Effect of the structure of polarimeter characteristic matrix on light polarization measurements
In the paper, we carried out the comparative analysis of three polarimeters among the most usable their variants: (i) Stokes polarimeter based on phenomenological definition of Stokes parameters; (ii) Stokes polarimeter based on the method of four intensities; (iii) Stokes dynamic polarimeter. We...
Збережено в:
| Дата: | 2009 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2009
|
| Назва видання: | Semiconductor Physics Quantum Electronics & Optoelectronics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/118872 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Effect of the structure of polarimeter characteristic matrix on light polarization measurements / S.N. Savenkov, Ye.A. Oberemok, O.S. Klimov, О.I. Barchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 3. — С.264-271. — Бібліогр.: 26 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-118872 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1188722017-06-01T03:05:14Z Effect of the structure of polarimeter characteristic matrix on light polarization measurements Savenkov, S.N. Oberemok, Ye.A. Klimov, O.S. Barchuk, О.I. In the paper, we carried out the comparative analysis of three polarimeters among the most usable their variants: (i) Stokes polarimeter based on phenomenological definition of Stokes parameters; (ii) Stokes polarimeter based on the method of four intensities; (iii) Stokes dynamic polarimeter. We show that, since the accuracy in determination of individual Stokes parameter is different for different types of polarimeters, and, therewith, it depends on polarization of input light. All that strongly motivates the choice of type of polarimeter to provide minimum errors in determination of polarization parameters (ellipticity angle ε, azimuth β, and degree of polarization P). 2009 Article Effect of the structure of polarimeter characteristic matrix on light polarization measurements / S.N. Savenkov, Ye.A. Oberemok, O.S. Klimov, О.I. Barchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 3. — С.264-271. — Бібліогр.: 26 назв. — англ. 1560-8034 PACS 07.60.Fs http://dspace.nbuv.gov.ua/handle/123456789/118872 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
In the paper, we carried out the comparative analysis of three polarimeters
among the most usable their variants: (i) Stokes polarimeter based on phenomenological
definition of Stokes parameters; (ii) Stokes polarimeter based on the method of four
intensities; (iii) Stokes dynamic polarimeter. We show that, since the accuracy in
determination of individual Stokes parameter is different for different types of
polarimeters, and, therewith, it depends on polarization of input light. All that strongly
motivates the choice of type of polarimeter to provide minimum errors in determination
of polarization parameters (ellipticity angle ε, azimuth β, and degree of polarization P). |
| format |
Article |
| author |
Savenkov, S.N. Oberemok, Ye.A. Klimov, O.S. Barchuk, О.I. |
| spellingShingle |
Savenkov, S.N. Oberemok, Ye.A. Klimov, O.S. Barchuk, О.I. Effect of the structure of polarimeter characteristic matrix on light polarization measurements Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Savenkov, S.N. Oberemok, Ye.A. Klimov, O.S. Barchuk, О.I. |
| author_sort |
Savenkov, S.N. |
| title |
Effect of the structure of polarimeter characteristic matrix on light polarization measurements |
| title_short |
Effect of the structure of polarimeter characteristic matrix on light polarization measurements |
| title_full |
Effect of the structure of polarimeter characteristic matrix on light polarization measurements |
| title_fullStr |
Effect of the structure of polarimeter characteristic matrix on light polarization measurements |
| title_full_unstemmed |
Effect of the structure of polarimeter characteristic matrix on light polarization measurements |
| title_sort |
effect of the structure of polarimeter characteristic matrix on light polarization measurements |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118872 |
| citation_txt |
Effect of the structure of polarimeter characteristic matrix
on light polarization measurements / S.N. Savenkov, Ye.A. Oberemok, O.S. Klimov, О.I. Barchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 3. — С.264-271. — Бібліогр.: 26 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT savenkovsn effectofthestructureofpolarimetercharacteristicmatrixonlightpolarizationmeasurements AT oberemokyea effectofthestructureofpolarimetercharacteristicmatrixonlightpolarizationmeasurements AT klimovos effectofthestructureofpolarimetercharacteristicmatrixonlightpolarizationmeasurements AT barchukoi effectofthestructureofpolarimetercharacteristicmatrixonlightpolarizationmeasurements |
| first_indexed |
2025-07-08T14:49:00Z |
| last_indexed |
2025-07-08T14:49:00Z |
| _version_ |
1837090619748515840 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 264-271.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
