Fitting with masks

In this example we demonstrate how to mask certain areas on the detector image to exclude their influence on the fitting procedure.  This can be done by invoking the method addMask on a simulation object.

simulation = GISASSimulation()
simulation.addMask(Rectangle(x1, y1, x2, y2), mask_value)

where Rectangle is related to the shape of the mask in detector coordinates, mask_value can be either True (area is excluded from the simulation and fit) or False (area will stay in the simulation and will be taken into account in Chi2 calculations during the fit). There can be an arbitrary number of masks of various shapes added to the simulation one after another. Each subsequent mask overrides the previously defined mask_value in the given area.

  • In the given example we simulate cylinders on top of substrate without interference. The fitting procedure looks for the cylinder's height and radius.
  • Line 130 contains a call to add_mask_to_simulation function which applies masks to the detector in such a way, that simulated image looks like a Pac-Man from the ancient arcade game.
  • In this function we start from masking the whole detector (Line 88) and then we unmask the area of an elliptic shape (Line 91) to simulate Pacman's head. Then we keep adding masks of different shapes to get the final picture.
Intensity Image: 
Python Script: 
Fitting example: fit with masks

from __future__ import print_function
from matplotlib import pyplot as plt
import math
import random
import bornagain as ba
from bornagain import deg, angstrom, nm

def get_sample(radius=5*nm, height=10*nm):
    Build the sample representing cylinders on top of
    substrate without interference.
    m_air = ba.HomogeneousMaterial("Air", 0.0, 0.0)
    m_substrate = ba.HomogeneousMaterial("Substrate", 6e-6, 2e-8)
    m_particle = ba.HomogeneousMaterial("Particle", 6e-4, 2e-8)

    cylinder_ff = ba.FormFactorCylinder(radius, height)
    cylinder = ba.Particle(m_particle, cylinder_ff)

    particle_layout = ba.ParticleLayout()

    air_layer = ba.Layer(m_air)

    substrate_layer = ba.Layer(m_substrate, 0)
    multi_layer = ba.MultiLayer()
    return multi_layer

def get_simulation():
    Create and return GISAXS simulation with beam and detector defined
    simulation = ba.GISASSimulation()
    simulation.setDetectorParameters(100, -1.0*deg, 1.0*deg,
                                     100, 0.0*deg, 2.0*deg)
    simulation.setBeamParameters(1.0*angstrom, 0.2*deg, 0.0*deg)
    return simulation

def create_real_data():
    Generating "real" data by adding noise to the simulated data.
    sample = get_sample(5.0*nm, 10.0*nm)

    simulation = get_simulation()

    real_data = simulation.getIntensityData()

    # spoiling simulated data with the noise to produce "real" data
    noise_factor = 0.5
    for i in range(0, real_data.getTotalNumberOfBins()):
        amplitude = real_data.getBinContent(i)
        sigma = noise_factor*math.sqrt(amplitude)
        noisy_amplitude = random.gauss(amplitude, sigma)
        if noisy_amplitude