Resolution effects in TOF Reflectometry

In real experiments, the $q_z$ resolution is non infinite. To take this into account in TOF simulations, one needs to define the spread in $q$ as $dq$, set up a distribution with a given number of samples, n_samples, and define the desired sigma factor, n_sig (e.g. the range in standard deviations to take into account during the sample generation).

    qzs = np.linspace(0.01, 1.0, scan_size)  # qz-values
    dq = 0.03 * qzs
    n_sig = 2.0
    n_samples = 25

    distr = ba.RangedDistributionGaussian(n_samples, n_sig)

    scan = ba.QSpecScan(qzs)
    scan.setAbsoluteQResolution(distr, dq)

    simulation = ba.SpecularSimulation()
    simulation.setScan(scan)

In the snippet above, a Gaussian distribution has been used, but there are several distributions available to chose from:

  • Gate: RangedDistributionGate(n_samples, sigma_factor, min, max)
  • Lorentz: RangedDistributionLorentz(n_samples, hwhm_factor, min, max)
  • Gaussian: RangedDistributionGaussian(n_samples, sigma_factor, min, max)
  • LogNormal: RangedDistributionLogNormal(n_samples, sigma_factor, min, max)
  • Cosine: RangedDistributionCosine(n_samples, sigma_factor, min, max)

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
#!/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, std_samples


def get_sample():
    return std_samples.alternating_layers()


def get_simulation(sample):
    """
    Defines and returns specular simulation
    with a qz-defined beam
    """
    n = bp.simargs['n']

    qzs = np.linspace(0.01, 1, n)  # qz-values
    dq = 0.03*qzs
    n_sig = 2.0
    n_samples = 25

    distr = ba.RangedDistributionGaussian(n_samples, n_sig)

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

    return ba.SpecularSimulation(scan, sample)


if __name__ == '__main__':
    bp.parse_args(sim_n=500)
    sample = get_sample()
    simulation = get_simulation(sample)
    result = simulation.simulate()
    bp.plot_simulation_result(result)
Examples/specular/TOFRWithResolution.py