264
PACS 07.60.Fs
Effect of the structure of polarimeter characteristic matrix
on light polarization measurements
S.N. Savenkov1, Ye.A. Oberemok, O.S. Klimov, О.I. Barchuk
Taras Shevchenko Kyiv National University, Radiophysics Department,
64, Volodymyrska str., 01601 Kyiv, Ukraine,
Phone: (380-44)526-05-80; e-mail: sns@univ.kiev.ua1
Abstract. In the paper, we carried out the comparative analysis of three polarimeters
among the most usable their variants: (i) Stokes polarimeter based on phenomenological
definition of Stokes parameters; (ii) Stokes polarimeter based on the method of four
intensities; (iii) Stokes dynamic polarimeter. We show that, since the accuracy in
determination of individual Stokes parameter is different for different types of
polarimeters, and, therewith, it depends on polarization of input light. All that strongly
motivates the choice of type of polarimeter to provide minimum errors in determination
of polarization parameters (ellipticity angle ε, azimuth β, and degree of polarization P).
Keywords: Stokes vector, Stokes polarimeter, Stokes parameter.
Manuscript received 27.03.09; accepted for publication 14.05.09; published online 15.05.09.
1. Introduction
Polarization state of electromagnetic radiation changes
when interacting with various media and is an additional
source of information about their properties.
Polarimetric methods through their high sensitivity (in
particular to object anisotropy) could be used even at a
negligible level of input light intensities. The time of
measurement and errors are key factors in experimental
investigation of different types of media by polarimetric
methods [1-6]. The state of light polarization can be
completely characterized by Stokes parameters, which
allow describing both completely and partially polarized
light. This makes the development of the systems
measuring Stokes parameters (Stokes polarimeters) to be
highly important for further improvement of polarimetric
methods in medium investigations.
Up to date, it has been proposed a lot of schemes
for Stokes polarimeter [7-10]. In all of them, to
transform light polarization, used are polarization
transformers with computer controlled parameters. The
only polarimeter with division of intensities is exception
[11], in which polarization transformers remain
invariable. However, this results in considerable
complication of the polarimeter calibration.
Stokes polarimeters with a mechanically controlled
polarization transformer (e.g. with rotating optical
elements) are useful in the view of realization simplicity,
adjustment and exploitation. Now, the most usable
variants of polarimeters are as follows: (i) Stokes
polarimeter based on phenomenological definition of
Stokes parameters [12]; (ii) Stokes polarimeter based on
the method of four intensities [13]; (iii) dynamic Stokes
polarimeter [14, 15]. A plethora of papers [10, 13, 16-
25] is devoted to polarimeter optimization in respect of
gaining the minimal errors in measurements of Stokes
parameters. In particular, derived were the optimal
values of phase shifts and angular positions of phase
plates. Also, it has been studied the question concerning
the systematic error resulted from imperfectness of
polarization elements used [22-24]. However, systematic
analysis of random errors was not carried out for optimal
regimes of the above types of Stokes-polarimeters.
Besides, the most of papers, in which errors of
polarimetric measurements are considered, supposes that
the Stokes parameters are measured with an equal
accuracy – but this is not the case in practice. In what
follows, we show that individual errors in measurements
of Stokes parameters depend on exact strategy of
polarimetric measurements.
The aim of this paper is to estimate individual
errors in measurements of Stokes parameters and effect
of these errors on determination of light polarization
parameters: ellipticity, azimuth and degree of
polarization for the above mentioned strategies of
polarimetric measurements.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 264-271.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
265
2. Stokes polarimeter based on phenomenological
definition of Stokes parameters
According to phenomenological definition, four Stokes
parameters 41S have the following physical meaning:
1S is a sum of light intensities that pass through
polarizers with the orientation 0 and 90 (i.e. the total
light intensity); 2S – difference between the same
intensities; 3S – difference between intensities for light
that pass through polarizers with the orientation 45 and
135; 4S – difference between intensities for light that
pass through polarization elements transmitting light
with either left or right circular polarization (for
example, the quarter-wave plate and linear polarizer with
the orientation 45 or 135 relative to fast axis of the
plate). These definitions can be expressed in the form:
,;
;;
4135453
90029001
RL IISIIS
IISIIS
(1)
where xI is the light intensity that pass through
corresponding polarization elements.
