## 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 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72  #!/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 angstrom def get_sample(): """ Defines sample and returns it. Note that SLD-based materials are used. """ # creating materials m_ambient = ba.MaterialBySLD("Ambient", 0, 0) m_ti = ba.MaterialBySLD("Ti", -1.9493e-06, 0) m_ni = ba.MaterialBySLD("Ni", 9.4245e-06, 0) m_substrate = ba.MaterialBySLD("SiSubstrate", 2.0704e-06, 0) # creating layers ambient_layer = ba.Layer(m_ambient) ti_layer = ba.Layer(m_ti, 30*angstrom) ni_layer = ba.Layer(m_ni, 70*angstrom) substrate_layer = ba.Layer(m_substrate) # creating multilayer multi_layer = ba.MultiLayer() multi_layer.addLayer(ambient_layer) for i in range(10): multi_layer.addLayer(ti_layer) multi_layer.addLayer(ni_layer) multi_layer.addLayer(substrate_layer) return multi_layer def get_simulation(sample, scan_size=500): """ Defines and returns specular simulation with a qz-defined beam """ qzs = np.linspace(0.01, 1, 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) simulation.setSample(sample) return simulation if __name__ == '__main__': import ba_plot sample = get_sample() simulation = get_simulation(sample) ba_plot.run_and_plot(simulation) 
TOFRWithResolution.py