Resolution effects in TOF Reflectometry

In the following reflectometry example, each scan point has a distribution of $q_z$ values.

The constructor

ba.DistributionGaussian(0., 1., 25, 2.)

specifies a Gaussian distribution with mean 0, standard deviation 1, 25 sampling points, and a cut-off at 2 sigma. For other distributions (besides Gaussian), see distributions.

The statements

scan = ba.QzScan(qzs)
scan.setVectorResolution(distr, dq)

take arrays qzs and dq as arguments. These arrays must have the same length n. For each scan point (i=0,..,n-1), the $q_z$ values have a Gaussian distribution with mean qzs[i] and dq[i].

TOF simulation without resolution effects

TOF simulation with $dq = 0.03\,q$

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
#!/usr/bin/env python3
"""
An example of defining reflectometry instrument
for time of flight experiment. In this example
we will use purely qz-defined beam,
without explicitly specifying
incident angle or a wavelength.
Additionally we will set pointwise resolution
to the scan.
Note that these approaches work with SLD-based
materials only.
"""
import numpy as np
import bornagain as ba
from bornagain import ba_plot as bp, nm


def get_sample():
    """
    Twenty alternating Ti and Ni layers on a silicon substrate.
    """
    ambient_mat = ba.Vacuum()
    ti_mat = ba.SLDMaterial("Ti", (0.05, 0.62, 0.55), -1.9493e-6, 0)
    ni_mat = ba.SLDMaterial("Ni", (0.93, 0.48, 0.14), 9.4245e-6, 0)
    substrate_mat = ba.SLDMaterial(
        "SiSubstrate", (0.28, 0.57, 0.82), 2.0704e-6, 0)

    stack = ba.LayerStack(10)
    stack.addLayer(ba.Layer(ti_mat, 3*nm))
    stack.addLayer(ba.Layer(ni_mat, 7*nm))

    sample = ba.Sample()
    sample.addLayer(ba.Layer(ambient_mat))
    sample.addStack(stack)
    sample.addLayer(ba.Layer(substrate_mat))
    return sample


def get_simulation(sample):
    "Specular simulation with a qz-defined beam"
    n = 500

    qzs = np.linspace(0.01, 1, n)  # qz-values
    dq = 0.03*qzs
    distr = ba.DistributionGaussian(0., 1., 25, 2.)

    scan = ba.QzScan(qzs)
    scan.setVectorResolution(distr, dq)

    return ba.SpecularSimulation(scan, sample)


if __name__ == '__main__':
    sample = get_sample()
    ba.showSample3D(sample, sample_size=120*nm, seed=0)
    simulation = get_simulation(sample)
    result = simulation.simulate()
    bp.plot_datafield(result)
    bp.plt.show()
auto/Examples/specular/TOFRWithResolution.py