Table I
Spherical Targets of Pure Acrylic and Acrylic–Water Composite Used in Experimental Measurements
Target  Radius of the sphere (cm)  Water in acrylic by volume (%)  Mode radius r_{m} of spherical water inclusions (cm) 

311  3.1731  0  — 
314  3.1744  1.6  0.02 
315  3.1731  2.7  0.02 
Table II
Phase Function Measurements of Homogeneous Acrylic Sphere and AcrylicWater Composite Spheres for Linearly Polarized Radiation of Wavelength λ = 3.1835 cm with Electric Vector E in the Scattering Plane
 Phase function I_{22} of a spherical target 




Scattering angle (deg)   314  315 

311  98.4% Acrylic  97.3% Acrylic 

100% Acrylic  1.6% Water  2.7% Water 

5  456.90  577.33  583.61 
10  278.67  398.08  419.21 
15  149.24  258.83  285.44 
20  48.97  125.98  143.59 
25  24.21  67.03  70.42 
30  17.68  24.61  19.52 
35  15.16  9.03  3.73 
40  18.12  6.23  2.97 
45  22.84  10.64  7.77 
50  21.95  13.44  10.88 
55  25.90  19.10  13.51 
60  13.10  12.52  8.13 
65  11.71  8.80  4.63 
70  16.89  9.43  5.77 
75  29.12  17.94  11.29 
80  21.17  15.21  10.10 
85  8.47  7.66  5.14 
90  3.24  3.01  3.04 
95  6.48  3.86  3.86 
100  16.68  11.09  9.77 
105  19.06  14.74  12.88 
110  9.96  9.02  8.62 
115  2.36  3.03  3.10 
120  4.23  0.92  1.74 
125  4.53  2.60  2.13 
130  3.91  3.76  3.13 
135  1.59  3.88  4.06 
140  1.37  1.24  1.98 
145  8.73  2.47  2.32 
150  16.46  4.59  3.26 
155  16.50  4.44  2.48 
160  11.01  1.68  1.22 
165  9.60  3.05  1.24 
170  29.98  17.88  7.83 
Note: The crosspolarized component of scattered radiation was found to be zero for all three spheres.
Table III
Results of a Waveguide Method of Determination of the Refractive Index of Pure Acrylic and of the Effective Refractive Index m_{7} of the Acrylic–Water Composite with the Mode Radius of Spherical Water Inclusions r_{m} = 0.02 cm
Material  Real part of refractive index  Imaginary part of refractive index 

100% Acrylic  1.686  −0.007 
98% Acrylic  1.718  −0.011 
1.6% Water   
97.3% Acrylic  1.750  −0.013 
2.7% Water   
Table IV
Measured Normalized Extinction Cross Section Q_{ext} and Normalized Scattering CrossSection Q_{sc} Obtained by Numerical Integration of the Measured Phase Function and Calculated Normalized Absorption CrossSection Q_{abs} of Investigated Targets at the Wavelength λ = 3.1835 cm
Target  Q_{ext}  Q_{sc}  Q_{abs} 

311 Pure acrylic  2.24 ± 0.05  2.08 ± 0.05  0.16 ± 0.10 
314 1.6% Water  2.41 ± 0.05  2.06 ± 0.05  0.35 ± 0.10 
315 2.7% Water  2.48 ± 0.05  2.02 ± 0.05  0.46 ± 0.10 
Note: Radiation is linearly polarized with electric vector
E in the scattering plane.
Table V
Effective Refractive Indices of Acrylic–Water Composite Material Calculated Using the Eight Different Effective Medium Approximation Described in the Text
 1.6% Water  2.7% Water 





Effective refractive index given by  Re(m)  Im(m)  Re(m)  Im(m) 

Eq. (1) m_{1} Volume average of refractive indices  1.782  −0.045  1.848  −0.073 
Eq. (2) m_{2} Volume average of dielectric constants  1.916  −0.165  2.065  −0.254 
Eq. (3) m_{3} Bruggeman mixing rule  1.723  −0.009  1.750  −0.011 
Eq. (4) m_{4} Maxwell Garnett mixing rule  1.722  −0.009  1.747  −0.011 
Eq. (5) m_{5} Maxwell Garnett inverted  1.847  −0.116  1.953  −0.183 
Eq. (11) m_{6} ChylekSrivastava rule with modified gamma size distribution  1.724  −0.011  1.752  −0.013 
Measured, m_{7} Waveguide method  1.718  −0.011  1.750  −0.013 
Note: Refractive index of water at λ = 3.1835 cm is taken to be
m_{A} = 7.70–2.48
i and of acrylic to be
m_{0} = 1.686–0.007
i.
Table VI
Reduced χ^{2} Values Characterizing the Goodness of the Fit Between the Measured Phase Function and Phase Function Calculated Using Considered Effective Medium Approximations
 Reduced χ^{2} value for 




 1.6% Water  2.7% Water 

Eq. (1) m_{1} Volume average of refractive indices  6.01  4.21 
Eq. (2) m_{2} Volume average of dielectric constants  11.45  8.45 
Eq. (3) m_{3} Bruggeman mixing rule  0.80  2.01 
Eq. (4) m_{4} Maxwell Garnett mixing rule  0.81  2.03 
Eq. (5) m_{5} Maxwell Garnett inverted  10.66  8.27 
Eq. (6)–(10), m_{6} Modified gamma size distribution  0.62  1.41 
Waveguide measurement, m_{7}  0.63  1.41 
Note: Approximations leading to reduced
χ^{2} ≤ 2 are considered to be acceptable, while those with
χ^{2} > 2 are considered nonacceptable. The
χ^{2} value for a homogeneous acrylic sphere is found to be 0.55.
Table VII
Normalized Extinction, Scattering, and Absorption Cross Section of Acrylic–Water Composite Spheres at λ = 3.1835 cm Calculated from the Mie Theory Using Effective Refractive Indices from Table V
 Sphere 314  Sphere 315 

 1.6% Water  2.7% Water 





Effective refractive index given by  Q_{ext}  Q_{sc}  Q_{abs}  Q_{ext}  Q_{sc}  Q_{abs} 

Eq. (1) m_{1} Volume average of refractive indices  2.74  1.81  0.93  2.82  1.78  1.03 
Eq. (2) m_{2} Volume average of dielectric constants  2.62  1.37  1.25  2.51  1.26  1.25 
Eq. (3) m_{3} Bruggeman mixing rule  2.47  2.14  0.33  2.49  2.12  0.37 
Eq. (4) m_{4} Maxwell Garnett mixing rule  2.46  2.14  0.32  2.49  2.13  0.36 
Eq. (5) m_{5} Maxwell Garnett inverted  2.72  1.52  1.20  2.57  1.32  1.25 
Eq. (6)–(10), m_{6} ChylekSrivastava iteration with modified gamma size distribution  2.46  2.11  0.35  2.51  2.08  0.43 
Waveguide measurement, m_{7}  2.46  2.09  0.37  2.50  2.09  0.41 
Experimental results  2.41  2.06  0.35  2.48  2.02  0.46 
 ±0.05  ±0.05  ±0.10  ±0.05  ±0.05  ±0.10 
Note: Radiation is linearly poolarized with electric vector
E in the scattering plane.