#### Table 1.

Relationships between Basic Matrices a, b, c, and d

| Product $\mathbf{u}\mathbf{v}$ for $\mathbf{v}=$ | | | |
---|

Base u | a | b | c | d | Transpose ${\mathrm{u}}^{\mathrm{T}}$ | ${\mathrm{u}}^{3}$ | ${\mathrm{u}}^{4}$ |
---|

**a** | **a** | **b** | **c** | **d** | **a** | **a** | **a** |

**b** | **b** | **a** | **d** | **c** | **b** | **b** | **a** |

**c** | **c** | $-\mathbf{d}$ | **a** | $-\mathbf{b}$ | **c** | **c** | **a** |

**d** | **d** | $-\mathbf{c}$ | **b** | $-\mathbf{a}$ | $-\mathbf{d}$ | $-\mathbf{d}$ | **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 ${\mathbf{M}}_{\mathrm{a}}$ for Scattering by a Needle Spheroid.

| Linear | |
---|

| Magnitude | Orientation | Circular |
---|

Dichroism | $\xi =1.618$ | ${\theta}_{\xi}=86.42\xb0$ | $\zeta =0.234$ |

Birefringence | $\tau =13.65\xb0$ | ${\theta}_{\tau}=-6.23\xb0$ | $\varphi =-26.25\xb0$ |

Offset | $\phi =-3.63\xb0$ | $\mathrm{\Delta}\theta =92.65\xb0$ | |

#### Table 4.

Diagonal Elements of $\u3008\mathrm{m}\u3009$ and $D$ for ${\mathbf{M}}_{\mathrm{b}}$ for Diffraction by a Holographic Grating

${\mathrm{Element}}_{\mathrm{jj}}$ | $\u3008{m}_{\mathrm{j}\mathrm{j}}\u3009$ | ${D}_{\mathrm{j}}$ |
---|

00 | 0.9179 | 0.0821 |

11 | 0.9086 | 0.0864 |

22 | 0.7266 | $-0.0476$ |

33 | 0.7320 | $-0.0700$ |

#### Table 5.

Polarization Properties for ${\mathbf{M}}_{\mathrm{b}}$ for Diffraction by a Holographic Grating

| Apparent | Intrinsic |
---|

Linear Dichroism $\xi $ | 0.259 | 0.292 |

Orientation ${\theta}_{\xi}$ | $-86.86\xb0$ | $-86.48\xb0$ |

Birefringence $\tau $ | 35.99° | 33.73° |

Orientation ${\theta}_{\tau}$ | $-3.30\xb0$ | $-3.20\xb0$ |

Circular dichroism $\zeta $ | $-0.122$ | $-0.119$ |

Optical activity $\varphi $ | $-1.51\xb0$ | $-1.61\xb0$ |

Offset angle $\phi $ | 0.88° | |

#### Table 6.

Our Decomposition for the Matrix of a Biotissue Measured by Ghosh *et al.* [16]

| | Apparent | Intrinsic |
---|

| Polarization $P$ | Magnitude | Orientation ${\theta}_{\mathrm{a}}$ | Magnitude | Orientation $\theta $ |
---|

Linear dichroism | ${P}_{\mathrm{x}}=0.0181$ | ${\xi}_{\mathrm{a}}=0.019$ | 5.00° | $\xi =0.023$ | 5.44° |

Linear birefringence | ${P}_{\mathrm{z}}=0.5877$ | ${\tau}_{\mathrm{a}}=48.26\xb0$ | $-88.70\xb0$ | $\tau =47.18\xb0$ | $-88.70\xb0$ |

Circular dichroism | ${P}_{\mathrm{c}}=0.0034$ | ${\zeta}_{\mathrm{a}}=0.004$ | | $\zeta =0.004$ | |

Optical activity | ${P}_{\mathrm{r}\mathrm{d}}=0.0465$ | ${\varphi}_{\mathrm{a}}=2.04\xb0$ | | $\varphi =1.87\xb0$ | |

Offset | | $\phi =0.80\xb0$ | $\mathrm{\Delta}{\theta}_{\mathrm{a}}=93.70\xb0$ | | $\mathrm{\Delta}\theta =94.14\xb0$ |

Overall | $P=0.8004$ | | | $D=0.1996$ | |

#### 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 | $-0.84$ | $-0.823$ |

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 | $-1.429$ | $-1.464$ |

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 | |