Retardance polarization measurement based on a dual rotating polarizer arrangement

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Retardance polarization
measurement based on a dual
rotating polarizer arrangement
Serrano-García, David, Macías-Mendoza, Humberto,
Flores, Jorge L., García-Torales, Guillermo, Parra-
Escamilla, Gelizlte, et al.
David I. Serrano-García, Humberto Macías-Mendoza, Jorge L. Flores,
Guillermo García-Torales, Gelizlte A. Parra-Escamilla, Antonio Muñoz,
"Retardance polarization measurement based on a dual rotating polarizer
arrangement," Proc. SPIE 10765, Infrared Remote Sensing and
Instrumentation XXVI, 107650N (18 September 2018); doi:
10.1117/12.2321676
Event: SPIE Optical Engineering + Applications, 2018, San Diego, California,
United States
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Retardance Polarization Measurement Based on a Dual Rotating
Polarizer Arrangement
David I. Serrano-García1, Humberto Macías-Mendoza1, Jorge L. Flores1, Guillermo García-Torales1,
Geliztle A. Parra-Escamilla1 and Antonio Muñoz2
1Electronic Engineering Department, University of Guadalajara, Av. Revolución No. 1500, CP. 44430 Guadalajara, Jalisco, México
2 Departamento de Ingenierías, Universidad de Guadalajara, Av. Independencia Nacional 151, C.P. 48900 Autlán, Jalisco, México
ABSTRACT
We present a polarization sensitive measurement focused on retrieve elliptical phase retardation properties. The system
is based on rotating two linear polarizers. And a demodulation algorithm is proposed to retrieve a partial matrix of
Muller from the intensity output signal. The polarimetry setup also employs a monochrome camera as detection system
and a HeNe laser as light source. Simulation and experimental results in transparent samples are presented showing the
feasibility of the measurement and the potential usage in a multiwavelength arrangement.
Keywords: Polarization, Polarimetry, Mueller Matrix, Measurement Techniques
1. INTRODUCTION
Polarimetry is an experimental technique to determine the optical properties of a sample by measuring the polarization
variation of light reflected or transmitted by the sample under study providing extra measurement metrics with potential
usage in developing new measurement systems. In the last decades, the polarimetric measurements have been applied in
atmospheric sensing for characterizing the pollution particles on the environment [1,2] and climate variations [3] for
mention some ones. In the remote sensing detection, polarimetry has been used widely in analyze reflective objects as
metals, glasses among others [4]. In the biomedical field, it has been proposed as a marker for identify cancerous tissue
at early stages [5] and applied in ophthalmic applications by the combination with OCT techniques [6].
Several polarimeter designs to determine the Mueller matrix information can be found in the literature, for example,
based on dual rotating retarder configuration [7,8], phase modulators [9] and the usage of liquid crystal retarders [10,11].
The dual rotating retarder configuration is a well standardized configuration [12-14] and it is based on a fixed polarizer
and a rotating retarder that composes a polarization state generator (PSG) to produce various polarizing states in the
input, and a rotating retarder and a fixed analyzer working as a polarizing state analyzer (PSA) dedicated to detecting
various polarization states at the output after passing through the sample [7,8]. The retrieving of the Mueller matrix is
based on the frequency response obtained through the rotation of the retarders.
The Mueller matrix information is arranged in a 4×4 matrix and it can be decomposed in three polarimetric properties
known as: diattenuation, retardance and depolarization. These properties describe the polarization dependence of
attenuation, retardance and its possibility to maintain polarization properties of the light that pass through it [15,16].
Each of these properties can be associated to physical properties of the sample under test, for example, the linear and
circular diattenuation can be associated with the scattering and chirality measurement; the circular retardance property is
helpful for glucose measurement and the birefringence can be associated with stress analysis and more recently the
depolarization properties are having potential usage on cancer diagnosis [16,17].
In this work we propose a technique for retardance polarization measurement based on a dual rotating polarizer
arrangement. Our purpose retrieves a partial Mueller matrix of a transparent sample, to later be associated to its phase
retardation properties. Our focus in this property comes in the interest of compare the phase information retrieved with
common interferometry techniques and the phase retardation obtained with this polarimetric measurement.
Infrared Remote Sensing and Instrumentation XXVI, edited by Marija Strojnik,
Maureen S. Kirk, Proc. of SPIE Vol. 10765, 107650N · © 2018 SPIE
CCC code: 0277-786X/18/$18 · doi: 10.1117/12.2321676
Proc. of SPIE Vol. 10765 107650N-1
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Through the
two rotatin
g
enhancing t
h
wavelength,
visible rang
e
The rest of t
h
and 4, nume
r
2. D
U
Theoretical
A typical im
=632.8

