py-pol 0.1.4

Jones and Mueller polarization - Optics

===================
Python polarization
===================


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* Free software: MIT license
* Documentation: https://py-pol.readthedocs.io/en/latest/


Features
--------
Py-pol is a Python library for Jones and Stokes-Mueller polarization optics. It has 4 main module:

* jones_vector - for generation of polarization states in 2x1 Jones formalism.

* jones_matrix - for generation of 2x2 matrix polarizers.

* stokes - for generation of polarization states in 2x2 Stokes formalism.

* mueller - for generation of 4x4 matrix polarizers.


Each one has its own class, with multiple methods for generation, operation and parameters extraction.

Examples
-----------

Jones formalism
=================

Generating Jones vectors and Matrices

.. code:: python

from py_pol.jones_vector import Jones_vector
from py_pol.jones_matrix import Jones_matrix
from py_pol.utils import degrees

j0 = Jones_vector("j0")
j0.linear_light(angle=45*degrees)

m0 = Jones_matrix("m0")
m0.diattenuator_linear( p1=0.75, p2=0.25, angle=45*degrees)

m1 = Jones_matrix("m1")
m1.quarter_wave(angle=0 * degrees)

j1=m1*m0*j0

Extracting information form Jones Vector.

.. code:: python

print(j0,'\n')
print(j0.parameters)
____

j0 = [+0.707; +0.707]'

parameters of j0:
intensity : 1.000 arb.u
alpha : 45.000º
delay : 0.000º
azimuth : 45.000º
ellipticity angle: 0.000º
a, b : 1.000 0.000

.. code:: python

print(j1,'\n')
print(j1.parameters)
____

m1 * m0 @45.00º * j0 = [+0.530+0.000j; +0.000+0.530j]'

parameters of m1 * m0 @45.00º * j0:
intensity : 0.562 arb.u
alpha : 45.000º
delay : 90.000º
azimuth : 8.618º
ellipticity angle: -45.000º
a, b : 0.530 0.530


Extracting information form Jones Matrices.

.. code:: python

print(m0,'\n')
print(m0.parameters)
____

m0 @45.00º =
[+0.500, +0.250]
[+0.250, +0.500]

parameters of m0 @45.00º:
is_homogeneous: True
delay: 0.000ª
diattenuation: 0.800


.. code:: python

print(m1,'\n')
print(m1.parameters)
____

m1 =
[+1+0j, +0+0j]
[+0+0j, +0+1j]

parameters of m1:
is_homogeneous: True
delay: 90.000ª
diattenuation: 0.000




Stokes-Mueller formalism
=================

Generating Stokes vectors and Mueller matrices.


.. code:: python

from py_pol.stokes import Stokes
from py_pol.mueller import Mueller
from py_pol.utils import degrees

j0 = Stokes("j0")
j0.linear_light(angle=45*degrees)

m1 = Mueller("m1")
m1.diattenuator_linear(p1=1, p2=0, angle=0*degrees)

j1=m1*j0


Extracting information from Stokes vectors.


.. code:: python

i1=j0.parameters.intensity()
print("intensity = {:4.3f} arb. u.".format(i1))
____

intensity = 1.250 arb. u.

.. code:: python

print(j0,'\n')
print(j0.parameters)
____

j0 = [+1.250; +0.530; -0.562; +0.530]

parameters of j0:
intensity : 1.250 arb. u.
degree polarization : 0.750
degree linear pol. : 0.618
degree circular pol.: 0.424
alpha : 27.775º
delay : 43.314º
azimuth : 23.343º
ellipticity angle : 17.225º
ellipticity param : 0.310
eccentricity : 0.951
polarized vector : [+0.938; +0.530; -0.562; +0.530]'
unpolarized vector : [+0.312; +0.000; +0.000; +0.000]'


Extracting information from Mueller matrices.

.. code:: python

print(m1,'\n')
print(m1.parameters)
____

m1 =
[+0.531, +0.469, +0.000, +0.000]
[+0.469, +0.531, +0.000, +0.000]
[+0.000, +0.000, +0.250, +0.000]
[+0.000, +0.000, +0.000, +0.250]

.. code:: python

print(j1)
print(j1.parameters)
____

m1 * j0 = [+0.913; +0.868; -0.141; +0.133]

parameters of m1 * j0:
intensity : 0.913 arb. u.
degree polarization : 0.974
degree linear pol. : 0.963
degree circular pol.: 0.145
alpha : 6.279º
delay : 43.314º
azimuth : 4.603º
ellipticity angle : 4.289º
ellipticity param : 0.075
eccentricity : 0.997
polarized vector : [+0.889; +0.868; -0.141; +0.133]'
unpolarized vector : [+0.024; +0.000; +0.000; +0.000]'

Drawings
===========

The modules also allows to obtain graphical representation of polarization.

Drawing polarization ellipse for Jones vectors.

.. image:: ellipse_Jones_1.png
:width: 600

.. image:: ellipse_Jones_3.png
:width: 600


Drawing polarization ellipse for Stokes vectors with random distribution due to unpolarized part of light.

.. image:: ellipse_Stokes_1.png
:width: 600

.. image:: ellipse_Stokes_2.png
:width: 600

Drawing Stokes vectors in Poincaré sphere.

.. image:: poincare2.png
:width: 600

.. image:: poincare3.png
:width: 600

.. image:: poincare4.png
:width: 600

Authors
----------------

* Luis Miguel Sanchez Brea <[e-mail]>
* Jesus del Hoyo <[e-mail]>

**Universidad Complutense de Madrid**,
Faculty of Physical Sciences,
Department of Optics
Plaza de las ciencias 1,
ES-28040 Madrid (Spain)

Citing
----------------
L.M. Sanchez Brea, J. del Hoyo "py-pol, python module for polarization optics", https://pypi.org/project/py-pol/ (2019)

References
------------

* D Goldstein "Polarized light" 2nd edition, Marcel Dekker (1993).

* JJ Gil, R. Ossikovsky "Polarized light and the Mueller Matrix approach", CRC Press (2016).

* C Brosseau "Fundamentals of Polarized Light" Wiley (1998).

* R Martinez-Herrero, P.M. Mejias, G.Piquero "Characterization of partially polarized light fields" Springer series in Optical sciences (2009).

* JM Bennet "Handbook of Optics 1" Chapter 5 'Polarization'.

* RA Chipman "Handbook of Optics 2" Chapter 2 'Polarimetry'.

* SY Lu and RA Chipman, "Homogeneous and inhomogeneous Jones matrices", J. Opt. Soc. Am. A 11(2) 766 (1994).


Credits
-------

This package was created with Cookiecutter_ and the `audreyr/cookiecutter-pypackage`_ project template.

.. _Cookiecutter: https://github.com/audreyr/cookiecutter
.. _`audreyr/cookiecutter-pypackage`: https://github.com/audreyr/cookiecutter-pypackage


=======
History
=======

0.1.1 (2018-12-22)
------------------

* First release on PyPI in pre-alpha state.


0.1.3 (2019-01-22)
------------------

alpha state

* Jones_vector, Jones_matrix, Stokes works.
* Mueller is in progress.
* Functions = 9/10, Documentation = 8/10 Tutorial = 7/10. Examples = 6/10.
* Drawing = 0/10.


0.1.4 (2019-02-03)
------------------

alpha state

* Jones_vector, Jones_matrix, Stokes works.
* Mueller is in progress.
* Functions = 9/10, Documentation = 8/10 Tutorial = 7/10. Examples = 7/10.
* Drawing = 10/10. Finished. Polarization ellipse for Jones and Stokes (partially random). Stokes on Poincaré sphere.