Polarization

Processing and polarization analysis

vampires_dpp.pdi.processing.polarization_calibration_triplediff(filenames, derotate=True)

Return a Stokes cube using the bona fide triple differential method. This method will split the input data into sets of 16 frames- 2 for each camera, 2 for each FLC state, and 4 for each HWP angle.

Pupil-tracking mode

For each of these 16 image sets, it is important to consider the apparant sky rotation when in pupil-tracking mode (which is the default for most VAMPIRES observations). With this naive triple-differential subtraction, if there is significant sky motion, the output Stokes frame will be smeared.

The parallactic angles for each set of 16 frames should be averaged (average_angle) and stored to construct the final derotation angle vector

Parameters:

• filenames (Sequence[str]) – list of input filenames to construct Stokes frames from

• derotate (bool)

Raises:

ValueError: – If the input filenames are not a clean multiple of 16. To ensure you have proper 16 frame sets, use pol_inds with a sorted observation table.

Returns:

(4, t, y, x) Stokes cube from all 16 frame sets.

Return type:

NDArray

vampires_dpp.pdi.utils.measure_instpol(I, X, r=5, expected=0)

Use aperture photometry to estimate the instrument polarization.

Parameters:

• stokes_cube (NDArray) – Input Stokes cube (4, y, x)

• r (float, optional) – Radius of circular aperture in pixels, by default 5

• expected (float, optional) – The expected fractional polarization, by default 0

• **kwargs

• I (ndarray[tuple[int, ...], dtype[_ScalarType_co]])

• X (ndarray[tuple[int, ...], dtype[_ScalarType_co]])

Returns:

The instrumental polarization coefficient

Return type:

float

vampires_dpp.pdi.utils.radial_stokes(stokes_cube, stokes_err=None, phi=0)

Calculate the radial Stokes parameters from the given Stokes cube (4, N, M)

\[\begin{split}Q_\phi = -Q\cos(2\theta) - U\sin(2\theta) \\ U_\phi = Q\sin(2\theta) - U\cos(2\theta)\end{split}\]

Parameters:

• stokes_cube (ArrayLike) – Input Stokes cube, with dimensions (4, N, M)

• phi (float) – Radial angle offset in radians, by default 0

• stokes_err (_Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None)

Returns:

Returns the tuple (Qphi, Uphi, Qphi_err, Uphi_err)

Return type:

NDArray, NDArray

Mueller calculus

vampires_dpp.pdi.mueller_matrices.generic(theta=0, epsilon=0, delta=0)

Return a generic optic with diattenuation epsilon and phase retardance delta oriented at angle theta.

Parameters:

• theta (float, optional) – Rotation angle of the fast-axis in radians, by default 0

• epsilon (float, optional) – Diattenuation, by default 0

• delta (float, optional) – Retardance in radians, by default 0

Returns:

(4, 4) Mueller matrix for the optic

Return type:

NDArray

Examples

>>> generic() # Identity
array([[ 1.,  0.,  0.,  0.],
       [ 0.,  1.,  0., -0.],
       [ 0.,  0.,  1.,  0.],
       [ 0.,  0., -0.,  1.]])

>>> generic(epsilon=0.01, delta=np.pi) # mirror with diatt.
array([[ 1.     ,  0.01   ,  0.     ,  0.     ],
       [ 0.01   ,  1.     ,  0.     , -0.     ],
       [ 0.     ,  0.     , -0.99995,  0.     ],
       [ 0.     ,  0.     , -0.     , -0.99995]])

vampires_dpp.pdi.mueller_matrices.hwp(theta=0)

Return the Mueller matrix for an ideal half-wave plate (HWP) with fast-axis oriented to the given angle, in radians.

Parameters:

theta (float, optional) – Rotation angle of the fast-axis, in radians. By default 0

Returns:

(4, 4) Mueller matrix representing the HWP

Return type:

NDArray

Examples

>>> hwp(0)
array([[ 1.,  0.,  0.,  0.],
       [ 0.,  1.,  0.,  0.],
       [ 0.,  0., -1.,  0.],
       [ 0.,  0.,  0., -1.]])

>>> hwp(np.deg2rad(45))
array([[ 1.,  0.,  0.,  0.],
       [ 0., -1.,  0.,  0.],
       [ 0.,  0.,  1.,  0.],
       [ 0.,  0.,  0., -1.]])

vampires_dpp.pdi.mueller_matrices.linear_polarizer(theta=0)

Return the Mueller matrix for an ideal linear polarizer oriented at the given angle.