monochrom
e
orientation r
e
employing
a
retarder,(
Figure 1: Du
a
By the Mue
l
retardance a
n
and the sam
p
 is describe
Mueller matri
x
g
linear polari
z
h
e response b
y
the approach
h
e
and same pro
c
h
is paper is or
g
r
ical simulatio
n
U
AL ROTA
T
Approach
aging
p
olarim
e

, a spatial
e
camera for c
a
e
ference of th
a
n electronic


,

,

) and
a
l rotating polar
i
l
ler matrix ap
p
n
d depolarizat
i
p
le is depicted
d by [18-20]

(
x
approach, w
z
ers and
b
y
e
y
the rotating
c
h
as
p
otential
t
c
edures can b
e
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anized as fol
l
n
s and experi
m
T
ING PO
L
et
ric system is
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pture the two
-
e measureme
n
controlled m
e
it is placed be
i
meter sensitive
t
p
roach, any p
o
i
on [18, 19].
A
as an elliptica
l
(
)=


1
cos(
2
sin(
2
0
e developed a
e
mploying fre
c
omponents.
A
t
o be used wit
h
e
transferred to
l
ows. In the ne
m
ental results
a
L
ARIZER P
RETARD
A
presented in
F
a
m expander
-
dimensional
d
n
t and the oth
e
e
chanical rota
t
tween the last
t
o elliptical reta
r
o
larization sen
A
s our approac
l
retarder [ER]
cos
(
2
)cos

(
2
)cos(2)

0
calibration pr
o
quency filters
A
lthough the
pr
h
an RGB ca
m
a different w
a
xt section, we
a
re presen
t
ed.
F
OLARIM
E
A
TION PA
R
F
ig. 1. The op
t
lens, three l
i
d
istribution of
t
e
r ones, 󰇟(

t
ion stage. T
h
two polarizers
r
dance paramet
e
sitive system
c
h is based on
t
,the Mueller
m
(
2)
(
2)cos

(2)
0
o
cedure consi
d
. Also, we d
e
r
oposed syste
m
m
era and a wh
i
a
velength regi
o
describe in so
m
F
inally, the co
n
E
TER SEN
S
R
AMETER
t
ical setup con
s
i
near polarize
r
t
he intensity.
T

),(4)󰇠, r
o
h
e transparent
.
e
rs.
c
an be descri
b
t
he usage of t
h
m
atrix of a lin
e
sin(2)
(2)sin(2)
sin

(2)
0
d
ering initial a
n
e
veloped a d
e
m
has
b
een im
p
i
te light sourc
e
o
n like near in
fr
m
e detail our
p
n
clusions are p
r
S
ITIVE TO
s
ists of a laser
r
s [ (0°),

T
he first polari
z
o
tate at an an
g
sample is t
r
b
ed by the ma
t
h
ree linear pol
a
e
ar polarize
r

0
0
0
0.
n
gles orientati
o
e
modulation a
l
p
lemented at
s
e
to be worki
n
fr
ared o
r
UV r
e
p
roposal. In S
e
r
esented in Se
c
ELLIPTI
C
illumination
s

