=[q_edges])
sample_q_summed = sample_q_binned.sum('detector_id')
sc.plot(sample_q_summed, norm="log")
Normalize by the super-mirror¶
To perform the normalization, we load the super-mirror reference.nxs
file.
[13]:
reference = amor.load(amor.data.get_path("reference.nxs"),
beamline=amor_beamline)
reference.coords['position'].fields.y += pixel_position_correction(reference)
reference
Downloading file 'reference.nxs' from 'https://public.esss.dk/groups/scipp/ess/amor/1/reference.nxs' to '/home/runner/.cache/ess/amor/1'.
[13]:
- detector_id: 9216
- tof: 1
- beam_size()float64m0.001
Values:
array(0.001) - detector_id(detector_id)int321, 2, ..., 9215, 9216
Values:
array([ 1, 2, 3, ..., 9214, 9215, 9216], dtype=int32) - detector_spatial_resolution()float64m0.0025
Values:
array(0.0025) - gravity()vector3m/s^2[ 0. -9.80665 0. ]
Values:
array([ 0. , -9.80665, 0. ]) - position(detector_id)vector3m[-0.064 0.14089401 4.12644383], [-0.05987097 0.14089401 4.12644383], ..., [0.05987097 0.04487779 4. ], [0.064 0.04487779 4. ]
Values:
array([[-0.064 , 0.14089401, 4.12644383], [-0.05987097, 0.14089401, 4.12644383], [-0.05574194, 0.14089401, 4.12644383], ..., [ 0.05574194, 0.04487779, 4. ], [ 0.05987097, 0.04487779, 4. ], [ 0.064 , 0.04487779, 4. ]]) - sample_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - sample_rotation()float64deg0.7989
Values:
array(0.7989) - sample_size()float64m0.01
Values:
array(0.01) - source_chopper()Dataset<scipp.Dataset> Dimensions: Sizes[] Data: frequency float64 [Hz] () [6.66667] phase float64 [deg] () [-8] position vector3 [m] () [(0, 0, -15)]
Values:
<scipp.Dataset> Dimensions: Sizes[] Data: frequency float64 [Hz] () [6.66667] phase float64 [deg] () [-8] position vector3 [m] () [(0, 0, -15)] - source_position()vector3m[ 0. 0. 30.]
Values:
array([ 0., 0., 30.]) - tof(tof [bin-edge])float64µs0.0, 7.500e+04
Values:
array([ 0., 75000.])
- (detector_id, tof)DataArrayViewbinned data [len=1, len=4, ..., len=0, len=0]
Values:
[<scipp.DataArray> Dimensions: Sizes[event:1, ] Coordinates: pulse_time datetime64 [ns] (event) [2020-11-25T15:57:08.000000000] tof float64 [µs] (event) [39553.5] Data: float32 [counts] (event) [1] [1] , <scipp.DataArray> Dimensions: Sizes[event:4, ] Coordinates: pulse_time datetime64 [ns] (event) [2020-11-25T16:01:47.000000000, 2020-11-25T16:01:02.000000000, 2020-11-25T16:03:00.000000000, 2020-11-25T16:06:11.000000000] tof float64 [µs] (event) [19204.7, 44955.1, 19295.1, 22223.5] Data: float32 [counts] (event) [1, 1, 1, 1] [1, 1, 1, 1] , ..., <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] tof float64 [µs] (event) [] Data: float32 [counts] (event) [] [] , <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] tof float64 [µs] (event) [] Data: float32 [counts] (event) [] [] ]
- base_position(detector_id)vector3m[-0.064 0.09459759 4.12644383], [-0.05987097 0.09459759 4.12644383], ..., [0.05987097 0. 4. ], [0.064 0. 4. ]
Values:
array([[-0.064 , 0.09459759, 4.12644383], [-0.05987097, 0.09459759, 4.12644383], [-0.05574194, 0.09459759, 4.12644383], ..., [ 0.05574194, 0. , 4. ], [ 0.05987097, 0. , 4. ], [ 0.064 , 0. , 4. ]]) - com()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T15:56:46.562691840] Data: float64 [None] (time, dim_1) [-2] - coz()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T15:56:47.647848960] Data: float64 [None] (time, dim_1) [143.175] - experiment_title()stringcommissioning
Values:
'commissioning' - horizontal()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - instrument_name()stringAMOR
Values:
'AMOR' - sample_base_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - sample_transform()Variable<scipp.Variable> () translation3 [m] [(0, 0, 0)]
Values:
<scipp.Variable> () translation3 [m] [(0, 0, 0)] - slot()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - som()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T15:56:46.595666944] Data: float64 [None] (time, dim_1) [0.999] - source_base_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - source_transform()Variable<scipp.Variable> () affine_transform3 [m] [ 1 0 0 0 0 1 0 0 0 0 1 30 0 0 0 1]
Values:
<scipp.Variable> () affine_transform3 [m] [ 1 0 0 0 0 1 0 0 0 0 1 30 0 0 0 1] - soz()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T15:56:29.621954048] Data: float64 [None] (time, dim_1) [-0.2] - start_time()string2020-11-25T16:56:50.000000000
Values:
'2020-11-25T16:56:50.000000000' - vertical()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) []
We convert the reference to wavelength using the same graph
[14]:
reference_wav = reference.transform_coords(["wavelength"], graph=graph)
reference_wav = sc.bin(reference_wav, edges=[wavelength_edges])
reference_wav.bins.concatenate('detector_id').plot()
And we then convert to \(Q\) as well
[15]:
reference_q = reference_wav.transform_coords(["Q"], graph=graph)
reference_q_binned = sc.bin(reference_q, edges=[q_edges])
reference_q_summed = reference_q_binned.sum('detector_id')
sc.plot(reference_q_summed, norm="log")
Finally, we divide the sample by the reference to obtain
[16]:
normalized = sample_q_summed / reference_q_summed
sc.plot(normalized, norm="log")
Make a \((\lambda, \theta)\) map¶
A good sanity check is to create a two-dimensional map of the counts in \(\lambda\) and \(\theta\) bins. To achieve this, we request two output coordinates from the transform_coords
method.
[17]:
sample_theta = sample.transform_coords(["theta", "wavelength"], graph=graph)
sample_theta
[17]:
- detector_id: 9216
- theta: 1
- beam_size()float64m0.001
Values:
array(0.001) - detector_id(detector_id)int321, 2, ..., 9215, 9216
Values:
array([ 1, 2, 3, ..., 9214, 9215, 9216], dtype=int32) - detector_spatial_resolution()float64m0.0025
Values:
array(0.0025) - sample_size()float64m0.01
Values:
array(0.01) - source_position()vector3m[ 0. 0. 30.]
Values:
array([ 0., 0., 30.]) - theta(detector_id, theta [bin-edge])float64rad0.020, 0.020, ..., -0.003, -0.003
Values:
array([[ 0.02018338, 0.01987196], [ 0.02018389, 0.01987247], [ 0.02018437, 0.01987295], ..., [-0.00272555, -0.0030312 ], [-0.00272572, -0.00303137], [-0.00272589, -0.00303156]]) - wavelength(detector_id, theta [bin-edge])float64Å0.0, 15.510, ..., 0.0, 15.615
Values:
array([[ 0. , 15.51033551], [ 0. , 15.51038573], [ 0. , 15.51043259], ..., [ 0. , 15.61539766], [ 0. , 15.61534863], [ 0. , 15.6152961 ]])
- (detector_id, theta)DataArrayViewbinned data [len=0, len=0, ..., len=0, len=0]
Values:
[<scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] theta float64 [rad] (event) [] wavelength float64 [Å] (event) [] Data: float32 [counts] (event) [] [] Attributes: tof float64 [µs] (event) [] , <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] theta float64 [rad] (event) [] wavelength float64 [Å] (event) [] Data: float32 [counts] (event) [] [] Attributes: tof float64 [µs] (event) [] , ..., <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] theta float64 [rad] (event) [] wavelength float64 [Å] (event) [] Data: float32 [counts] (event) [] [] Attributes: tof float64 [µs] (event) [] , <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] theta float64 [rad] (event) [] wavelength float64 [Å] (event) [] Data: float32 [counts] (event) [] [] Attributes: tof float64 [µs] (event) [] ]
- L1()float64m15.0
Values:
array(15.) - L2(detector_id)float64m4.129, 4.129, ..., 4.001, 4.001
Values:
array([4.12934447, 4.12928254, 4.12922474, ..., 4.0006401 , 4.00069976, 4.00076368]) - Ltotal(detector_id)float64m19.129, 19.129, ..., 19.001, 19.001
Values:
array([19.12934447, 19.12928254, 19.12922474, ..., 19.0006401 , 19.00069976, 19.00076368]) - base_position(detector_id)vector3m[-0.064 0.09459759 4.12644383], [-0.05987097 0.09459759 4.12644383], ..., [0.05987097 0. 4. ], [0.064 0. 4. ]
Values:
array([[-0.064 , 0.09459759, 4.12644383], [-0.05987097, 0.09459759, 4.12644383], [-0.05574194, 0.09459759, 4.12644383], ..., [ 0.05574194, 0. , 4. ], [ 0.05987097, 0. , 4. ], [ 0.064 , 0. , 4. ]]) - com()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:55.427112960] Data: float64 [None] (time, dim_1) [-1.599] - coz()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:57.533574144] Data: float64 [None] (time, dim_1) [114.52] - experiment_title()stringcommissioning
Values:
'commissioning' - gravity()vector3m/s^2[ 0. -9.80665 0. ]
Values:
array([ 0. , -9.80665, 0. ]) - horizontal()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - incident_beam()vector3m[ 0. 0. 15.]
