katsu.mueller module

katsu.mueller.decompose_depolarizer(M, return_all=False)

Decompose M into a depolarizer using the Polar decomposition

from Lu & Chipman 1996 https://doi.org/10.1364/JOSAA.13.001106

Parameters:

M (numpy.ndarray) – Mueller Matrix to decompose

return_allbool

Whether to return the depolaarizer, retarder and diattenuator vs just the retarder. Defaults to False, which returns just the depolarizer

Returns:

Decomposed mueller matrix

Return type:

numpy.ndarray or arrays

katsu.mueller.decompose_diattenuator(M, normalize=False)

Decompose M into a diattenuator using the Polar decomposition

from Lu & Chipman 1996 https://doi.org/10.1364/JOSAA.13.001106

Parameters:

M (numpy.ndarray) – Mueller Matrix to decompose

Returns:

Diattenuator component of mueller matrix

Return type:

numpy.ndarray

katsu.mueller.decompose_retarder(M, return_all=False, normalize=False)

Decompose M into a retarder using the Polar decomposition

from Lu & Chipman 1996 https://doi.org/10.1364/JOSAA.13.001106

Note: this doesn’t work if the diattenuation can be described by a pure polarizer, because the matrix is singular and therefore non-invertible

Parameters:

  • M (numpy.ndarray) – Mueller Matrix to decompose

  • return_all (bool) – Whether to return the retarder and diattenuator vs just the retarder. Defaults to False, which returns both

Returns:

Retarder component of mueller matrix

Return type:

numpy.ndarray

katsu.mueller.depolarization_index(Md)

compute the depolarization index from a Mueller Matrix

Eq. 6.79 in CLY

Parameters:

Md (numpy.ndarray) – depolarizer to compute the DI of

Returns:

depolarization index

Return type:

numpy.ndarray

katsu.mueller.depolarizer(angle, a, b, c, shape=None)

returns a diagonal depolarizer

Parameters:

  • angle (float, or numpy.ndarray) – angle of the transmission axis w.r.t. horizontal in radians. If numpy array, must be the same shape as shape

  • a (float or numpy.ndarray) – depolarization of Q

  • b (float or numpy.ndarray) – depolarization of U

  • c (float or numpy.ndarray) – depolarization of V

  • shape (list, optional) – shape to prepend to the mueller matrix array, see _empty_mueller. By default None

Returns:

depolarizer Mueller matrix

Return type:

numpy.ndarray

katsu.mueller.diattenuation_from_mueller(M)

compute the total diattenuation from a Mueller matrix

Eq. 6.21 in CLY

Parameters:

M (numpy.ndarray) – array containing Mueller matrices in the last two dimensions

Returns:

diattenuation of the Mueller matrices

Return type:

numpy.ndarray

katsu.mueller.diattenuation_parameters_from_mueller(M)

compute diattenuation decomposed into horizontal, +45, and circular parameters

Parameters:

M (numpy.ndarray) – array containing Mueller matrices in the last two dimensions

Returns:

arrays corresponding to horizontal, +45, and RC diattenuation

Return type:

numpy.ndarray, numpy.ndarray, numpy.ndarray

katsu.mueller.linear_diattenuator(a, Tmin, Tmax=1, shape=None)

returns a homogenous linear diattenuator

See Equation 6.54 in CLY

Parameters:

  • a (float, or numpy.ndarray) – angle of the transmission axis w.r.t. horizontal in radians. If numpy array, must be the same shape as shape

  • Tmin (float, or numpy.ndarray) – Minimum transmission of the state orthogonal to maximum transmission. If numpy array, must be the same shape as shape

  • shape (list, optional) – shape to prepend to the mueller matrix array, see _empty_mueller. By default None

Returns:

linear diattenuator array

Return type:

numpy.ndarray

katsu.mueller.linear_polarizer(a, shape=None)

returns a homogenous linear polarizer

Parameters:

  • a (float, or numpy.darray) – angle of the transmission axis w.r.t. horizontal in radians. If numpy array, must be the same shape as shape