(),(4)
z
er, (0°), a
g
ular velocity
r
r
eated as an
e
t
rices of diatt
e
a
rizers [LP
0
,
L
() for a gi
v
o
n of the
l
gorithm
s
pecified
n
g in the
e
gion.
e
ctions 3
c
tion 5.
C
AL
s
ource of
] and a
c
t
s as an
r
atio 1:4
e
lliptical
e
nuation,
LP
1
,LP
2
],
v
en angle
(1)
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While, for an elliptical retarder ,, with its fast axis orientated at given angle , its total retardance  and an
ellipticity related parameter  given by [20]
,,=
10 0 0
0
−−+2(∙+∙)−2(∙+∙)
02
(∙−∙)−−−+2(∙−∙)
0−2
(∙−∙)−2(∙−∙)−−−+. (2)
Where, =cos2cos(2)(/2), =cos2sin(2)sin(/2),
=2sin(/2), =cos(/2).
(3)
By following the polarization states after each component, the detected intensity can be retrieved that later will serve as
our model to retrieve the retardation properties of the sample. The output stokes vector can be obtained as the
product of the Mueller matrixes
=(4)∙,,∙()∙(0) (4)
and by taking non-polarizing light as input as  =1
0
0
0. The detected intensity can be obtained by obtaining the first
element of  as
=(1)=1
8+1
8cos(2)−1
64

cos(4)−1
32

cos(6)−1
64(

+

)cos(8)
−1
32cos(10)−1
64cos(12)−1
64sin(4)
−1
32

sin(6)−1
64(

+

)sin(8)−1
32

sin(10)−1
64

sin(12)
(5)
where

=−4cos2sin
2−4cos()
=−4cos(4)cos2sin
2
=4sin2sin()

=−4sin(4)cos2sin
2
(6)
From Eq. (4) and Eq. (6) one can observe that these four terms can be retrieved from the detected intensity and they are
related directly to the sample information ,,. For that, Equation 5 is arranged as a sum of sinusoidal functions,
i.e., =+∑󰇟cos()+sin()󰇠. (7)
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C)
11 [o]
10.5
10
9.5
9
Each coefficient
󰇟,󰇠 can be retrieved by taking the Fast Fourier Transform of the acquired intensity, i.e., output
signal from our polarimeter. Then, the coefficients 󰇟,,,󰇠 depicted in Eq. 6 can be obtained as

