We present a simple experiment developed for the advanced physics instructional laboratory to calculate the Mueller matrix of a microscopic sample. The Mueller matrix is obtained from intensity-based images of the sample acquired by a polarization-sensitive microscope. The experiment requires a bright-field microscope and standard polarizing optical components such as linear polarizers and waveplates. We provide a practical procedure for implementing the apparatus, measuring the complete Mueller matrix of linear polarizers used as samples, and discuss the possibility of analyzing biological samples using our apparatus and method. Due to the simplicity of the apparatus and method, this experiment allows students to increase their knowledge about light polarization and initiate their training in optical instrumentation.
REFERENCES
1.
2.
M.
Bass
, Handbook of Optics Vol 2: Devices, Measurements, and Properties
, 2nd ed. (
McGraw-Hill
,
New York
, 1994
).3.
P. S.
Theocaris
and
E. E.
Gdoutos
, Matrix Theory of Photoelasticity
, 1st ed. (
Springer-Verlag
,
Berlin, Heidelberg
, 1979
).4.
A.
Lanin
and
I.
Fedik
, Thermal Stress Resistance of Materials
(
Springer
,
Berlin, Heidelberg
, 2008
).5.
M. W.
Davidson
and
M.
Abramowitz
, “
Optical microscopy
,” Encycl. Imaging Sci. Technol.
2
, 1
–41
(2002
).6.
J. M.
Rodríguez
, “
Polarización de la luz: Conceptos básicos y aplicaciones en astrofísica
,” Rev. Bras. Ensino Fís.
40
(4
), 5
–6
(2018
).7.
M. J.
Lopera
and
C.
Trujillo
, “
Linear diattenuation imaging of biological samples with digital lensless holographic microscopy
,” Appl. Opt.
61
(5
), B77
–B82
(2022
).8.
T.
Colomb
,
F.
Durr
,
E.
Cuche
,
P.
Marquet
,
H. G.
Limberger
,
R. P.
Salath
, and
C.
Depeursinge
, “
Polarization microscopy by use of digital holography: Application to optical-fiber birefringence measurements
,” Appl. Opt.
44
(21
), 4461
–4469
(2005
).9.
B.
Bai
,
H.
Wang
,
T.
Liu
,
Y.
Rivenson
,
J.
FitzGerald
, and
A.
Ozcan
, “
Pathological crystal imaging with single-shot computational polarized light microscopy
,” J. Biophotonics
13
(1
), e201960036
(2020
).10.
D. F.
McAllister
, “
Stereo and 3-D display technologies
,” Encycl. Imaging Sci. Technol.
2
, 1
–293
(2002
).11.
M.
Bass
, Handbook of Optics: Volume I-Geometrical and Physical Optics, Polarized Light, Components and Instruments
, 3rd ed. (
McGraw-Hill Professional
,
New York
, 2010
).12.
J.
Wang
,
L.
Dong
,
H.
Chen
, and
S.
Huang
, “
Birefringence measurement of biological tissue based on polarization-sensitive digital holographic microscopy
,” Appl. Phys. B
124
(12
), 1
–9
(2018
).13.
Y.
Wang
,
H.
He
,
J.
Chang
,
N.
Zeng
,
S.
Liu
,
M.
Li
, and
H.
Ma
, “
Differentiating characteristic microstructural features of cancerous tissues using Mueller matrix microscope
,” Micron
79
, 8
–15
(2015
).14.
J. F.
de Boer
,
T. E.
Milner
,
M. J. C.
van Gemert
, and
J. S.
Nelson
, “
Two-dimensional birefringence imaging in biological tissue using phase and polarization sensitive optical coherence tomography
,” Opt. Lett.
22
(12
), 934
–936
(1997
).15.
F.
Palacios
,
O.
Font
,
G.
Palacios
,
J.
Ricardo
,
M.
Escobedo
,
L.
Ferreira Gomes
,
I.
Vasconcelos
,
M.
Muramatsu
,
D.
Soga
,
A.
Prado
, and
V.
Jos
, “
Phase and polarization contrast methods by use digital holographic microscopy: Applications by different types of biological samples
,” in Holography-Basic Principles and Contemporary Applications
(
Intech Open
,
Rijeka
, 2013
).16.
C. W.
Pirnstill
and
G. L.
Cot
, “
Malaria diagnosis using a mobile phone polarized microscope
,” Sci. Rep.
5
(1
), 1
–13
(2015
).17.
S. C.
Gladden
, “
An experiment on Malus' law for the elementary laboratory
,” Am. J. Phys.
