# Polarization Sensitive Optical Coherence Tomography: A Review of Technology and Applications
## 2 Principles of Light Polarization and PS-OCT
### Polarization Effects  
The polarization state of a light beam can be affected by interaction with optical components or sample structures [7]. In the following, four polarization effects will be described which are relevant for PS-OCT imaging. * Preserved polarization. Many optical components and materials do not (or only negligibly) change the polarization state of light traversing them, i.e., \(J=1\) and \(M=1\). Their interaction can be described by \(e_{out}=Je_{in}=e_{in}\) and \(S_{out}=MS_{in}=S_{in}\). * Birefringence. In birefringent media, differently oriented polarization states experience different speeds of light. When these basis polarizations are orthogonal linear polarizations (as in Figure 2a along the \(x\)- and \(y\)-axes), the effect is referred to as linear birefringence. Birefringence may also be circular or elliptical for respective different bases (eigenvectors); in this review, however, we restrict our discussion to linear birefringence. Linear birefringence occurs for instance in retarders such as wave plates, in crystals, and in many tissues with an oriented (e.g., fibrous) microstructure. Birefringence--i.e., the difference \(\Delta n\) of the refractive indices along the two axes-produces a phase retardation \(\delta\), which is proportional to the length \(L\) of the retarder, \(\delta=\Delta n\cdot L\). The retardation \(\delta\) of a  
Figure 2: Polarization of light. (**a**) Jones vectors. Depending on the amplitudes \(A_{x,y}\) and the relative phase retardation \(\delta\) of the transverse light wave components oscillating in \(x\) and \(z\) direction, different polarization states such as linear for \(\delta=0^{\circ}\) and \(\delta=180^{\circ}\), circular for \(\delta=\pm 45^{\circ}\) and equal amplitudes \(A_{x}=A_{y}\), or elliptical for all other combinations can be described. The vector \(e=[A_{x}\), \(A_{y}\) exp\((i\delta)]^{T}\) is called Jones vector; (**b**) Stokes–Müller representation of polarization states. Vectors in the 3D space spanned by horizontal/vertical linear state, \(+45^{\circ}/-45^{\circ}\) linear state, and right-/left-hand circular state are called Stokes vectors. Stokes vectors (red) describe any elliptical polarization state and their length scales with intensity of polarized light. The unit sphere is called a Poincaré sphere; (**c**) The interaction of a Jones vector with a sample can be described by multiplication with a Jones matrix describing the tissue properties; (**d**) Likewise, the interaction of a Stokes vector with a sample can be calculated by multiplying with a so-called Müller matrix describing the sample polarization properties. quarter wave plate (QWP) for example amounts to 90\({}^{\circ}\) (\(\pi/2\) rad). If aligned with its slow and fast axes at 45\({}^{\circ}\) with respect to the \(x\)- and \(y\)-axes, the QWP would render a horizontal or vertical linear state into a circular polarization state (Figure 2a, center). The Jones matrix of a retarder with a retardation \(\delta\) and aligned with an orientation \(\delta=0\) is represented by \[J_{ret}(\delta,\vartheta=0)=\left[ \begin{array}{cc}e^{i\delta/2}&0\\ 0&e^{-i\delta/2}\end{array} \right]\] (1) If an optical element such as a retarder is rotated by an angle \(\vartheta\), its Jones matrix \(J=J(\vartheta=0)\) is transformed into \(T(\vartheta)\)\(J\)\(T(-\vartheta)\) where \(T(\vartheta)\) is a rotation matrix. In Stokes-Muller formalism, the propagation of light through birefringent tissue is represented by a circular rotation of the Stokes vector tip on the Poincare sphere. PS-OCT approaches based on Jones calculus or Stokes-Muller formalism enable depth-resolved measurements of phase retardation and of birefringent axis orientation [8; 13; 14; 15; 16]. * Diattenuation. Diattenuation (or dichroism) refers to a polarization dependent attenuation in an optical medium. When the axes of a diattenuating optical element or structure are aligned with the \(x\)- and \(y\)-direction, its Jones matrix is represented by \[J_{diatt}(p_{1},p_{2},\vartheta=0)=\left[