=−


=−


=−


=−
. (8)
While, the sample information can be obtained as
()=




cos()=
󰇡
−󰇢.
sin2=


4sin()
(9)
By these procedures we could retrieve the retardance information of the sample from the intensity modulation. The
theoretical approach depicted can be improved by considering diattenuation parameters of the polarizers.
.
3. NUMERIAL SIMULATIONS
In this section, we conducted a series of computer simulations to test the performance of our approach. First a spatial
distribution commonly employed for supper-resolution applications or vector beam generation was used to emulate a Q-
Plate retarder as test object, see Fig. 2. Figure 2.a) shows the retardance variation,, following a radial distribution
laying in 25±5° range; Fig. 2.b) shows the angular variation, , laying in a range of 45±25° and Fig. 2.c) the
ellipticity phase parameter,, of 10° equally distributed in space. Simulations were performed in a grid of 200x200
pixels. Uniform distributable noise was added in the input vector =
0
0
0 in equation 4 with =.9875±.012. The
noise emulates variations on the illumination source during the measurement in space and angular variation.
Figure 2.- Spatial distributions used for simulation. a) Retardance (,), b) angular orientation (,) and c) ellipticity phase
parameter(,).
As presented in Eq. 5, the acquired intensity will be modulated by the rotation of the linear polarizers. Our approach
assumes a rotation ratio of 1:4 and considering the rotation θ,aspresentedinEq.(5), from 0 to 360 degrees and with
an increment of 2.5 deg. We simulated the output signals acquired by the CCD camera as a function of θ and the
introduced noise will affect in the spatial and angular coordinate. In Fig. 3 we show 5 simulated intensities for θ = 0,
12.5, 20, 27.5, and 37.5 degrees. Lower row shows same intensity patterns but displayed in a smaller range for a better
appreciation of the intensity modulation obtained.
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B=0° D.5
a.u]
a)[a.u]0.485
0.48
0.475
0.47
B = 12.5°
III 0.5
[a.u]
VI0
b) [a.u]
0.275
0.27
0.265
0.26
= 20° B = 27.5°
0.5
[a.u]
B = 37.5°
0.5
[a.u]
0
a.u] x103
15
10
5
0
0.5
[a.u]
0
[a.u]
0.07
0.06
0.6
0.4
0.2
0.15
0.1
0.05
tp
0
-0.05-12 -10 -8 -6 -4 -2 02 4 6810 12
k
iy-/ \r i i i i a)
50 100 150 200 250 300 350 400
ak
Angular Rotation O [0]
a) 1.01
-12 -10 -8 -6 -4 -2 0246810 12
k
Figure 3.- Simulated intensity detected. Upper row shows same intensity range and lower row each image in a reduce range.
After obtaining the intensity we will arrange the information in a 3D matrix where the first two axis are the spatial
coordinates [x,y] and the third axis correspond to the angular orientation of the polarizers []. By taking the 1D Fourier
transform along the third axis, angular orientation , we could retrieve the coefficients for each frequency coefficient
given in Eq. 5. Figure 3, upper image, shows the intensity modulation obtained by the central pixel and its corresponding
coefficients from the Fourier transform, lower row. Each coefficient in  and  correspond to the coefficient of the
sin󰇟󰇠 and cos󰇟󰇠 terms in Eq. (5) with k=2,4…12.
Figure 4.- Simulated modulated intensity by rotating polarizers at ration 1:4. a) Modulated intensity obtained at central pixel, b)
Fourier Coefficients  and c) Fourier Coefficients  obtained by the 1D Fourier transform.
After obtaining each coefficient, our approach results in the calculation of four parameters that depends of the sample.
Figure 5 shows the calculation obtained as presented in Eq. 8 and in Fig. 6.a) to 6.c) we show the results obtained from
the simulated intensity patterns and using the proposed approach. Also, in Fig. 6.d) to 6.f), we show the difference
between the simulated input parameters (which are in Fig. 1) and the calculated ones after applying a 2D median filter.
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:[a.u.]
-3.7
-3.75
-3.8
-3.85
:[a.u.]
0.65
0.6
0.55
0.5
0.1
0.1
0
0
-0.1
-0.2
]
30 [0]
25
20
0.5 [0]
0
-0.5
70
60
50
40
30
20
0.5[0]
-0.5
10.5 [01
9.5
0.5 [0]
-0.5
We showed the process for retrieving the elliptical retardation parameters [,,] taking into account noise variation
in the illumination source. The coefficients [A1,A2,A3,A4] are dependent solely of the sample information and retrieved
by the Fourier coefficient of the detect intensity. It is worth to mention that information is retrieved by arguments of