Values:
array([ 0., 0., 15.]) - instrument_name()stringAMOR
Values:
'AMOR' - position(detector_id)vector3m[-0.064 0.14089401 4.12644383], [-0.05987097 0.14089401 4.12644383], ..., [0.05987097 0.04487779 4. ], [0.064 0.04487779 4. ]
Values:
array([[-0.064 , 0.14089401, 4.12644383], [-0.05987097, 0.14089401, 4.12644383], [-0.05574194, 0.14089401, 4.12644383], ..., [ 0.05574194, 0.04487779, 4. ], [ 0.05987097, 0.04487779, 4. ], [ 0.064 , 0.04487779, 4. ]]) - sample_base_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - sample_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - sample_rotation()float64deg0.7989
Values:
array(0.7989) - sample_transform()Variable<scipp.Variable> () translation3 [m] [(0, 0, 0)]
Values:
<scipp.Variable> () translation3 [m] [(0, 0, 0)] - scattered_beam(detector_id)vector3m[-0.064 0.14089401 4.12644383], [-0.05987097 0.14089401 4.12644383], ..., [0.05987097 0.04487779 4. ], [0.064 0.04487779 4. ]
Values:
array([[-0.064 , 0.14089401, 4.12644383], [-0.05987097, 0.14089401, 4.12644383], [-0.05574194, 0.14089401, 4.12644383], ..., [ 0.05574194, 0.04487779, 4. ], [ 0.05987097, 0.04487779, 4. ], [ 0.064 , 0.04487779, 4. ]]) - slot()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - som()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:54.339492096] Data: float64 [None] (time, dim_1) [0.799] - source_base_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - source_chopper()Dataset<scipp.Dataset> Dimensions: Sizes[] Data: frequency float64 [Hz] () [6.66667] phase float64 [deg] () [-8] position vector3 [m] () [(0, 0, -15)]
Values:
<scipp.Dataset> Dimensions: Sizes[] Data: frequency float64 [Hz] () [6.66667] phase float64 [deg] () [-8] position vector3 [m] () [(0, 0, -15)] - source_transform()Variable<scipp.Variable> () affine_transform3 [m] [ 1 0 0 0 0 1 0 0 0 0 1 30 0 0 0 1]
Values:
<scipp.Variable> () affine_transform3 [m] [ 1 0 0 0 0 1 0 0 0 0 1 30 0 0 0 1] - soz()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T09:04:32.611630848] Data: float64 [None] (time, dim_1) [-0.2] - start_time()string2020-11-25T16:03:10.000000000
Values:
'2020-11-25T16:03:10.000000000' - tof(theta [bin-edge])float64µs0.0, 7.500e+04
Values:
array([ 0., 75000.]) - vertical()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) []
Then, we concatenate all the events in the detector_id
dimension
[18]:
sample_theta = sample_theta.bins.concatenate('detector_id')
sample_theta
[18]:
- theta: 1
- beam_size()float64m0.001
Values:
array(0.001) - detector_spatial_resolution()float64m0.0025
Values:
array(0.0025) - sample_size()float64m0.01
Values:
array(0.01) - source_position()vector3m[ 0. 0. 30.]
