Jones and Mueller polarization - Optics
Project description
Python polarization
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
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_waveplate(angle=0 * degrees)
j1=m1*m0*j0
Extracting information form Jones Vector.
print(j0,'\n')
print(j0.parameters)
j0 = [+0.707; +0.707]'
parameters of j0:
intensity : 1.000 arb.u
alpha : 45.000 deg
delay : 0.000 deg
azimuth : 45.000 deg
ellipticity angle: 0.000 deg
a, b : 1.000 0.000
phase : 0.000 deg
print(j1,'\n')
print(j1.parameters)
m1 * m0 @45.00 deg * j0 = [+0.530+0.000j; +0.000+0.530j]'
parameters of m1 * m0 @45.00 deg * j0:
intensity : 0.562 arb.u
alpha : 45.000 deg
delay : 90.000 deg
azimuth : 8.618 deg
ellipticity angle: -45.000 deg
a, b : 0.530 0.530
phase : 0.000 deg
Extracting information form Jones Matrices.
print(m0,'\n')
print(m0.parameters)
m0 @45.00 deg =
[+0.500, +0.250]
[+0.250, +0.500]
parameters of m0 @45.00 deg:
is_homogeneous: True
delay: 0.000 deg
diattenuation: 0.800
print(m1,'\n')
print(m1.parameters)
m1 =
[+1+0j, +0+0j]
[+0+0j, +0+1j]
parameters of m1:
is_homogeneous: True
delay: 90.000 deg
diattenuation: 0.000
Stokes-Mueller formalism
Generating Stokes vectors and Mueller matrices.
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.
Determining the intensity of a Stokes vector:
i1=j0.parameters.intensity()
print("intensity = {:4.3f} arb. u.".format(i1))
intensity = 1.000 arb. u.
Determining all the parameters of a Stokes vector:
print(j0,'\n')
print(j0.parameters)
j0 = [ +1; +0; +1; +0]
parameters of j0:
intensity : 1.000 arb. u.
amplitudes : E0x 0.707, E0y 0.707, E0_unpol 0.000
degree polarization : 1.000
degree linear pol. : 1.000
degree circular pol.: 0.000
alpha : 45.000 deg
delay : 0.000 deg
azimuth : 45.000 deg
ellipticity angle : 0.000 deg
ellipticity param : 0.000
eccentricity : 1.000
polarized vector : [+1.000; +0.000; +1.000; +0.000]'
unpolarized vector : [+0.000; +0.000; +0.000; +0.000]'
print(j1,'\n')
print(j1.parameters)
m1 * j0 = [+0.500; +0.500; +0.000; +0.000]
parameters of m1 * j0:
intensity : 0.500 arb. u.
amplitudes : E0x 0.707, E0y 0.000, E0_unpol 0.000
degree polarization : 1.000
degree linear pol. : 1.000
degree circular pol.: 0.000
alpha : 0.000 deg
delay : 0.000 deg
azimuth : 0.000 deg
ellipticity angle : 0.000 deg
ellipticity param : 0.000
eccentricity : 1.000
polarized vector : [+0.500; +0.500; +0.000; +0.000]'
unpolarized vector : [+0.000; +0.000; +0.000; +0.000]'
Extracting information from Mueller matrices.
m2 = Mueller("m2")
m2.diattenuator_retarder_linear(D=90*degrees, p1=1, p2=0.5, angle=0)
delay = m2.parameters.retardance()
print("delay = {:2.1f}º".format(delay/degrees))
delay = 90.0º
There is a function in Parameters_Jones_Vector class, .get_all() that will compute all the parameters available and stores in a dictionary .dict_params(). Info about dict parameters can be revised using the print function.
print(m2,'\n')
m2.parameters.get_all()
print(m2.parameters)
m2 =
[+0.6250, +0.3750, +0.0000, +0.0000]
[+0.3750, +0.6250, +0.0000, +0.0000]
[+0.0000, +0.0000, +0.0000, +0.5000]
[+0.0000, +0.0000, -0.5000, +0.0000]
Parameters of m2:
Transmissions:
- Mean : 62.5 %.
- Maximum : 100.0 %.
- Minimum : 25.0 %.
Diattenuation:
- Total : 0.600.
- Linear : 0.600.
- Circular : 0.000.
Polarizance:
- Total : 0.600.
- Linear : 0.600.
- Circular : 0.000.
Spheric purity : 0.872.
Retardance : 1.571.
Polarimetric purity : 1.000.
Depolarization degree : 0.000.
Depolarization factors:
- Euclidean distance : 1.732.
- Depolarization factor : 0.000.
Polarimetric purity indices:
- P1 : 1.000.
- P2 : 1.000.
- P3 : 1.000.
There are many types of Mueller matrices. The Check_Mueller calss implements all the checks that can be performed in order to clasify a Mueller matrix. They are stored in the checks field of Mueller class.
m1 = Mueller("m1")
m1.diattenuator_linear(p1=1, p2=0.2, angle=0*degrees)
print(m1,'\n')
c1 = m1.checks.is_physical()
c2 = m1.checks.is_homogeneous()
c3 = m1.checks.is_retarder()
print('The linear diattenuator is physical: {}; hogeneous: {}; and a retarder: {}.'.format(c1, c2, c3))
m1 =
[+0.520, +0.480, +0.000, +0.000]
[+0.480, +0.520, +0.000, +0.000]
[+0.000, +0.000, +0.200, +0.000]
[+0.000, +0.000, +0.000, +0.200]
The linear diattenuator is physical: True; hogeneous: True; and a retarder: False.
Drawings
The modules also allows to obtain graphical representation of polarization.
Drawing polarization ellipse for Jones vectors.
Drawing polarization ellipse for Stokes vectors with random distribution due to unpolarized part of light.
Drawing Stokes vectors in Poincare sphere.
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).
Acknowlegments
This software was initially developed for the project Retos-Colaboración 2016 “Ecograb” RTC-2016-5277-5: Ministerio de Economía y Competitivdad (Spain) and the European funds for regional development (EU), led by Luis Miguel Sanchez-Brea
Credits
This package was created with Cookiecutter and the audreyr/cookiecutter-pypackage project template.
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 = 8/10.
Examples = 8/10.
Tests = 8/10
Drawing = 10/10. Finished. Polarization ellipse for Jones and Stokes (partially random). Stokes on Poincaré sphere.
0.1.5 (2019-02-25)
alpha state
Jones_vector, Jones_matrix, Stokes works.
Jones_vector: simplify function to represent better Jones vectors.
tests drawing: Made tests for drawing
Mueller is in progress.
Functions = 9/10
Documentation = 8/10
Tutorial = 8/10.
Examples = 8/10.
Tests = 8/10
Drawing = 10/10. Finished. Polarization ellipse for Jones and Stokes (partially random). Stokes on Poincaré sphere.
0.2.0 (2019-05-25)
beta state
Upgrade to Python 3
Stable version including tests
0.2.1 (2019-09-04)
beta state
Bug fixes.
Solve incidents.
Start to homogenize structures for both Jones and Stokes.
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