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 modules:
- jones_vector - Light polarization states in Jones formalism (2x1 vectors).
- jones_matrix - Optical elements polarization properties in Jones formalism (2x2 matrices).
- stokes - Light polarization states in Mueller-Stokes formalism (4x1 vectors).
- mueller - Optical elements polarization properties in Mueller-Stokes formalism (4x4 matrices).
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
- Hoyo, L. M. Sanchez-Brea, A. Soria-Garcia, “Open source library for polarimetric calculations “py_pol””, Proc. SPIE 11875, Computational Optics 2021, 1187506 (14 September 2021); doi: 10.1117/12.2597163, https://spie.org/Publications/Proceedings/Paper/10.1117/12.2597163?SSO=1.
- del Hoyo, L.M. Sanchez Brea, “py-pol, Python module for polarization optics”, https://pypi.org/project/py-pol/ (2019)
References
- Goldstein “Polarized light” 2nd edition, Marcel Dekker (1993).
- Gil, R. Ossikovsky “Polarized light and the Mueller Matrix approach”, CRC Press (2016).
- Brosseau “Fundamentals of Polarized Light” Wiley (1998).
- Martinez-Herrero, P. M. Mejias, G. Piquero “Characterization of partially polarized light fields” Springer series in Optical sciences (2009).
- Bennet “Handbook of Optics 1” Chapter 5 ‘Polarization’.
- Chipman “Handbook of Optics 2” Chapter 2 ‘Polarimetry’.
- 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) and “Teluro-AEI” (RTC2019-007113-3) of Ministerio de EconomÃa 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
1.1.0 (2022-3-31)
- Added base class Py_pol
- Objects are now iterable
- 3D drawings changed to Plotly
- New density and existence methods
1.0.4 (2022-02-07)
- Bug fix related to variable limits
1.0.4 (2021-07-19)
- Bug fixes
1.0.3 (2021-01-22)
- Bug fixes
1.0.2 (2020-07-04)
- Implemented workaround of axis_equal issue.
1.0.0 (2020-06-04)
py_pol multidimensional. Alpha state
This is a big overhaul with many changes. All of them are based on the possibility of storing several vector/matrices in the same object. This reduces significantly the time required to perform the same operation to multiple vectors/matrices, using numpy methods instead of for loops. We have calculated that the reduction is around one order of magnitude.
New methods have been introduced. First, methods available for Mueller / Stoes modules have been created also for Jones (when possible). Also, some bugs and errors in the calculations have been solved.
Finally, some method and argument names have been changed to be consistent between different classes. Also, the default value of arguments with the same name have also been unified.
The biggest TO DO we have are tests. Right now, we only have tests for the Jones_vector class. However, we thought that it would be useful to release this version so the community can use it.
NOTE: Due to the change of argument and method names, this version is not compatible with the previous ones.
0.2.2 (2019-09-04)
- Bug fixes.
0.2.1 (2019-09-04)
- Bug fixes.
- Solve incidents.
- Start to homogenize structures for both Jones and Stokes.
0.2.0 (2019-05-25)
pre-alpha state
- Upgrade to Python 3
- Stable version including tests
0.1.5 (2019-02-25)
- 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.
0.1.4 (2019-02-03)
- bug fixes
0.1.3 (2019-01-22)
- Fixed axis_equal issue.
- 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.
0.1.1 (2018-12-22)
- First release on PyPI in alpha state.
0.0.0 (2018-11-22)
First implementation of py_pol.
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