Values:
array([ 0., 0., 30.]) - theta(theta [bin-edge])float64rad-0.003, 0.020
Values:
array([-0.00303156, 0.02018747])
- (theta)DataArrayViewbinned data [len=261790]
Values:
[<scipp.DataArray> Dimensions: Sizes[event:261790, ] Coordinates: pulse_time datetime64 [ns] (event) [2020-11-25T15:04:39.000000000, 2020-11-25T15:03:23.000000000, ..., 2020-11-25T15:03:38.000000000, 2020-11-25T15:05:09.000000000] theta float64 [rad] (event) [0.020137, 0.0199556, ..., 0.00735572, 0.00734498] wavelength float64 [Å] (event) [6.19738, 13.3795, ..., 4.4004, 5.26105] Data: float32 [counts] (event) [1, 1, ..., 1, 1] [1, 1, ..., 1, 1] Attributes: tof float64 [µs] (event) [29966.7, 64694.6, ..., 21135.4, 25269.2] ]
- L1()float64m15.0
Values:
array(15.) - com()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:55.427112960] Data: float64 [None] (time, dim_1) [-1.599] - coz()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:57.533574144] Data: float64 [None] (time, dim_1) [114.52] - experiment_title()stringcommissioning
Values:
'commissioning' - gravity()vector3m/s^2[ 0. -9.80665 0. ]
Values:
array([ 0. , -9.80665, 0. ]) - horizontal()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - incident_beam()vector3m[ 0. 0. 15.]
Values:
array([ 0., 0., 15.]) - instrument_name()stringAMOR
Values:
'AMOR' - sample_base_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - sample_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - sample_rotation()float64deg0.7989
Values:
array(0.7989) - sample_transform()Variable<scipp.Variable> () translation3 [m] [(0, 0, 0)]
Values:
<scipp.Variable> () translation3 [m] [(0, 0, 0)] - slot()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - som()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:54.339492096] Data: float64 [None] (time, dim_1) [0.799] - source_base_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - source_chopper()Dataset<scipp.Dataset> Dimensions: Sizes[] Data: frequency float64 [Hz] () [6.66667] phase float64 [deg] () [-8] position vector3 [m] () [(0, 0, -15)]
Values:
<scipp.Dataset> Dimensions: Sizes[] Data: frequency float64 [Hz] () [6.66667] phase float64 [deg] () [-8] position vector3 [m] () [(0, 0, -15)] - source_transform()Variable<scipp.Variable> () affine_transform3 [m] [ 1 0 0 0 0 1 0 0 0 0 1 30 0 0 0 1]
Values:
<scipp.Variable> () affine_transform3 [m] [ 1 0 0 0 0 1 0 0 0 0 1 30 0 0 0 1] - soz()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T09:04:32.611630848] Data: float64 [None] (time, dim_1) [-0.2] - start_time()string2020-11-25T16:03:10.000000000
Values:
'2020-11-25T16:03:10.000000000' - vertical()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) []
Finally, we bin into the existing theta
dimension, and into a new wavelength
dimension, to create a 2D output
[19]:
nbins = 165
theta_edges = sc.linspace(dim='theta', start=0.4, stop=1.2, num=nbins, unit='deg')
wavelength_edges = sc.linspace(dim='wavelength', start=1.0, stop=15.0, num=nbins, unit='angstrom')
binned = sc.bin(sample_theta, edges=[sc.to_unit(theta_edges, 'rad'), wavelength_edges])
binned
[19]:
- theta: 164
- wavelength: 164
- beam_size()float64m0.001
Values:
array(0.001) - detector_spatial_resolution()float64m0.0025
Values:
array(0.0025) - sample_size()float64m0.01
Values:
array(0.01) - source_position()vector3m[ 0. 0. 30.]