The polarimeter operating accordingly to the
definition Eq. (1) is presented in Fig. 1.
Here P is the polarizer with the azimuth θ and PhPl
is the phase plate with the shift 904/ and
azimuth 0 , which can be introduced before the
polarizer in the necessary steps of measurements.
The signal of photodetector (Fig. 1) depends on the
position of polarization elements and the state of input
polarization as follows:
1
1
1
1
1
1
135
45
90
0
)0,90()135(
)0,90()45(
)135(
)45(
)90(
)0(
SMM
SMM
SM
SM
SM
SM
I
PhPlP
PhPlP
P
P
P
P
R
L
I
I
I
I
I
I
, (2)
where MP(θ), MPhPl(δ, ), S = [S1 S2 S3 S4]
T denote
the Mueller matrices of the polarizer as well as phase
plate and Stokes vector for input light and have the form,
correspondingly:
1000
0)2(sin)2sin()2cos()2sin(
0)2sin()2cos()2(cos)2cos(
0)2sin()2cos(1
2
1
)( 2
2
PM ,
(3)
From Eq. (2), we can get the equation for
determination of required Stokes parameters in the
matrix form:
IAS 1 , (5)
where 1A is the inverse matrix to the characteristic
matrix of polarimeter A , which in this case, substituting
Eqs. (3) and (4) in Eq. (2), will have the following form:
5.0005.0
5.0005.0
05.005.0
05.005.0
005.05.0
005.05.0
A . (6)
We assume that positioning of polarizer and phase
plate occur with errors θ and , correspondingly.
Besides, we assume also the deviations of phase shift
from δ = /4 with value δ, and errors of intensity
measurement I (additive noise) take place.
Taking into account these values of errors θ, ,
δ and I to estimate the individual measurement errors
of each of four Stokes parameters, we use the following
relation [25]:
N
n
n
n
ni
Ni y
y
yF
yyyF
1
20
21
)(
),...,,( , (7)
where ),...,,( 21 Ni yyyF denote the parameters
calculated basing on the measured parameters ny . 0
ny is
an exact value of measured parameter ny .
Accordingly to Eqs. (5) and (7), the values of errors
for Stokes parameters can be written in the following
form:
2226
1
2
I
I
SSSS
S iii
k k
i
i .
(8)
Using Eq. (8) and setting the values of errors as
δ = 0.5º, = 0.2º, θ = 0.2º, and I = I0.001 (here
S1 = I = 1 is the light intensity of the beam incident on
the phase plate (see Fig. 1)), we derive the dependences
of the measurement errors for Stokes parameters on the
incident light polarization state (β is an azimuth and ε is
an ellipticity angle for polarization ellipse of input light)
(see Fig. 2).
0)sin()2cos()sin()2sin(0
)sin()2cos()cos()2(cos)2(sin))cos(1)(2sin()2cos(0
)sin()2sin()))cos(1)((2sin()2cos()cos()2(sin)2(cos0
0001
),( 22
22
PhPlM . (4)
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 264-271.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
266
0.000560.00210.00210.0020S 0.00770.00490.00490.0024 ppS
Fig. 2. Dependences of the values of Si on polarization of input light for the Stokes polarimeter based on phenomenological
definition of Stokes parameters.
S(,)
MP() MPhPl(δ,)
Photo-
detector
a
y
x
b
= arctg(b/a);
I = a2+b2;
Fig. 1. Stokes-polarimeter setup.
It can be seen that errors in parameters strongly
depend on the polarization state of incident light. Mean
errors (shown at the bottom of Fig. 2 as the vector S )
are equal for parameters S1, S2 and S3, and grow for
parameters S4 by 2.6 times.
