## Find background

This example demonstrates how to introduce a background in the simulation and fit its value. Here we are simulating cylinders on top of a substrate without interference. The function get_simulation requires 4 parameters:

• the height of the cylinders
• the radius of the cylinders
• the value of the constant background
• a scale factor for the beam’s intensity

The radius and height of the cylinders are passed to the function constructing the multi layer while the scale and background values are used to initialize the instrument.

  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  #!/usr/bin/env python3 """ Fitting example: looking for background. Real data contains some "unknown" background. In the fit we are trying to find cylinder radius and height and background. """ from matplotlib import pyplot as plt import bornagain as ba from bornagain import nm, ba_fitmonitor import model1_cylinders as model def get_simulation(P): """ Create and return GISAXS simulation with beam and detector defined """ background = P["background"] simulation = model.get_simulation(P) simulation.setBackground(ba.ConstantBackground(background)) return simulation def fake_data(): """ Generating "real" data by adding noise, background and scale to the simulated data. Cylinder radius is set to 5nm, cylinder height to 10nm. During the fit we will try to find cylinder height and radius and scale, background factors. """ P = { 'radius': 5*nm, 'height': 10*nm, 'background': 1000 } simulation = get_simulation(P) result = simulation.simulate() return result if __name__ == '__main__': data = fake_data() fit_objective = ba.FitObjective() fit_objective.addFitPair(get_simulation, data, 1) fit_objective.initPrint(10) observer = ba_fitmonitor.PlotterGISAS() fit_objective.initPlot(10, observer) P = ba.Parameters() P.add("radius", 5.*nm, vary=False) P.add("height", 9.*nm, min=8.*nm, max=12.*nm) P.add("background", 200, min=100, max=2000, step=100) minimizer = ba.Minimizer() minimizer.setMinimizer("Minuit2", "Migrad", "MaxFunctionCalls=0") result = minimizer.minimize(fit_objective.evaluate, P) fit_objective.finalize(result) plt.show() 
auto/Examples/fit/scatter2d/find_background.py