cosine, sine and tangent functions wrapping the information, in case of retardance values higher of 180° a more
specialized numerical analysis need to be done considering a proper unwrapping process.
Figure 5.- Simulated coefficients obtained depending of the
sample properties, Equation 8. a) A1, b) A2 c) A3 and d) A4
Figure 6.- Simulation results obtained by the proposed method: a)
Retardance (,), b) Angular orientation (,), c) Ellipticity
related parameter(,), d) Retardance difference, e) Angular
orientation difference and f) ellipticity related parameter difference.
4. IMPLEMENTATION AND EXPERIMENTAL RESULT
The implemented configuration is composed by two rotating linear polarizers and the other one fix, which is used as a
reference, see Fig. 1. For illumination purposes we employed a He-Ne laser with working wavelength of λ=632.8 nm,
the beam is spatially filter and expanded to 25 mm in diameter. The images were acquired with an 8-bit single-CMOS
camera (model acA2000-340km, Basler) with 2048 x 1088 pixels, and an imaging system focused between the two
rotating polarizers, where the object under test is located, giving a spatial resolution of 14.25 cycles/mm i.e. a line width
of 35.08 microns, which was determined by employing a standard USAF resolution chart observing the group 3 element
4. The polarizers used on the system are the common polarizer sheets working at visible range. These polarizers are
mounted on rotary station Parker Serie 81. The rotary station provides a resolution of 1’125,000 steps per revolution
resulting that 1°=3,125, more information can be encountered in [21].
We made a retardance variance phantom by stacking several layer of transparent scotch tapes as it is commonly used in
photoelasticity experiments due of the induced birefringence [22]. Figure 7 depicts preliminary experimental results with
the phantom showing 6 regions. The first region corresponds to the response in air, region 2 corresponds to the response
obtained with the glass slide, region 3 corresponds to one layer of the scotch tape, region 4 with 2 layers, region 5 with 3
layers and region 6 with 4 layers. Figure 7 a) shows one intensity frame, θ=0°, b) the arrangement of the scotchlayers on
the glass slide, c) retardance (,), d) the angular orientation (,) and e) the ellipticity related parameter (,).
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100
200
300
400
[px l ] soo
600
700
800 200 400 600
x[pxl] 800
C)
A200
80 300
Y400
[px l ] 600
600
700
70 800 200 400 600
x[pxl] d)800
40 [0] 100
30
20 200
10 300
0[px7] 400
CG
500
-20 600
a0 700
-00 800
b)
oLayer 4
Layer 1
Glass Slide
200 400 600
x [pxl]
800e)
20 [0]
15
0
0
s
-10
-15
-20
Figure. 7. Experimental result obtained by placing stacked layers of scotchtape emulating a retardance variation sample. Six regions
are identified, Region 1 corresponds to air, Region 2 glass slide and Region 3 to 6 corresponds from 1 layer to 3 stacked layers. a)One
intensity frame, θ=0°, b) the arrangement of the scotchlayers on the glass slide, c) Retardance (,), d) Orientation (,) and
e) the ellipticity related parameter (,).
In Figure. 7 The experimental results are shown, and they represent an incremental variation on the retardance
parameter, . As our retrieval process is based on argument of trigonometric functions, the information will be wrapped
in certain range and this can be noted in Figure 7 c) by increasing the numbers of layers, the values remain on a range
from 70° to 85°. Same wrapping process arises in the ellipticity related parameter, Fig. 7 e), that remain in a range from -
20° to 5°. Another point of notice arises in the region 1 were air need to provide minimum value of retardance but its
value remains in a range of 80°, by the preliminary results obtained it arises that a calibration process taking into account
a baseline retardance information need to be subtracted.
5. CONCLUSIONS AND FINAL REMARKS
We developed a retardance dependent polarimeter system based on a dual rotating polarizer configuration. The system
was developed focusing on retrieve the full retardance parameters of a sample. Through the Mueller matrix approach a
demodulation algorithm was developed by obtaining the frequency response due of the rotating polarizer used on the
detection. Simulation and preliminary experimental results are presented showing the feasibility of the implementation.