The range of error changes (shown as the vector
ppS at the bottom of Fig. 2) is equal for parameters S2
and S3. For S1 range of error changes is two times less
than that for the parameters S2 and S3, but for S4 is
approximately 1.6 times larger. The value of the
measurement error for Stokes parameters increases upon
the average with decrease of the ellipticity angle ε of
incident light.
The Stokes parameters are determined with
minimum errors for light with polarization closing to the
circular polarization (ε = ±π/4). Also it can be seen that
the errors for S1 and S3 for input polarization with the
azimuth β =±45º relatively to analyzer (θ = 0º) become
minimum, and it is practically irrespective to the
ellipticity angle. A similar situation with the parameter
S2 is observed for polarization of input light with the
azimuth β = 0±90º.
3. Stokes polarimeter based on the method of four
intensities
On the assumption of dimension of the Stokes vector,
the set of equations for determining the vector
parameters should contain four equations. This set of
equations can be obtained by measuring the light
intensity Ii after the polarizer MP(0º) (Fig. 1) with the
fixed orientation θ = 0º and phase plate MPhPl(δ, i) with
the fixed phase shift δ and four angular positions i. The
expression for a light intensity Ii incident on the detector
can be written in the form:
.)sin()2sin())cos(1)(2sin()2cos(
)cos()2sin()2cos(
),()0(),,(
43
2
22
1
0
SS
SS
I
iii
ii
iPhPlPii
SMMS
(9)
Thus, from Eq. (9) for Stokes parameters Si we get
the following matrix equation:
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 264-271.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
267
It follows from Eq.(10) that the measurement errors
Si are determined by errors Ii , δ and i. Values of
the Stokes parameters can be derived as functions of Ii ,
δ, i from Eq. (10) making use of Eq. (5).
Then, in conformity with Eq. (7), Si are:
4
1
222
k k
i
k
ii
i I
I
SSS
S .
(11)
As it was in the previous case, Si depend on the
polarization state (β, ε) of input light. Fig. 3 presents the
dependences of Si as functions of (β, ε), which gives
the following values for the parameters of the phase
plate: δ = 132º, i = (–51.7º, –15º, 15º, 51.7º) that were
defined in [16], and imperfections of polarimeter
parameters: δ = 0.5º, = 0.2º, I = I00.001.
It can be seen that locations of maximum and
minimum for errors of Stokes parameters Si are
antisymmetric with respect to β = 0º.
As it follows from values for the vector S (see
Fig. 3), the Stokes parameter S4 was measured in this
case with the largest errors. The parameter S2 is
characterized by the greatest range ppS depending on
the polarization state of input light. We show that a
uniform distribution of angular orientations of phase
plate i (say, for example, i = (–60º, –30º, 30º, 60º))
removes the asymmetric locations of maximum and
minimum values of Si, but the mean error S is
increased essentially.
4. Dynamic Stokes polarimeter
Dynamic Stokes-polarimeter contains a retarder
MPhPl(δ, ωt) before the polarizer P (see Fig. 1) rotating
with a fixed frequency ω. Thus, in this case the detector
signal has the form:
).2(sin)(sin)4(sin))(cos1(5.0
))2(sin)(cos)2((cos
),()0(),,(
43
22
21
1
tStS
ttSS
ttI PhPlP
SMMS
(12)
Eq. (12) reduces to the following set of equations
for Stokes parameters Si:
Here, φ0 is the initial position of the phase plate; ak,
bk are the amplitudes of harmonics sin(kωt) and cos(kωt),
respectively:
N
i
iI
N
a
1
0 ),,(
1
S ,
)1(
2
cos),,(
2
1
i
N
k
I
N
a
N
i
ik S ,
)1(
2
sin),,(
2
1
i
N
k
I
N
b
N
i
ik S , (14)
where N is a number of samplings within the period
T = 2π/ω; i – position of the phase plate at i-th
sampling.
The analysis shows that minimum values of errors
δ and φ0 are achieved for δ = 129.6º and φ0 = 0º.