Parameters:

theta (float, optional) – Angle of rotation, in radians. By default 0

Returns:

(4, 4) Mueller matrix for the linear polarizer

Return type:

NDArray

Examples

>>> linear_polarizer(0)
array([[0.5, 0.5, 0. , 0. ],
       [0.5, 0.5, 0. , 0. ],
       [0. , 0. , 0. , 0. ],
       [0. , 0. , 0. , 0. ]])

>>> linear_polarizer(np.deg2rad(45))
array([[0.5, 0. , 0.5, 0. ],
       [0. , 0. , 0. , 0. ],
       [0.5, 0. , 0.5, 0. ],
       [0. , 0. , 0. , 0. ]])

vampires_dpp.pdi.mueller_matrices.qwp(theta=0)

Return the Mueller matrix for an ideal quarter-wave plate (QWP) with fast-axis oriented to the given angle, in radians.

Parameters:

theta (float, optional) – Rotation angle of the fast-axis in radians. By default 0

Returns:

(4, 4) Mueller matrix representing the QWP

Return type:

NDArray

Examples

>>> qwp(0)
array([[ 1.,  0.,  0.,  0.],
       [ 0.,  1.,  0., -0.],
       [ 0.,  0.,  0.,  1.],
       [ 0.,  0., -1.,  0.]])

>>> qwp(np.deg2rad(45))
array([[ 1.,  0.,  0.,  0.],
       [ 0.,  0.,  0., -1.],
       [ 0.,  0.,  1.,  0.],
       [ 0.,  1., -0.,  0.]])

vampires_dpp.pdi.mueller_matrices.rotator(theta=0)

Return the Mueller matrix for rotation clockwise about the optical axis.

Parameters:

theta (float, optional) – Angle of rotation, in radians. By default 0

Returns:

(4, 4) Mueller matrix

Return type:

NDArray

Examples

>>> rotator(0)
array([[ 1.,  0.,  0.,  0.],
       [ 0.,  1.,  0.,  0.],
       [ 0., -0.,  1.,  0.],
       [ 0.,  0.,  0.,  1.]])

>>> rotator(np.deg2rad(45))
array([[ 1.,  0.,  0.,  0.],
       [ 0.,  0.,  1.,  0.],
       [ 0., -1.,  0.,  0.],
       [ 0.,  0.,  0.,  1.]])

vampires_dpp.pdi.mueller_matrices.waveplate(theta=0, delta=0)

Return the Mueller matrix for a waveplate with arbitrary phase retardance.

Parameters:

• theta (float, optional) – Rotation angle of the fast-axis in radians. By default 0

• delta (float, optional) – Retardance in radians, by default 0

Returns:

(4, 4) Mueller matrix representing the waveplate

Return type:

NDArray

Examples

>>> waveplate(0, np.pi) # HWP
array([[ 1.,  0.,  0.,  0.],
       [ 0.,  1.,  0., -0.],
       [ 0.,  0., -1.,  0.],
       [ 0.,  0., -0., -1.]])

>>> waveplate(np.deg2rad(45), np.pi/2) # QWP at 45°
array([[ 1.,  0.,  0.,  0.],
       [ 0.,  0.,  0., -1.],
       [ 0.,  0.,  1.,  0.],
       [ 0.,  1., -0.,  0.]])

vampires_dpp.pdi.mueller_matrices.wollaston(ordinary=True, eta=1)

Return the Mueller matrix for a Wollaston prism or polarizing beamsplitter.

Parameters:

• ordinary (bool, optional) – Return the ordinary beam’s Mueller matrix, by default True

• eta (float, optional) – For imperfect beamsplitters, the diattenuation of the optic, by default 1

Returns:

(4, 4) Mueller matrix for the selected output beam

Return type:

NDArray

Examples

>>> wollaston()
array([[0.5, 0.5, 0. , 0. ],
       [0.5, 0.5, 0. , 0. ],
       [0. , 0. , 0. , 0. ],
       [0. , 0. , 0. , 0. ]])

>>> wollaston(False, eta=0.8)
array([[ 0.5, -0.4,  0. ,  0. ],
       [-0.4,  0.5,  0. ,  0. ],
       [ 0. ,  0. ,  0.3,  0. ],
       [ 0. ,  0. ,  0. ,  0.3]])