In this work, we present an experimental method to characterize variable optical retarders, which can have linear or non-linear behavior of the retardance variation. A theoretical analysis of such is presented using a combination of Stokes vectors and Mueller matrixes for three different optical retarders. A straightforward method for phase unwrapping, or reconstructing the original phase from the measured retardance, is proposed that yields high-accuracy results. This work can be used in an undergraduate optics lab to help students understand the concepts of retardance and its control and also how variable retardance devices work.
References
1.
2.
F. Y.
Yap
, “Some more simple laser experiments for the undergraduate laboratory
,” Am. J. Phys.
37
, 1204
–1206
(1969
).3.
B. S.
Perkalskis
and J. R.
Freeman
, “Demonstrating Fresnel's model for optical activity
,” Am. J. Phys.
66
, 452
–453
(1998
).4.
P. R.
Camp
, “Demonstrating optical birefringence—A modification of Schneider's experiment
,” Am. J. Phys.
65
, 672
–674
(1997
).5.
W. S.
Bickel
and W. M.
Bailey
, “Stokes vectors, Mueller matrices, and polarized scattered light
,” Am. J. Phys.
53
, 468
–478
(1985
).6.
D.
Goldstein
, Polarized Light
, 2nd ed. (Marcel Dekker, Inc.
, New York
, 2003
), Chaps. 1, 27, and 28.7.
O. G.
Rodríguez-Herrera
, D.
Lara
, and C.
Dainty
, “Far-field polarization-based sensitivity to sub-resolution displacements of a sub-resolution scatterer in tightly focused fields
,” Opt. Express
18
(6
), 5609
–5628
(2010
).8.
D.
Lara
and C.
Dainty
, “Axially resolved complete Mueller matrix confocal microscopy
,” Appl. Opt.
45
(9
), 1917
–1930
(2006
).9.
E.
Collet
, Polarized Light for Scientists and Engineers
, 1st ed. (The PolaWave Group
, New Jersey
, 2012
).10.
G.
Martínez-Ponce
, C.
Solano
, and C.
Pérez-Barrios
, “Hybrid complete Mueller polarimeter based on phase modulators
,” Opt. Lasers Eng.
49
, 723
–728
(2011
).11.
R. L.
Heredero
, N.
Uribe-Patarroyo
, T.
Belenguer
, G.
Ramos
, A.
Sánchez
, M.
Reina
, V. Martínez
Pillet
, and A.
Álvarez-Herrero
, “Liquid-crystal variable retarders for aerospace polarimetry applications
,” Appl. Opt.
46
(5
), 689
–698
(2007
).12.
P.
Terrier
, J. M.
Charbois
, and V.
Devlaminck
, “Fast-axis orientation dependence on driving voltage for a Stokes polarimeter based on concrete liquid-crystal variable retarders
,” Appl. Opt.
49
(22
), 4278
–4283
(2010
).13.
J.
Delgado-Aguillón
, J.
Garduño-Mejía
, J. M.
López-Téllez
, N. C.
Bruce
, M.
Rosete-Aguilar
, C. J.
Román-Moreno
, and R.
Ortega-Martínez
, “Direct inversion methods for spectral amplitude modulation of femtosecond pulses
,” Rev. Sci. Instrum.
85
(4
), 043105
(2014
).14.
M. A.
Schofield
and Y.
Zhu
, “Fast phase unwrapping algorithm for interferometric applications
,” Opt Lett.
28
(14
), 1194
–1196
(2003
).15.
R. M.
Goldstein
, H. A.
Zebker
, and C. L.
Werner
, “Satellite radar interferometry: Two-dimensional phase unwrapping
,” Radio Sci.
23
, 713
–720
, doi: (1988
).16.
S.
Chavez
, Q. S.
Xiang
, and A.
Li
, “Understanding phase maps in MRI: A new cutline phase unwrapping method
,” IEEE Trans. Med. Imag.
21
(8
), 966
–977
(2002
).17.
L.
Aiello
, D.
Riccio
, P.
Ferraro
, S.
Grilli
, L.
Sansone
, G.
Coppola
, S. D.
Nicola
, and A.
Finizio
, “Green's formulation for robust phase unwrapping in digital holography
,” Opt. Lasers Eng.
45
, 750
–755
(2007
).18.
K.
Itoh
, “Analysis of the phase unwrapping algorithm
,” Appl. Opt.
21
(14
), 2470
(1982
).19.
S. A.
Karout
, M. A.
Gdeisat
, D. R.
Burton
, and M. J.
Lalor
, “Two-dimensional phase unwrapping using a hybrid genetic algorithm
,” Appl. Opt.
46
(5
), 730
–743
(2007
).20.
M.
Arevalillo-Herráez
, M. A.
Gdeisat
, and D. R.
Burton
, “Hybrid robust and fast algorithm for three-dimensional phase unwrapping
,” Appl. Opt.
48
(32
), 6313
–6323
(2009
).21.
See <http://www.ljmu.ac.uk/GERI/90202.htm/> for more information about the phase unwrapping problem.
22.
D. C.
Ghiglia
and M. D.
Pritt
, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software
(John Wiley & Sons
, New York
, 1998
).23.
See <www.meadowlark.com/> for more information on the fabrication and operation of the Liquid-Crystal Variable Retarders.
24.
See <www.cri-inc.com/> for more information on the fabrication and operation of the Amplitude Spatial-Light-Modulator.
25.
See <www.thorlabs.com/> for more information on the fabrication and operation of the Soleil-Babinet Compensator.
26.
J. M.
López-Téllez
and N. C.
Bruce
, “Stokes polarimetry using analysis of the nonlinear voltage-retardance relationship for liquid-crystal variable retarders
,” Rev. Sci. Instrum.
85
(3
), 033104
(2014
).27.
J. M.
López-Téllez
and N. C.
Bruce
, “Mueller polarimeter using analysis of the nonlinear voltage-retardance relationship for liquid-crystal variable retarders
,” Appl. Opt.
53
(24
), 5359
–5366
(2014
).28.
H. R.
Phillip
, Handbook of optical constants of solids
, edited by E. D.
Palik
(Academic Press London
, 1985
), p. 719
.29.
Ealing Catalog Web Site, <http://www.ealingcatalog.com/pdf/Prisms.pdf/>.
© 2015 American Association of Physics Teachers.
2015
American Association of Physics Teachers
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.