It follows from Eqs. (13) and (14) that errors Si in
dynamic Stokes-polarimeter depend on values δ, i
and φ0. Thus, in according with Eqs. (13), (14) and (7)
the expression for Si takes the form:
N
k k
i
k
iii
i I
I
SSSS
S
1
222
0
0
2
.
(15)
Fig. 4 shows the dependences Si on polarizations
(β and ε) of input light, which gives the optimal set of
parameters for the phase plate MPhPl (Fig. 1): δ = 129.6º
and φ0 = 0º. The number of samplings was chosen as
N = 360. The error in initial orientation of the phase
plate is φ0 = 0.2º. Other three values Ii, δ, i are the
same as in previous cases.
As it can be seen from Fig. 4 the parameters S2 and
S3 have been determined upon the average with equal
errors and are only different in locations of maxima. The
mean value of 4S is 1.3 times less than that of 2S
and 3S . The value of the parameter S1 has been
determined more precisely as compared with S2 and S3
(approximately by 2.6 times) and S4 (approximately by
1.9 times). The value of errors ppS for parameters S2
and S3 are equal and less than that of the parameter S1 by
2.3 times and that of S4 by 5.2 times.
ISA
4
3
2
1
4
3
2
1
444
2
4
2
4
333
2
3
2
3
222
2
2
2
2
111
2
1
2
1
)sin()2sin())cos(1)(2sin()2cos()cos()2sin()2cos(1
)sin()2sin())cos(1)(2sin()2cos()cos()2sin()2cos(1
)sin()2sin())cos(1)(2sin()2cos()cos()2sin()2cos(1
)sin()2sin())cos(1)(2sin()2cos()cos()2sin()2cos(1
I
I
I
I
S
S
S
S
. (10)
ISA
4
4
2
0
4
3
2
1
00
00
0
0)4cos())cos(1(5.0)4sin())cos(1(5.00
0)4sin())cos(1(5.0)4cos())cos(1(5.00
)sin()2cos(000
00))cos(1(5.01
b
a
b
a
S
S
S
S
. (13)
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 264-271.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
268
0.00760.00570.00550.0036S 0.00320.0560.00610.0042 ppS
Fig. 3. Dependences of the Si values on polarization of input light for the Stokes polarimeter based on the method of four
intensities.
0.00460.00620.00620.0024S 0.00730.00140.00140.0032 ppS
Fig. 4. Dependences of the Si values on polarization of input light for the dynamic Stokes polarimeter.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 264-271.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
269
.10.0,13.0,25.0,13.0;0039.0,0040.0 ppppppPP
a)
15.0,26.0,16.0,17.0,0034.0,0083.0 ppppppPP
b)
31.0,37.0,18.0,11.0,0058.0,0076.0 ppppppPP
c)
Fig. 5. Dependences of the P, ε, β values for different polarizations of input light: (a) Stokes polarimeter based on
phenomenological definition of Stokes parameters; (b) dynamic Stokes polarimeter; (c) Stokes polarimeter based on the method
of four intensities.
5. The effect of measurement errors Si on
determination of polarization parameters
of input light
The given Stokes parameters, Si, polarization
parameters, intensity I, degree of polarization P,
ellipticity angle ε and azimuth of polarization ellipse β
can be determined in the following manner:
.arctg
2
1
,arcsin
2
1
,,
2
3
2
4
2
3
2
2
4
2
1
2
4
2
3
2
2
1
S
S
SSS
S
S
SSS
PSI
(16)
Errors in values of Stokes parameters will be
transferred into errors of polarization parameters
Eq. (16). To estimate this effect, we use Eq. (7):
.
,,
4
1
2
4
1
24
1
2
i
i
i
i
i
ii
i
i
S
S
S
S
S
S
P
P
(17)
Since the values Si (β, ε) are different for different
Stokes-polarimeters discussed above, thus, the errors of
polarization parameters Eq. (17) are different for
different Stokes-polarimeters as well. Fig. 5 exemplifies
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 264-271.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
270
the dependences P(β, ε), ε(β, ε) and β(β, ε) for three
types of polarimeters discussed above.
