Table 1.
Relationships between Basic Matrices a, b, c, and d
| Product for | | | |
---|
Base u | a | b | c | d | Transpose | | |
---|
a | a | b | c | d | a | a | a |
b | b | a | d | c | b | b | a |
c | c | | a | | c | c | a |
d | d | | b | | | | a |
Table 2.
Induced Polarizations by Coupling of Any Two Responses of Type b, c, and d
Coupling | Linear Dichroism | Linear Birefringence |
---|
Linear dichroism | Rotation | Circular dichroism |
Linear birefringence | Circular dichroism | Rotation |
Circular dichroism | Linear birefringence | Linear dichroism |
Circular birefringence | Linear dichroism | Linear birefringence |
Table 3.
Polarization Properties Obtained for for Scattering by a Needle Spheroid.
| Linear | |
---|
| Magnitude | Orientation | Circular |
---|
Dichroism | | | |
Birefringence | | | |
Offset | | | |
Table 4.
Diagonal Elements of and for for Diffraction by a Holographic Grating
| | |
---|
00 | 0.9179 | 0.0821 |
11 | 0.9086 | 0.0864 |
22 | 0.7266 | |
33 | 0.7320 | |
Table 5.
Polarization Properties for for Diffraction by a Holographic Grating
| Apparent | Intrinsic |
---|
Linear Dichroism | 0.259 | 0.292 |
Orientation | | |
Birefringence | 35.99° | 33.73° |
Orientation | | |
Circular dichroism | | |
Optical activity | | |
Offset angle | 0.88° | |
Table 6.
Our Decomposition for the Matrix of a Biotissue Measured by Ghosh et al. [16]
| | Apparent | Intrinsic |
---|
| Polarization | Magnitude | Orientation | Magnitude | Orientation |
---|
Linear dichroism | | | 5.00° | | 5.44° |
Linear birefringence | | | | | |
Circular dichroism | | | | | |
Optical activity | | | | | |
Offset | | | | | |
Overall | | | | | |
Table 7.
Comparison between the Results of Ghosh et al. Polar Decomposition [16] and Ours
Decomposition | Ghosh et al. Input | Ghosh et al. Results | Nee’s Apparent | Nee’s Intrinsic |
---|
Linear retardance (rad) | 0.83 | 0.79 | | |
Optical rotation (°) | 2.14 | 2.05 | 2.04 | 1.87 |
Depolarization | 0.19 | 0.21 | 0.200 | 0.200 |
Diattenuation | 0 | 0.02 | 0.019 | |
Table 8.
Comparison Between Kumar et al. Decompositions by Differential Method [28] and Ours
Decomposition | Kumar et al. input | Kumar et al. results | Nee’s Apparent | Nee’s Intrinsic |
---|
Linear retardance (rad) | 1.574 | 1.386 | | |
Optical rotation (rad) | 0.030 | 0.030 | 0.034 | 0.028 |
Depolarization | 0.188 | 0.211 | 0.209 | 0.209 |
Diattenuation | 0 | 0.030 | 0.028 | |