### Polarized specular reflectometry with non-perfect polarizer and analyzer

In this example, we show how to perform a specular reflectometry simulation with polarized neutrons and both a non-perfect polarizer as well as analyzer. The example is inspired by and performed with parameters close to the ones in the paper by Devishvili et al.. This example is a saturated iron film on top of a MgO substrate. On top of the iron layer is a thin Pd cap layer.

We don’t explain the whole script in detail here, it combines all concepts that were introduced before in the polarized reflectometry section. Instrument resolution is simulated as explained in the ToF - Resolution effects example. Furthermore, a constant background is added:

    simulation.setBackground( ba.ConstantBackground( 1e-7 ) )

For a more detailed explanation we refer to the example on adding a constant background.

The values for the efficiency of the polarizer and analyzer are taken from the above mentioned paper by Devishvili et al.:

    polarizer_efficiency = 0.986
    analyzer_efficiency  = 0.970

These values are used to initialize the polarizer and analyzer:

    simulation.setBeamPolarization(polarization * polarizer_efficiency)
    simulation.setAnalyzerProperties(analyzer, analyzer_efficiency, 0.5)

This setup is then utilized to simulate the four reflectivity channels

    results_pp = run_simulation(polarization = R3(0, 1, 0),
                                analyzer     = R3(0, 1, 0),
                                polarizer_efficiency = polarizer_efficiency,
                                analyzer_efficiency  = analyzer_efficiency )
    results_mm = run_simulation(polarization = R3(0, -1, 0),
                                analyzer     = R3(0, -1, 0),
                                polarizer_efficiency = polarizer_efficiency,
                                analyzer_efficiency  = analyzer_efficiency )

    results_pm = run_simulation(polarization = R3(0,  1, 0),
                                analyzer     = R3(0, -1, 0),
                                polarizer_efficiency = polarizer_efficiency,
                                analyzer_efficiency  = analyzer_efficiency )
    results_mp = run_simulation(polarization = R3(0, -1, 0),
                                analyzer     = R3(0,  1, 0),
                                polarizer_efficiency = polarizer_efficiency,
                                analyzer_efficiency  = analyzer_efficiency )

The computed reflectivity looks like this:

Reflectivity

Due to the different values for the polarizer and analyzer efficiency, we obtain different reflectivity curves for the two spin-flip channels. As one can verify, these results are in good agreement with the measurement as well as the simulations presented by Devishvili et al.

Here is the complete example:

auto/Examples/specular/MagneticLayerImperfect.py

- Introduction
  - Functionality overview
  - Architectural overview

- Install or build
  - Install Python
    - Python on Linux
    - Python on Windows
    - Python on Mac
    - Python modules
  - Install BornAgain
    - Linux
    - Windows
    - MacOS
    - Development snapshot
  - Build BornAgain
    - Unix
      - Install third-party software
      - Get the source
      - Build and install BornAgain
      - Run a first simulation
    - Windows

- Graphical user interface
  - Quick Start
  - GUI overview
  - Fitting in the GUI

- Python scripting
  - Run a script
  - Understand the syntax
  - Fitting
  - Upgrading

- Reference
  - Simulation model
    - Simulation classes
      - Specular
        - Example
      - Scattering
        - Examples
          - GISAS
          - without DWBA terms
          - with specular peak
          - SAS
          - Polarized SANS
          - Monte-Carlo
      - Off-specular
        - Off-specular
      - Depth probe
        - Examples
          - Thin film
          - Transmitted modulus
          - Resonator
    - Common settings
      - Background
      - Options
        - Monte-Carlo
        - # threads
        - Average materials
        - Include specular
      - Progress monitor
  - Instrument model
    - Beam
      - Footprint
      - Beam divergence
    - Scan
      - TOF reflectometry
      - TOF resolution
      - Beam Angular Spread
      - Beam Wavelength Spread
    - Detectors
      - SphericalDetector
      - 2d detector resolution
      - Offspec detector
    - Neutron polarization
      - Spin asymmetry example
    - Examples
      - 2D detector resolution
      - Neutron polarization
        - Magnetic layer
        - Ditto, realistic instrument
        - Polarized scattering
  - Sample model
    - Materials
      - Magnetization
    - Sample
      - Layer
      - LayerStack
      - Layout
    - Roughness
      - Interface model
      - Transient
      - Cross-correlation
      - Examples
        - GISAS
        - Reflectivity
    - Particles
      - Form factor
        - Hard particles
          - Bipyramid4
          - Box
          - CantellatedCube
          - Cone
          - Cylinder
          - Dodecahedron
          - EllipsoidalCylinder
          - HemiEllipsoid
          - HorizontalCylinder
          - Icosahedron
          - PlatonicOctahedron
          - PlatonicTetrahedron
          - Prism3
          - Prism6
          - Pyramid2
          - Pyramid3
          - Pyramid4
          - Pyramid6
          - Sphere
          - SphericalSegment
          - Spheroid
          - SpheroidalSegment
          - TruncatedCube
        - Ripples
          - Bar ripple
          - Cosine ripple
          - Sawtooth ripple
        - Soft particles
          - FuzzySphere
          - Gauss
        - Custom formfactor
      - Composite particles
        - Core and shell
        - Compound particle
        - Mesocrystal
      - Examples
        - Compound particle
        - Core and shell
        - Crossing an interface
        - Mesocrystal
        - Rotation example
        - Dense cylinders
        - Dense hemispheres
        - Uncorrelated mixture
        - Polydispersity
    - Particle assemblies
      - Grating
        - 1D lattice
        - Cosine ripples in a lattice
        - Triangular ripples in a lattice
      - 2D lattice
        - Square lattice
        - Lattice orientation distribution
        - Finite square lattice
        - Lattice with basis
        - Multi-layer lattice
        - Position variance
      - Radial paracrystal
      - 2D paracrystal
      - Others
        - Size-distribution model: decoupling approximation
        - Size-distribution model: local monodisperse approximation
        - Size-distribution model: size-spacing coupling approximation
  - Model modifiers
    - Rotation
    - Distributions
  - Data types
    - Class Datafield
      - Export
      - Find intensity peaks
    - SLD profile
      - SLD profile with rough interfaces
      - SLD profile with a sliced particle layer
  - Plotting
    - Functions
    - Configuration
    - Heat map
    - LaTeX markup
    - Export
    - Plot axes in different units
  - Fitting
    - Data import
      - TIFF
    - Minimizer settings
    - Multiple datasets
    - Examples
      - Fitting with masks
      - Custom objective function
      - Fitting along slices
      - GISAS 2D fits
      - Experiment at GALAXI
      - Find background
      - Minimizer settings
      - Bayesian Sampling
      - Consecutive fitting
      - Considering uncertainties
      - External minimizer
      - External minimizer: plotting
      - Simultaneous fit of two datasets
      - Spin asymmetry fit example
      - Reflectometry: Fit Pt layer
      - Reflectometry: Fit honeycomb

- Literature
  - Babonneau2010
  - Babonneau2013
  - Croset2021
  - Lazzari2002
  - Lazzari2006
  - Pospelov2020
  - Renaud2009
  - Sears1992
  - Wuttke2021

- How to
  - Get announcements
  - Solve known problems
    - Set Python environmental variables under Windows
  - Request help or report bugs
  - Cite BornAgain

- Developers' corner
  - Configure
    - Build
    - Pyenv
  - Develop
    - Manual checks
    - Debug
    - Webdoc
    - Code analyses
  - Release
    - Manual GUI test