It follows from Fig. 5 that the ellipticity of
polarization ellipse has been determined with the
minimum errors by dynamic Stokes-polarimeter.
Whereas, the polarization degree P and azimuth of
polarization ellipse β are determined with minimum
errors by Stokes polarimeter based on phenomenological
definition of Stokes parameters. For Stokes polarimeter
based on the method of four intensities, the effect of
polarization of input light on the errors P, ε and β is
minor. More sensitive to the polarization state of input
light is the dynamic Stokes-polarimeter.
6. Conclusion
In summary, we have analyzed the errors in
determination of the Stokes parameters for three types of
Stokes polarimeters: (i) Stokes polarimeter based on
phenomenological definition of Stokes parameters;
(ii) Stokes polarimeter based on the method of four
intensities; (iii) dynamic Stokes polarimeter. Also, we
have analyzed the transfer of the errors for Stokes
parameters Si into the errors in determination of
polarization parameters (degree of polarization P,
ellipticity angle ε and azimuth of polarization ellipse β)
of input light. We have shown that in general case the
Stokes parameters are determined with a different
accuracy both in scope of one measurement strategy and
by different measurement strategies. The Stokes vector
is measured as a whole with minimum errors by Stokes
polarimeter based on phenomenological definition of
Stokes parameters: 0017.04/
4
1
i
iS . The dynamic
Stokes polarimeter and Stokes polarimeter based on the
method of four intensities measure the Stokes vector
with a somewhat higher value of errors:
0049.04/
4
1
i
iS and 0056.04/
4
1
i
iS ,
respectively.
This is quite important fact because it means that,
under rest equal circumstances, the parameters of
polarization of input light are measured with different
errors by different polarimeters. Moreover, the errors
depend on the polarization state of input light as well.
The results obtained for errors of the Stokes parameters
allowed to determine that the ellipticity angle ε is
measured more precisely by dynamic Stokes-
polarimeter, whereas, the azimuth β and degree of
polarization P are measured more precisely by Stokes
polarimeter based on phenomenological definition of
Stokes parameters.
The results derived in this paper can be useful for
choosing the measurement strategy for given
polarization of input light. Indeed, the Stokes
polarimeter based on phenomenological definition of
Stokes parameters is complicated for automatization.
The dynamic Stokes polarimeter is evidently
unacceptable for imaging Stokes vector measurements
[10]. At the same time, the Stokes polarimeter based on
the method of four intensities, although characterized by
a relatively higher value of errors when determining
Stokes parameters, is simple for automatization and
promising for imaging Stokes polarimetry.
It is noteworthy that on the assumption of equality
of Si there exist no reasons to prefer one Stokes
polarimeter to another. An exception can be very likely
made only when concerning to assembling and operating
conveniences. Since the accuracy in determination of an
individual Stokes parameter is different for different
types of polarimeters and, therewith, it depends on
polarization of input light, then all these strongly
motivates the choice of polarimeter type to provide
minimum errors in determination of polarization
parameters (ellipticity angle ε, azimuth β, and degree of
polarization P). This gains even more important
significance, when the choice of measurement strategy
can be made only by software [27].
References
1. Ch. Brosseau, Fundamentals of Polarized Light. A
Statistical Optics Approach. North-Holland
Publishing Company, New York, p. 406, 1998.
2. M.I. Mishchenko, L.D. Travis, A.A. Lacis,
Scattering, Absorption, and Emission of Light by
Small Particles. Cambridge University Press,
Cambridge, p. 449, 2002.
3. S.L. Durden, J.J. van Zyl, and H.A. Zebker, The
unpolarized component in polarimetric radar
observations of forested areas // IEEE Trans.
Geoscience and Remote Sensing 28, p. 268-271
(1990).
4. S.L. Jacques, R.J. Roman and K. Lee, Imaging skin
pathology with polarized light // J. Biomed. Opt. 7,
p. 329-340 (2002).
5. S.P. Morgan, I.M. Stockford, Surface-reflection
elimination in polarization imaging of superficial
tissue // Opt. Lett. 28, p. 114-116 (2003).