Values:
array([ 0., 0., 30.]) - theta(theta [bin-edge])float64rad0.007, 0.007, ..., 0.021, 0.021
Values:
array([0.00698132, 0.00706646, 0.00715159, 0.00723673, 0.00732187, 0.00740701, 0.00749215, 0.00757728, 0.00766242, 0.00774756, 0.0078327 , 0.00791784, 0.00800297, 0.00808811, 0.00817325, 0.00825839, 0.00834353, 0.00842866, 0.0085138 , 0.00859894, 0.00868408, 0.00876922, 0.00885435, 0.00893949, 0.00902463, 0.00910977, 0.00919491, 0.00928004, 0.00936518, 0.00945032, 0.00953546, 0.0096206 , 0.00970573, 0.00979087, 0.00987601, 0.00996115, 0.01004629, 0.01013142, 0.01021656, 0.0103017 , 0.01038684, 0.01047198, 0.01055711, 0.01064225, 0.01072739, 0.01081253, 0.01089767, 0.0109828 , 0.01106794, 0.01115308, 0.01123822, 0.01132336, 0.01140849, 0.01149363, 0.01157877, 0.01166391, 0.01174905, 0.01183418, 0.01191932, 0.01200446, 0.0120896 , 0.01217474, 0.01225987, 0.01234501, 0.01243015, 0.01251529, 0.01260043, 0.01268556, 0.0127707 , 0.01285584, 0.01294098, 0.01302612, 0.01311125, 0.01319639, 0.01328153, 0.01336667, 0.01345181, 0.01353694, 0.01362208, 0.01370722, 0.01379236, 0.0138775 , 0.01396263, 0.01404777, 0.01413291, 0.01421805, 0.01430319, 0.01438832, 0.01447346, 0.0145586 , 0.01464374, 0.01472888, 0.01481401, 0.01489915, 0.01498429, 0.01506943, 0.01515457, 0.0152397 , 0.01532484, 0.01540998, 0.01549512, 0.01558026, 0.01566539, 0.01575053, 0.01583567, 0.01592081, 0.01600595, 0.01609108, 0.01617622, 0.01626136, 0.0163465 , 0.01643164, 0.01651677, 0.01660191, 0.01668705, 0.01677219, 0.01685733, 0.01694246, 0.0170276 , 0.01711274, 0.01719788, 0.01728302, 0.01736815, 0.01745329, 0.01753843, 0.01762357, 0.01770871, 0.01779384, 0.01787898, 0.01796412, 0.01804926, 0.0181344 , 0.01821953, 0.01830467, 0.01838981, 0.01847495, 0.01856009, 0.01864522, 0.01873036, 0.0188155 , 0.01890064, 0.01898578, 0.01907091, 0.01915605, 0.01924119, 0.01932633, 0.01941147, 0.0194966 , 0.01958174, 0.01966688, 0.01975202, 0.01983716, 0.01992229, 0.02000743, 0.02009257, 0.02017771, 0.02026285, 0.02034798, 0.02043312, 0.02051826, 0.0206034 , 0.02068854, 0.02077367, 0.02085881, 0.02094395]) - wavelength(wavelength [bin-edge])float64Å1.0, 1.085, ..., 14.915, 15.0
Values:
array([ 1. , 1.08536585, 1.17073171, 1.25609756, 1.34146341, 1.42682927, 1.51219512, 1.59756098, 1.68292683, 1.76829268, 1.85365854, 1.93902439, 2.02439024, 2.1097561 , 2.19512195, 2.2804878 , 2.36585366, 2.45121951, 2.53658537, 2.62195122, 2.70731707, 2.79268293, 2.87804878, 2.96341463, 3.04878049, 3.13414634, 3.2195122 , 3.30487805, 3.3902439 , 3.47560976, 3.56097561, 3.64634146, 3.73170732, 3.81707317, 3.90243902, 3.98780488, 4.07317073, 4.15853659, 4.24390244, 4.32926829, 4.41463415, 4.5 , 4.58536585, 4.67073171, 4.75609756, 4.84146341, 4.92682927, 5.01219512, 5.09756098, 5.18292683, 5.26829268, 5.35365854, 5.43902439, 5.52439024, 5.6097561 , 5.69512195, 5.7804878 , 5.86585366, 5.95121951, 6.03658537, 6.12195122, 6.20731707, 6.29268293, 6.37804878, 6.46341463, 6.54878049, 6.63414634, 6.7195122 , 6.80487805, 6.8902439 , 6.97560976, 7.06097561, 7.14634146, 7.23170732, 7.31707317, 7.40243902, 7.48780488, 7.57317073, 7.65853659, 7.74390244, 7.82926829, 7.91463415, 8. , 8.08536585, 8.17073171, 8.25609756, 8.34146341, 8.42682927, 8.51219512, 8.59756098, 8.68292683, 8.76829268, 8.85365854, 8.93902439, 9.02439024, 9.1097561 , 9.19512195, 9.2804878 , 9.36585366, 9.45121951, 9.53658537, 9.62195122, 9.70731707, 9.79268293, 9.87804878, 9.96341463, 10.04878049, 10.13414634, 10.2195122 , 10.30487805, 10.3902439 , 10.47560976, 10.56097561, 10.64634146, 10.73170732, 10.81707317, 10.90243902, 10.98780488, 11.07317073, 11.15853659, 11.24390244, 11.32926829, 11.41463415, 11.5 , 11.58536585, 11.67073171, 11.75609756, 11.84146341, 11.92682927, 12.01219512, 12.09756098, 12.18292683, 12.26829268, 12.35365854, 12.43902439, 12.52439024, 12.6097561 , 12.69512195, 12.7804878 , 12.86585366, 12.95121951, 13.03658537, 13.12195122, 13.20731707, 13.29268293, 13.37804878, 13.46341463, 13.54878049, 13.63414634, 13.7195122 , 13.80487805, 13.8902439 , 13.97560976, 14.06097561, 14.14634146, 14.23170732, 14.31707317, 14.40243902, 14.48780488, 14.57317073, 14.65853659, 14.74390244, 14.82926829, 14.91463415, 15. ])
