# Polarization Sensitive Optical Coherence Tomography: A Review of Technology and Applications
## 2 Principles of Light Polarization and PS-OCT  
### Polarization of Light  
Polarization of light describes the geometrical orientation of the oscillations of electromagnetic waves. When considering a light beam as a transverse wave propagating in \(z\)-direction, its electric field vector and magnetic field will not only be perpendicular to each other but also be perpendicular to \(z\). At any spatial coordinate and time point, such a wave can be characterized by the complex-valued field components \(e_{x,y}\) describing the oscillations in \(x\)- and \(y\)-direction, respectively. For a monochromatic plane wave travelling in \(z\)-direction, these two complex-valued components form the so-called Jones vector [11]. Depending on the amplitudes of \(e_{x}\) and \(e_{y}\) and on their respective phase delay \(\delta\), different states of polarization will be observed, as illustrated in Figure 2a. A Jones vector having a relative delay of \(0^{\circ}\) or \(180^{\circ}\) (i.e., half a wave) describes a linear polarization state. In case this linear state oscillates only in \(x\)-direction or only in \(y\)-direction, it is termed a horizontal or vertical linear state, respectively. When the \(x\)- and \(y\)-amplitudes are equal, the state is linear with an orientation of \(+45^{\circ}\) for \(\delta=0^{\circ}\) and linear with an orientation of \(-45^{\circ}\) for \(\delta=180^{\circ}\). If the amplitudes in \(x\)- and \(y\)-direction are equal but \(\delta\) is a quarter of a wave (i.e., \(\delta=\pm 90^{\circ}\)), the Jones vector will describe a right- or left-hand circular polarization state. In the general case of arbitrary \(\delta\) and amplitudes, the wave will be in an elliptical polarization state. As an alternative to describing polarization states by Jones vectors, a three-dimensional space spanned by horizontal/vertical linear state, \(+45^{\circ}/-45^{\circ}\) linear state, and right-/left-hand circular state can be used (Figure 2b). Four-component, real-valued vectors \([I\ Q\ U\ V]^{T}\), so-called Stokes vectors, describe polarization states in this space [12]. Here, \(I\) corresponds to the intensity of light, and \(Q\), \(U\), and \(V\) are the components along the three above-mentioned axes. Unlike Jones vectors, Stokes vectors enable the characterization of light depolarization. In case of fully polarized light, \(I\) corresponds to the length of the vector \([Q\ U\ V]\), i.e., \(I=\sqrt{Q^{2}+U^{2}+V^{2}}\). Then, the light's degree of polarization \(DOP=\sqrt{Q^{2}+U^{2}+V^{2}}/I\) equals unity. In case of depolarization, DOP is less than unity, and equals zero for completely depolarized light. The unit sphere in Figure 2b is called a Poincare sphere. In order to describe the interaction of light with an optical element (or a sample investigated by a PS-OCT system), an operator acts on the polarization vector of the interrogating light beam. In Jones calculus, this operator is a complex-valued 2 \(\times\) 2 matrix called Jones matrix (\(J\)) [11]. The evanescent light beam is represented by \(e_{out}=J\ e_{in}\), where \(e_{in}\) is the input Jones vector (Figure 2c). If the light beam traverses several optical elements (or sample structures), the resulting Jones vector can be calculated by multiplying a cascade of Jones matrices to the input vector, \(J_{N}J_{N-1}\cdots J_{2}J_{1}e_{in}\) where \(J_{1}\) through \(J_{N}\) represent the polarization properties of \(N\) elements (or sample layers). Analogously, real-valued 4 \(\times\) 4 matrices--so-called Muller matrices (\(M\))--are used to describe the interaction of Stokes vectors with optical elements by the Stokes-Muller formalism: \(S_{out}=MS_{in}\) (see Figure 2d) [12]. Different approaches of PS-OCT enable the pixelwise measurement of Jones vectors, Jones matrices, Stokes vectors, or Muller matrices. Since the display and interpretation of these multidimensional quantities is often not straight-forward (or even impossible), PS-OCT imagery usually displays physical polarization measures directly related to relevant sample properties.