  • shape (list, optional) – shape to prepend to the mueller matrix array, see _empty_mueller. by default None

Returns:

linear polarizer array

Return type:

numpy.ndarray

katsu.mueller.linear_retarder(a, r, shape=None)

returns a homogenous linear retarder

Parameters:

  • a (float, or numpy.ndarray) – angle of the fast axis w.r.t. horizontal in radians. If numpy array, must be 1D

  • r (float, or numpy.ndarray) – retardance in radians. If numpy array, must be the same shape as shape

  • shape (list, optional) – shape to prepend to the mueller matrix array, see _empty_mueller. by default None

Returns:

linear retarder array

Return type:

numpy.ndarray

katsu.mueller.mueller_rotation(angle, shape=None)

returns a Mueller rotation matrix

Parameters:

  • angle (float, or numpy.darray) – angle of the rotation w.r.t. horizontal in radians. If numpy array, must be the same shape as shape

  • shape (list, optional) – shape to prepend to the mueller matrix array, see _empty_mueller. by default None

Returns:

Mueller rotation matrix

Return type:

numpy.ndarray

katsu.mueller.mueller_to_jones(M)

Converts Mueller matrix to a relative Jones matrix. Phase aberration is relative to the Pxx component.

See Eq. 6.112 in CLY

Returns:

J – Jones matrix from Mueller matrix calculation

Return type:

2x2 ndarray

katsu.mueller.retardance_from_mueller(M)

compute the total retardance from a Mueller matrix

Eq. 6.21 in CLY

Parameters:

M (numpy.ndarray) – array containing Mueller matrices in the last two dimensions

Returns:

retardance of the Mueller matrices

Return type:

numpy.ndarray

katsu.mueller.retardance_parameters_from_mueller(M, tol=1e-10)

compute the retardance decomposed into horizontal, +45, and circular parameters

Eq. 6.30 in CLY

TODO: Investigate if this is actually the correct order of parameters, I think that horizontal and right-circular might be flipped in the text. Here lies the version which passes the physical test in test_mueller.py, so I believe the textboook is wrong.

Parameters:

  • M (numpy.ndarray) – array containing Mueller matrices in the last two dimensions

  • tol (float) – tolerance for considering the sin(retardance) to be zero. This is important for nearly half-wave pure retarders. Defaults to 1e-10.

Returns:

arrays corresponding to horizontal, +45, and RC retardance

Return type:

numpy.ndarray, numpy.ndarray, numpy.ndarray

katsu.mueller.stokes_from_parameters(I, Q, U, V, shape=None)

Generates a stokes vector array from the stokes parameters

Parameters:

  • I (float or numpy.ndarray) – Stokes parameter corresponding to intensity, must be float or numpy.ndarray with shape == shape

  • Q (float or numpy.ndarray) – Stokes parameter corresponding to H/V polarization, must be float or numpy.ndarray with shape == shape

  • U (float or numpy.ndarray) – Stokes parameter corresponding to +45/-45 polarization, must be float or numpy.ndarray with shape == shape

  • V (float or numpy.ndarray) – Stokes parameter corresponding to RHC/LHC polarization, must be float or numpy.ndarray with shape == shape

  • shape (list) – shape to prepend to the stokes array. shape = [32,32] returns an array of shape [32,32,4,1] where the vector is assumed to be in the last indices. Defaults to None, which returns a 4x1 array.

Returns:

array of stokes vectors

Return type:

numpy.ndarray

katsu.mueller.wollaston(beam=0, rotation=0.0, shape=None)

Method to construct the Mueller matrix of a Wollaston, Functionally just a hand-hold wrapper for linear_polarizer

Parameters:

  • beam (int, or str) – ‘Channel’ of wollaston prism, by default 0, which returns the Mueller matrix for the horizontally-polarized beam

  • rotation (float, optional) – Rotation of the Wollaston prism with respect to the laboratory’s horizontal axis, by default 0

  • shape (list, optional) – shape to prepend to the mueller matrix array, see _empty_mueller. By default None

Returns:

Mueller matrix of the chosen linear polarizer channel

Return type:

numpy.ndarray