The Determination of the Optical Constants of the
Plant Leaves with Polarized Emission Using.
A.G. Ushenko, A.V. Motrich, S.G. Guminietski
Chernivtsi National University, 2 Kotsyubinsky Str., 58012 Chernivtsi, Ukraine.
motrich@gmail.com
Abstract.
There have been given the results of the investigating the reflection coefficients of
some plants’ leaves with very smooth surfaces in the polarized light for those wave
lengths for which the inner composition in the reflected emission does not
practically exist. The optical constants for the mentioned objects of investigation
have been defined, also Fresnel formulas as well as the method of the determination
of the optical constants based on the measuring the reflection coefficients of the
polarized emission for the definite fixed angles of incidence.
Keywords: polarized emission, reflection coefficient, index of refraction, index of
absorption.
PACS: 42.25.Ja, 42.62.Be
1. Introduction
Determination of optical constants of matter is
one of actual tasks at its researches optical and
spectral, for example [1, 2]. The methods of
the determination of the optical constants of
different substances are widely presented in
the scientific research letters and mainly with
the polarized emission using in the matter of
the semiconductor crystals in operation [3].
As far as the biological objects are concerned,
for instance the plants’ leaves, then the index
of refraction n is evaluated for them as being
equal approximately to 1,4 while the index of
absorption k (extinction) is considered to be
far less to compare to it [4, 5]. Herewith the
radiated wave length λ has not being
concretized. That’s why the purpose of
writing this paper was in the determining the
exact values of n and k of the mentioned
objects for the definite wave lengths.
It becomes even more complicated even
because of that as it is known from [6, 7], in the
reflected emission from the plant leaf there two
components: a surface component (at the
expense of the reflection boundary air-leaf) and
the inner one (at the expense of the scattering
in the backward direction on the optical
heterogeneities of the leaf structure). As in
methods based on the Fresnel formulas the
reflection coefficient has being used only for
the boundary of two media (in our case it is an
air-leaf surface), then they could be used only
for those wave lengths λ, for which the inner
component is absent or I far less to compare to
a surface one. It is known that [4, 7], that is in
the field of λ < 420 nm and about 660 -670 nm.
measuring R  and R || does not exceed 0.2 –
2. Methods and the objects of
investigation
The reflection of the polarized emission from a
smooth surface boundary between two media
with the indexes of refraction n1 and n2 are
described by Fresnel coefficients rll and r –
are Fresnel coefficients for the wave which is
correspondingly polarized perpendicularly and
in parallels towards the incidence area.
The measured indexes of reflection R || and
R  are equal to the squares rll and r and are
the functions of three variables, i.e. R || (n, k, φ)
end R  (n, k, φ).
Thus, n 
n2
– is a relative index of refraction;
n1
k - is an index of extinction; φ – the angle of
incidence.
For the experimental determination of n and k it
is necessary to have two equations, which could
be obtained by the measuring of the indexes of
reflection R || and R  for two fixed angles of
incidence φ1 and φ2, then:
f1 (n,  , 1 ) 
f 2 ( n,  ,  2 ) 
R|| (n,  , 1 )
R (n,  , 1 )
,
R|| (n,  ,  2 )
R (n,  ,  2 )
(1)
.
they are solved by numerical, graphical or
computerized methods. The plants’ leaves
with very smooth surfaces served as the
objects of investigation such as ones of Ficus
australis, Philodendron selloun, Tetrastigma
voneriana, Opuntia compressa.
R || and R  measurements for two angles of
incidence φ1 = 40° , φ2 = 65° and R0 at the
normal incidence were done on the spherical
photometer and by the methods described in
[8, 9] with Nicol’s prism being used as a
polarizer at its inlet port. Relative error of
0.4 %. The investigation at the normal
incidence gave a possibility to choose those
wave lengths for which it is not essential to
insert into the value of the index of reflection
the diffusing scattered component out of the
inner leaf parts particularly for each of the
objects. However, using the given works [4]
was possible to take into account the size of the
internal diffusely dissipated constituent in the
values R  and R || at the calculations of n and k
for Ficusa australis. The choice of the indicated
angles of incidence is in a certain measure
arbitrary, but he must provide a sufficient
difference between the values R  and, that is
instrumental in more exact establishment of
functions f1 (n, k ,1 ) and f 2 (n, k , 2 ) .
The results of investigation for the chosen λ
are given in tabl.1- tabl.4.
Table 1
The reflection index value for Ficus australis
from the consideration internal diffusely
dissipated constituent.
φ1 = 400
φ2 = 650
λ, nm R0
RII
RII
R
R
280 0.050 0.072 0.046 0.137 0.057
340 0.051 0.067 0.047 0.140 0.049
380 0.051 0.071 0.042 0.155 0.051
420 0.051 0.070 0.042 0.161 0.054
480 0.051 0.071 0.042 0.162 0.057
550 0.047 0.082 0.032 0.232 0.057
620 0.047 0.070 0.037 0.170 0.041
660 0.042 0.060 0.031 0.149 0.043
680 0.045 0.068 0.036 0.166 0.049
Table 2
The reflection index value for Philodendron
selloun
φ1 = 400
φ2 = 650
λ, nm R0
RII
RII
R
R
280 0.052 0.080 0.043 0.180 0.050
320 0.052 0.073 0.043 0.174 0.035
360 0.051 0.070 0.036 0.165 0.031
420 0.049 0.067 0.037 0.169 0.028
460 0.048 0.067 0.037 0.169 0.028
660 0.050 0.076 0.032 0.170 0.029
It is known, that at the normal incidence
(n  1) 2  k 2
R0  R  R|| 
,
(n  1) 2  k 2
(2)
because as if n 2  k 2 , then with the
decrease of Ro the value of n also has to be
decreased; if R0 with the wave length is not
practically being changed then the value of n
would be invariable.