18
(6
), 395
–395
(1950
).18.
P. J.
Ouseph
,
K.
Driver
, and
J.
Conklin
, “
Polarization of light by reflection and the Brewster angle
,” Am. J. Phys.
69
(11
), 1166
–1168
(2001
).19.
B.
Schaefer
,
E.
Collett
,
R.
Smyth
,
D.
Barrett
, and
B.
Fraher
, “
Measuring the Stokes polarization parameters
,” Am. J. Phys.
75
(2
), 163
–168
(2007
).20.
J.
Park
,
H.
Yu
,
J.-H.
Park
, and
Y.
Park
, “
LCD panel characterization by measuring full Jones matrix of individual pixels using polarization-sensitive digital holographic microscopy
,” Opt. Express
22
(20
), 24304
–24311
(2014
).21.
M.
Bass
, Handbook of Optics, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments
(
McGraw-Hill
,
New York
, 1996
).22.
S.
Aknoun
,
P.
Bon
,
J.
Savatier
,
B.
Wattellier
, and
S.
Monneret
, “
Quantitative retardance imaging of biological samples using quadriwave lateral shearing interferometry
,” Opt. Express
23
, 16383
–16406
(2015
).23.
J. F.
de Boer
,
C. K.
Hitzenberger
, and
Y.
Yasuno
, “
Polarization sensitive optical coherence tomography: A review
,” Biomed. Opt. Express
8
(3
), 1838
–1873
(2017
).24.
X.
Li
and
G.
Yao
, “
Mueller matrix decomposition of diffuse reflectance imaging in skeletal muscle
,” Appl. Opt.
48
(14
), 2625
–2631
(2009
).25.
K.
Dev
and
A.
Asundi
, “
Mueller-Stokes polarimetric characterization of transmissive liquid crystal spatial light modulator
,” Opt. Lasers Eng.
50
(4
), 599
–607
(2012
).26.
L. V.
Wang
and
H.-I.
Wu
, Biomedical Optics: Principles and Imaging
(
Wiley
,
New York
, 2009
).27.
R. A.
Chipman
and
S.-Y.
Lu
, “
Interpretation of Mueller matrices based on polar decomposition
,” J. Opt. Soc. Am. A
13
(5
), 1106
–1113
(1996
).28.
C. A.
Cano Barrera
, “
Diseno e implementacion de un microscopio de luz polarizada para la medicion cuantitativa de propiedades polarimetricas en muestras biologicas
,” Ph.D. thesis (
Universidad EAFIT
, 2018
). http://hdl.handle.net/10784/12466.29.
R. A.
Chipman
, “
Polarimetry
,” in Handbook of Optics
(
McGraw-Hill
,
New York
, 1994
), Chap. 22.30.
E.
Garcia-Caurel
,
R.
Ossikovski
,
M.
Foldyna
,
A.
Pierangelo
,
B.
Drevillon
, and
A.
De Martino
, “
Advanced mueller ellipsometry instrumentation and data analysis
,” in Ellipsometry at the Nanoscale
, edited by
M.
Losurdo
and
K.
Hingerl
(
Springer
,
Berlin, Heidelberg
, 2013
), pp. 31
–143
.31.
J. J. G.
Perez
, Determination of Polarization Parameters in Matricial Representation, Theoretical Contribution and Development of an Automatic Measurement Device
(
University of Zaragoza
,
Zaragoza
, 1983
).32.
S.
Obando-Vasquez
,
A.
Doblas
, and
C.
Trujillo
, “
Muller-matrix-microscopy
” <https://oirl.github.io/Muller-Matrix-Microscopy/>.33.
L. M.
Sanchez-Brea
and
J.
Del Hoyo
, “
py-pol, python module for polarization optics” <
https://pypi.org/project/py-pol/>.34.
J.
del Hoyo
,
L. M.
Sanchez-Brea
, and
A.
Soria-Garcia
, “
Open source library for polarimetric calculations py-pol
,” Comput. Opt.
11875
, 12
–20
(2021
).35.
J. W.
Goodman
, Speckle Phenomena in Optics: Theory and Applications
, 2nd ed. (
SPIE
, 2020
).36.
O.
Arteaga
,
M.
Baldrís
,
J.
Antó
,
A.
Canillas
,
E.
Pascual
, and
E.
Bertran
, “
Mueller matrix microscope with a dual continuous rotating compensator setup and digital demodulation
,” Appl. Opt.
53
(10
), 2236
–2245
(2014
).© 2022 Author(s). Published under an exclusive license by American Association of Physics Teachers.
2022
Author(s)
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