Current work is focused in use standard retardance polarization samples for calibration and sensitivity response analysis.
ACKNOWLEDGEMENTS
D.I. Serrano-García acknowledges the support provided by the National Council of Science and Technology
(CONACYT) through the program “Apoyos para la Incorporación de Investigadores Vinculada a la Consolidación
Institucional de Grupos de Investigación y/o Fortalecimiento del Posgrado Nacional, Modalidad Repatriación”. H.
Macias-Mendoza also acknowledges the support provided by CONACYT for scholarship for his graduate studies and G.
A. Parra-Escamilla for through the program “Estancias Posdoctorales Vinculadas al Fortalecimiento de la Calidad del
Posgrado Nacional 2018”.
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REFERENCES
[1] J. C. Roger,R. Santer,M. HermanandJ. L. Deuzé, “Polarization of the solar light scattered by the earth-atmosphere
system as observed from the U.S. shuttle,” Remote Sensing of Environment, Vol. 48 (3) pp. 275-290. (1994).
[2] G. van Harten, J. de Boer, J. H. H. Rietjens, A. Di Noia, F. Snik, H. Volten, J. M. Smit, O. P. Hasekamp, J. S.
Henzing, and C. U. Keller, “Atmospheric aerosol characterization with a ground-based SPEX spectropolarimetric
instrument,” Atmospheric Measurement Technology, Vol. 7, pp 4341–4351, (2014).
[3] D. Li, N. Zeng, D. Zhan, Y. Chen, M. Zeng and H. Ma, “Differentiation of soot particulates in air using polarized
light scattering method,” Applied Optics, Vol. 56 (14), pp. 4123-4129. (2017)
[4] G. Calvert, J. Lesniak and M. Honlet, “Applications of modern automated photoelasticity to industrial problems, “
Insight, Vol. 44 (4), (2002)
[5] T. Novikova, A. Pierangelo, A. D. Martino, A. Benali and P. Validire, “Polarimetric Imaging for Cancer Diagnosis
and Staging, “Optics and Photonics News Vol. 23(10), pp. 26-33 (2012).
[6] B. Cense, D. T. Miller, B. J. King, T. Theelen and A. E. Elsner, “Measuring polarization changes in the human outer
retina with polarizationsensitive optical coherence tomography,” Journal of Biophotonics, Vol. 11 (5), (2018).
[7] R.M.A. Azzam, “Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected
signal,” Optics Letters Vol. 2 (6) pp. 148–150 (1978).
[8] D. H. Goldstein, “Mueller matrix dual-rotating retarder polarimeter,” Applied Optics, Vol. 31(31) pp. 6676–6683,
(1992).
[9] E. Compain, B. Drevillon, “Complete high-frequency measurement of Mueller matrices based on a new coupled-
phase modulator,” Review of Scientific Instruments, Vol. 68 (7), pp. 2671–2680 (1997).
[10] E. G. Caurel, A.D. Martino, B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,”
Thin Solid Films Vol. 455, pp. 120–123 (2004).
[11] B. L. Boulesteix, A.D. Martino, B. Drévillon, L. Schwartz, “Mueller polarimetric imaging system with liquid
crystals, Applied Optics, Vol. 43 (14), pp. 2824–2832, (2004).
[12] D.H. Goldstein, R.A. Chipman, “Error analysis of a Mueller matrix polarimeter, “Journal of the Optical Society of
America A, Vol. 7 (4), pp. 693–700, (1990).
[13] K. Bhattacharyya, D. I. Serrano-García and Y. Otani, “Accuracy enhancement of dual rotating mueller matrix
imaging polarimeter by diattenuation and retardance error calibration approach,” Optics Communications, Vol. 392,
pp. 48-53, (2017).
[14] K. M. Twietmeyer, R.A. Chipman, “Optimization of Mueller matrix polarimeters in the presence of error sources,”
Optics Express, Vol. 16 (15), pp. 11589–11603 (2008).
[15] S. Y. Lu, R.A. Chipman, Interpretation of Mueller matrices based on polar decomposition”, Journal of the Optical
Society of America A, Vol. 13 (5), pp. 1106–1113 (1996).
[16] D. Goldstein, “Polarized Light,” Marcel Dekker, Inc., (2003).
[17] R. A. Chipman, “Chapter 22 - Polarimetry” in Handbook of Optics, McGraw-Hill Professional, (1995).
[18] D. H. Goldstein, Polarized Light (CRC, 2010).
[19] R. A. Chipman, “Polarimetry,” in Handbook of Optics II, M. Bass, ed. (McGraw Hill, 1995), pp 22.1–22.37.
[20] D. Kliger and J. Lewis, Polarized Light in Optics and Spectroscopy (Academic, 2012).
[21] G. García-Torales; J. Flores ; Roberto Muñoz, “High precision prism scanning system,” Proc. SPIE. 6422, Sixth
Symposium Optics in Industry, (2007).
[22] S. J. Edwards and A. J. Langley, “On Producing Colours Using Birefringence Property of Transparent, Colourless
Stretched Cellophane,” Leonardo, Vol. 14 (3), pp. 187-190, (1981).
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