- (theta, wavelength)DataArrayViewbinned data [len=0, len=0, ..., len=0, len=0]
Values:
[<scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] theta float64 [rad] (event) [] wavelength float64 [Å] (event) [] Data: float32 [counts] (event) [] [] Attributes: tof float64 [µs] (event) [] , <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] theta float64 [rad] (event) [] wavelength float64 [Å] (event) [] Data: float32 [counts] (event) [] [] Attributes: tof float64 [µs] (event) [] , ..., <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] theta float64 [rad] (event) [] wavelength float64 [Å] (event) [] Data: float32 [counts] (event) [] [] Attributes: tof float64 [µs] (event) [] , <scipp.DataArray> Dimensions: Sizes[event:0, ] Coordinates: pulse_time datetime64 [ns] (event) [] theta float64 [rad] (event) [] wavelength float64 [Å] (event) [] Data: float32 [counts] (event) [] [] Attributes: tof float64 [µs] (event) [] ]
- L1()float64m15.0
Values:
array(15.) - com()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:55.427112960] Data: float64 [None] (time, dim_1) [-1.599] - coz()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:57.533574144] Data: float64 [None] (time, dim_1) [114.52] - experiment_title()stringcommissioning
Values:
'commissioning' - gravity()vector3m/s^2[ 0. -9.80665 0. ]
Values:
array([ 0. , -9.80665, 0. ]) - horizontal()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - incident_beam()vector3m[ 0. 0. 15.]
Values:
array([ 0., 0., 15.]) - instrument_name()stringAMOR
Values:
'AMOR' - sample_base_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - sample_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - sample_rotation()float64deg0.7989
Values:
array(0.7989) - sample_transform()Variable<scipp.Variable> () translation3 [m] [(0, 0, 0)]
Values:
<scipp.Variable> () translation3 [m] [(0, 0, 0)] - slot()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) [] - som()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T14:59:54.339492096] Data: float64 [None] (time, dim_1) [0.799] - source_base_position()vector3m[0. 0. 0.]
Values:
array([0., 0., 0.]) - source_chopper()Dataset<scipp.Dataset> Dimensions: Sizes[] Data: frequency float64 [Hz] () [6.66667] phase float64 [deg] () [-8] position vector3 [m] () [(0, 0, -15)]
Values:
<scipp.Dataset> Dimensions: Sizes[] Data: frequency float64 [Hz] () [6.66667] phase float64 [deg] () [-8] position vector3 [m] () [(0, 0, -15)] - source_transform()Variable<scipp.Variable> () affine_transform3 [m] [ 1 0 0 0 0 1 0 0 0 0 1 30 0 0 0 1]
Values:
<scipp.Variable> () affine_transform3 [m] [ 1 0 0 0 0 1 0 0 0 0 1 30 0 0 0 1] - soz()DataArray{dims=[time: 1, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:1, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [2020-11-25T09:04:32.611630848] Data: float64 [None] (time, dim_1) [-0.2] - start_time()string2020-11-25T16:03:10.000000000
Values:
'2020-11-25T16:03:10.000000000' - vertical()DataArray{dims=[time: 0, dim_1: 1], unit=None, coords=[time]}
Values:
<scipp.DataArray> Dimensions: Sizes[time:0, dim_1:1, ] Coordinates: time datetime64 [ns] (time) [] Data: float64 [None] (time, dim_1) []
[20]:
binned.bins.sum().plot()
This plot can be used to check if the value of the sample rotation angle \(\omega\) is correct. The bright triangles should be pointing back to the origin \(\lambda = \theta = 0\).
References¶
Stahn J., Glavic A., 2016, Focusing neutron reflectometry: Implementation and experience on the TOF-reflectometer Amor, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 821, 44-54