Table3
The reflection index value for Opuntia
compressa
λ, nm
R0
280
300
320
440
660
0.050
0.050
0.051
0.062
0.066
φ1 = 400
RII
R
0.070 0.045
0.066 0.045
0.066 0.045
0.079 0.056
0.082 0.060
φ2 = 650
RII
R
0.140 0.050
0.136 0.046
0.134 0.046
0.153 0.055
0.158 0.057
Table 4
The reflection index value for Tetrastigma
voneriana
φ1 = 400
Φ1 = 650
λ, nm R0
RII
RII
R
R
280 0.054 0.080 0.050 0.220 0.060
320 0.055 0.076 0.044 0.207 0.043
360 0.053 0.074 0.039 0.203 0.037
380 0.051 0.074 0.035 0.200 0.034
420 0.057 0.081 0.045 0.212 0.046
660 0.061 0.086 0.050 0.217 0.053
As the plant leaf is a dielectric then this
circumstance becomes a condition of making
the choice of those λ for which the inner
component at the reflection is yet not enough
significant to compare to a surface one and
what is shown in tabl.1- tabl.4. It’s
worthwhile to underline that the investigations
at λ < 280 nm were not carried out as nicol
does not practically transmit in this region,
though a spherical photometer gives such an
opportunity to arrange the measurement of the
reflection indexes starting from λ = 220 nm
[8,9].
Using measuring of value R || and R  and size
of relative errors here, on the basis of formulas
(1) it is possible to expect absolute errors in
determination of functions f1 (n, k ,1 ) and
f 2 (n, k ,2 ) . They are found within the limits
of 0.0016 – 0.0028 for f1 (n, k ,1 ) and 0.001 –
0.0017 for f 2 (n, k ,2 ) .
3. The determination of the optical
constants.
Using computer potentialities n and k could be
found in the following way. Let’s there were
experimentally found the relations R|| / R at the
angles of incidence 1  40 0 and  2  65 0
that are equal correspondingly to 1 and  2 .
It is apparent, that the functions are equal to
zero at the correct values of n and k.
f1 n, k , 1   f1 n, k , 1   1 ,
f 2 n, k ,  2   f 2 n, k ,  2    2
Fig. 1. Values of
(3)
f 1 k  - curve 1 and f 2 k 
- curve 2 for Ficus australis at   280 nm; n =
1.26.
In order to find these values it is necessary to
construct the relationships of f1 n, k , 1  and
f 2 n, k ,  2  in dependence from k, changing
values in wide limits and assuming the
reasonable values of n, as shown in fig.1 and
fig. 2, for the wave length   280 nm in case
of Ficus australis leaf.
At the selected value of n the points of crosssection of both curves with the axis f  0
(marked by the circles in fig. 1) suit the
equations (3) at various values of k. Changing
values of n (fig.2), it might be possible to
reduce two points of the cross-section into one.
2
1
Fig.2. Attached to the methods of the
determination of the optical constants n and
k for Ficus australis at   280 nm.
This condition meets the correct values of n
and k. We act in an analogous way towards all
other λ and the objects of investigation. The
determined in that way values of n and k are
given in table 5. For Ficus australis as the
graphs on fig.3.
Table 5
Values of the optical constants of plants’
leaves.
Tetrastigma Philodendron
Opuntia
λ, nm
voneriana
selloun
compressa
280
300
320
340
360
380
420
440
460
660
k
0.447
-0.447
-0.441
0.437
0.458
--0.480
n
1.325
-1.333
-1.315
1.290
1.330
--1.350
k
0.452
-0.431
-0.435
-0.418
-0.412
0.443
n
1.280
-1.325
-1.300
-1.310
-1.305
1.265
k
0.439
0.427
0.434
----0.479
-0.494
n
1.280
1.300
1.305
----1.355
-1.380
The values of absorption factor  , sm-1,
shown on it are obtained using equation

4  k

.
Similarly one can obtain the error values
of n and k using functions f1 (n, k ,1 )
and f 2 (n, k ,2 ) .
Thay are in range of 0.02 – 0.05 for k and
0.01 – 0.03 for n .
Fig.3. Spectrum: 1- of refraction index n; 2 –
absorption factor α.
Taken into account this fact, one can see
that the absorption factor k for investigated
leafs of plants in investigated spectral range is
practically equal, although in range of
  280 nm and   660 nm one can observe
maxima. At the same time, on the curve
n  f ( ) for leafs of Ficus australis one can
see two anomalous regions: in range   340
nm and near   600  620 nm (fig.3).
4. Conclusion
The determined values of the optical
constants of the plants’ leaves could be used
while studying the phenomena of absorption
and the emission scattering inside the plant
medium with using the methods of optics and
spectroscopy of the scattered objects [10, 11].
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