`Beam`

class nexus.Beam(polarization=1, mixing_angle=0, canting_angle=0, profile='g', fwhm=0, id='')

Constructor for the Beam class. Default values set a linear polarization along \(\sigma\). See Eq. (9), [Sturhahn2000], however, the canting angle given in Nexus is multiplied by 2 to give a polarization of \(\pi\) at 90 degree.

Parameters:

polarization (float) – Degree of polarization, 0 to 1.
mixing_angle (float) –
Mixing angle (deg)
- 0 degree linear polarization.
- +90 degree circular left polarization.
- -90 degree circular right polarization.
canting_angle (float) – Canting angle of the beam with respect to sigma direction (deg).
profile (string) –
Profile of the beam for grazing incidence scattering. The beam profile is only considered in the methods Reflectivity, Transmission, NuclearReflectivity and NuclearReflectivityEnergy.
- g - Gaussian profile.
- r - Rectangular profile.
- n - No beam profile correction.
Changed in version 1.0.2: Rectangular beam profile correction wrong prior to version 1.0.2
fwhm (float or Var) – Full width half maximum of the beam in the scattering plane of grazing scattering geometry (mm). Only needed for grazing incidence geometry.
id (string) – User identifier.

matrix

2x2 complex Jones matrix of the beam.

Type:: ndarray

jones_vector

Jones vector for a fully coherent beam, 2-element vector. Can only be set via :attr:` or special methods with fully polarized beam properties.

Type:: ndarray

profile

Profile of the beam for grazing incidence scattering. The beam profile is only considered in the methods Reflectivity, Transmission, NuclearReflectivity and NuclearReflectivityEnergy.

g - Gaussian profile.
r - Rectangular profile.
n - No beam profile correction.

Changed in version 1.0.2: Rectangular beam profile correction wrong prior to version 1.0.2

Type:: string

fwhm

Full width half maximum (FWHM) of the beam in the scattering plane of grazing scattering geometry (mm). Only needed for grazing incidence geometry.

Type:: Var

id

User identifier.

Type:: string

CircularLeft(): Set the beam to circular left polarized light.

CircularRight(): Set the beam to circular right polarized light.

Coherence()

Calculates the coherence of the beam [Born]

\[|\mu| = | \frac{J_{\sigma \pi}}{\sqrt(J_{\sigma \sigma}) \sqrt(J_{\pi \pi})} |\]

It is a measure of the correlation between the \(E\)-vector components.

If nan is returned one \(E\)-vector component is zero.

Returns:: Degree of coherence between \(E_{\sigma}\) and \(E_{\pi}\).
Return type:: float

ComplexCoherence()

Calculates the complex coherence of the beam [Born]

\[\mu = \frac{J_{\sigma \pi}}{\sqrt(J_{\sigma \sigma}) \sqrt(J_{\pi \pi})}\]

It is a measure of the correlation between the \(E\)-vector components.

If nan is returned one \(E\)-vector component is zero.

Returns:: Complex coherence between \(E_{\sigma}\) and \(E_{\pi}\).
Return type:: complex

LinearPi(): Set the beam to \(\pi\) polarized light.

LinearSigma(): Set the beam to \(\sigma\) polarized light.

PhaseDifference()

Calculates the phase difference between \(E_{\sigma}\) and \(E_{\pi}\) [Born]

If nan is returned one \(E\)-vector component is zero.

Returns:: Phase difference between \(E_{\sigma}\) and \(E_{\pi}\).
Return type:: float

Polarization()

Calculates the degree of polarization [Born]

\[P = \frac{I_{pol}}{I_{tot}} = \sqrt{1 - \frac{4|\mathbf{J}|}{(J_{\sigma \sigma} + J_{\pi \pi})^2}}\]

Returns:: Degree of polarization. 0 to 1.
Return type:: float

Rotate(angle)

Rotate the beam by the given angle. Jones vector and matrix are rotated.

Parameters:: angle (float) – angle of rotation (degree).

SetCoherencyMatrix(matrix)

Set the coherency matrix. The Jones vector is invalid in this case. To set a fully coherent beam use SetJonesVector or a specific method.

Parameters:: matrix (ndarray) – 2x2 complex coherency matrix.

SetJonesVector(jones_vector, angle=0)

Sets the Jones vector and the coherency matrix.

Parameters:

jones_vector (ndarray) – Two element Jones vector.
angle (float) – Rotation angle of Jones vector with respect to \(\sigma\) (deg).

Unpolarized(): Set the beam to unpolarized radiation.

ValidJonesVector()

Checks a valid Jones vector is set.

Returns:: True or False.
Return type:: bool

Different ways to define a Beam.

# initialize beam, standard is fully sigma polarized
beam = nx.Beam()

# set beam to pi polarization
beam.LinearPi()

print(beam.matrix)

# set beam to unpolarized
beam.Unpolarized()

print(beam)

# set beam to sigma polarization via initialization parameters
# Rectangular beam profile, beam with 1 mm height
beam = nx.Beam(polarization = 1, mixing_angle = 0, profile = "r", fwhm = 1)

# set beam along pi polarization via initialization parameters
beam = nx.Beam(polarization = 1, mixing_angle = 0, canting_angle = 90)

beam = nx.Beam()
# set coherency matrix for unpolarized detection
beam.SetCoherencyMatrix(np.array([[1,0], [0, 1]], dtype=complex))

beam = nx.Beam()
# set Jones vector for fully sigma polarized beam
beam.SetJonesVector(np.array([1,0], dtype=complex))

print(beam.jones_vector)
print(beam.matrix)

# circularly right polarized beam
beam = nx.Beam(polarization = 1, mixing_angle = -90)

print(beam.Polarization())
print(beam.Coherence())

beam = nx.Beam()
# linear polarization at 45 deg rotation
beam.SetJonesVector(np.array([1, 0], dtype=complex), 45)

Beam

`Beam`