6. J.M. Schmitt, A.H. Gandjbakhche and R.F. Bonner,
Use of polarized light to discriminate short path
photons in a multiply scattering medium // Appl.
Opt. 31, p. 6535-6546 (1992).
7. P.S. Hauge, Resent developments in
instrumentation in ellipsometry // Surf. Sci. 96,
p. 108-140 (1980).
8. A.M. Shutov, The optical systems of devices for
measuring the parameters of polarized radiation //
Optiko-mekhanicheskaya promyshlennost’ 11,
p. 52-56 (1985) (in Russian).
9. R.M.A. Azzam, Mueller-matrix ellipsometry:
review // Proc. SPIE 3121, p. 396-405 (1997).
10. J.S. Tyo, D.L. Goldstein, D.B. Chenault and
J.A. Shaw, Review of passive imaging polarimetry
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 264-271.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
271
for remote sensing applications // Appl. Opt.
45(22), p. 5453-5469 (2006).
11. R.M.A. Azzam, Arrangement of four
photodetectors for measuring the state of
polarization of light // Opt. Lett. 10, p. 309-311
(1985).
12. M. Born and E. Wolf, Principles of Optics.
Pergamon, New York, p. 554, 1975.
13. A. Ambirajan and D.C. Look, Optimum angles for
a polarimeter: part 1 // Opt. Eng. 34, p. 1651-1655
(1995).
14. P.S. Hauge and F.H. Dill, A rotating-compensator
Fourier ellipsometer // Opt. Communs. 14, p. 431-
437 (1975).
15. P.S. Huge, Generalized rotating-compensator
ellipsometry // Surf. Sci. 56, p. 148-160 (1976).
16. D.S. Sabatke, M.R. Descour and E.L. Dereniak,
Optimization of retardance for a complete Stokes
polarimeter // Opt. Lett. 25(11), p. 802-804 (2000).
17. I.J. Vaughn and B.G. Hoover, Noise reduction in a
laser polarimeter based on discrete waveplate
rotations // Opt. Exp. 16(3), p. 2091-2108 (2006).
18. R.M.A. Azzam, I.M. Elminyawi and A.M. El-Saba,
General analysis and optimization of the four-
detector photopolarimeter // J. Opt. Soc. Amer. A 5,
p. 681-689 (1988).
19. V.A. Dlugunovich, V.N. Snopko and
O.V. Tsaryuk, Analysis of a method for measuring
polarization characteristics with a Stokes
polarimeter having a rotating phase plate // J. Opt.
Technol. 68(4), p. 269-273 (2001).
20. J.S. Tyo, Noise equalization in Stokes parameter
images obtained by use of variable-retardance
polarimeters // Opt. Lett. 25, p. 1198-1200 (2000).
21. S.N. Savenkov, Optimization and structuring of the
instrument matrix for polarimetric measurements //
Opt. Eng. 41, p. 965-972 (2002).
22. V.A. Dlugunovich, E.A. Kuplevich and
V.N. Snopko, Minimizing the measurement error
of the Stokes parameters when the setting angles of
a phase plate are varied // J. Opt. Technol. 67(9),
p. 792-800 (2000).
23. J.S. Tyo, Design of optimal polarimeters: maximi-
zation of signal-to-noise ratio and minimization of
systematic errors // Appl. Opt. 41, p. 619-630 (2002).
24. J. Zallat, S. Ainouz, and M.Ph. Stoll, Optimal
configurations for imaging polarimeters: impact of
image noise and systematic errors // J. Opt. A 8,
p. 807-814 (2006).
25. J.R. Taylor, An Introduction to Error Analysis,
2 ed. Univ. Sci. Books, Mill Valley, p. 349, 1997.
26. F.R. Gantmacher, The Theory of Matrices. AMS
Chelsea Publishing, Reprinted by Amer. Mathemat.
Soc., p. 660, 2000.
S.N. Savenkov, Yu.A. Skoblya, K.E. Yushtin, and
A.S. Klimov, Mueller matrix polarimetry with
multi-purpose polarization transducer // Proc. SPIE
5772, p. 77-85 (2005).
|