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Poisson background

To add a Poisson background to a Simulation instance, use

bg = ba.PoissonBackground(seed=0)
simulation.setBackground(bg)

In this case, the output intensity is randomly distributed around the exact value with discrete Poisson statistics. The same seed reproduces the same noise realization.

The lower the intensity of the probing beam, the lower the signal-to-noise ratio.

Constant background

To add a constant background to a Simulation instance, use

bg = ba.ConstantBackground(1e3)
simulation.setBackground(bg)

Custom background

A Python object with a background method can transform the complete simulated field. The method receives the original Datafield and returns a new Datafield with the same frame. For example, a specular scan assembled from two exposure regions can use

class StitchedBackground:
    def __init__(self, boundary, left, right):
        self.boundary = boundary
        self.left = left
        self.right = right

    def background(self, field):
        x = np.asarray(field.xCenters())
        added = np.where(x < self.boundary, self.left, self.right)
        values = field.intensities() + added
        return ba.Datafield(field.title(), field.frame(), values.tolist())


bg = StitchedBackground(boundary=0.5*deg, left=20., right=100.)
simulation.setBackground(bg)

The input field provides the original intensities and all output-bin coordinates. A two-dimensional coordinate-dependent background can use

class CustomBackground:
    def background(self, field):
        x = np.asarray(field.xCenters())
        y = np.asarray(field.yCenters())
        values = field.intensities()
        values = values + 5. + 2.*x[np.newaxis, :] + 3.*y[:, np.newaxis]
        return ba.Datafield(field.title(), field.frame(),
                            values.ravel().tolist())

The callback is invoked after the scattering calculation. Its result must preserve the input frame and masked bins and contain finite, nonnegative intensities in all computed bins. This makes it suitable for interpolation of a measured background map without restricting the number of simulation threads.

Special cases

Specular simulation:

Specular simulation also transforms a zero field to obtain the background baseline used by its normalization. For an additive background (B(x)), a simulated reflected intensity (I(x)), and probe beam intensity (I_0), the result is ((I(x) + B(x)) / (I_0 + B(x))).

Depth probe simulation:

Background is not supported.

Examples

The specular Background example compares constant background with Poisson noise in a reflectometry scan.

Scattering intensity

Coordinate-dependent background

The GISAS script shows the same built-in constant and Poisson backgrounds.

Open the Background example.

The second script compares a simulation without background to one using a Python-defined background for four detector regions.

Open the Custom background example.