# Polarization Sensitive Optical Coherence Tomography: A Review of Technology and Applications
## 2 Principles of Light Polarization and PS-OCT
### Technical Approaches to PS-OCT
#### 2.4.2 PS-OCT Based on Multiple Input States  
PS-OCT systems using multiple polarization states as an input may provide access to additional polarization quantities. The scheme described in Section 2.4.1 is based on a single circular input state and relies on the assumptions that the sample is not diattenuating (which is a valid assumption for most biological tissues [17; 56]) and that the axis orientation of the birefringent structure does not change along depth [43; 44]. A method to overcome the latter limitation for retinal PS-OCT has been developed to remove the impact of corneal birefringence on birefringence measurements in the back of the eye [57]. Nevertheless, for applications such as PS-OCT in samples with strongly varying birefringent fiber orientations or for many approaches based on single-mode fiber optics, implementations based on multiple polarization states can provide access to Stokes vector quantification, Jones matrix characterization, and Muller matrix measurements [15; 16; 17; 35; 36; 37; 38; 58; 59; 60; 61; 62; 63]. In order to provide measurements of several polarization states, different approaches have been proposed, only a few of which are described here. By adding a polarization modulator (e.g., an electrooptic modulator) in the source arm, different input states can be produced in a sequential manner. In a commonly used scheme depicted in Figure 4c, a consecutive pair of polarization states corresponding to Stokes vectors perpendicular in a Poincare sphere representation is generated at the input of the interferometer. From the polarization states detected at the output of the interferometer, depth-resolved Stokes vectors can be computed [64; 65]. The retardation induced by birefringent tissue is related to the angle of rotation of Stokes vectors on the Poincare sphere. By computing this angle between the Stokes vectors at the sample surface and those within the tissue, cumulative phase retardation can be computed at any sample position [66; 67]. Furthermore, the direction of the optic axis can be determined from rotations of the pair of perpendicular Stokes vectors on the Poincare sphere [68]. In such dual-input PS-OCT systems, polarization parameters such as retardation, axis orientation, and diattenuation can also be assessed using the Jones formalism. In this approach, the measured polarization states in the sample originating from the pair of input polarization states are used to reconstruct the Jones matrix in every image pixel. An eigenvalue analysis of these measured Jones matrices enables the calculation of phase retardation and diattenuation [15; 16]. The Jones matrix approach to PS-OCT also enables the measurement of the optic axis orientation [15; 16]. Depth-resolved measurements of the birefringent axis orientation have recently gained interest for mapping the orientation of birefringent fibers in PS-OCT based tractography of collagenous tissue [69; 70]. Alternatively, using a Mach-Zehnder type interferometer, only the polarization state in the sample arm can be varied [71; 72] from one scan to the next. By multiplexing two different states using a passive polarization delay unit as shown in Figure 4d, the four elements of a Jones matrix can be measured simultaneously [18; 73; 74]. In that case, the sample beam is split into two orthogonal input Jones vectors which travel different path lengths in the sample arm and therefore generate signals at different depths in the OCT image. These two input vectors provide an orthogonal system and their response--i.e., the two Jones vectors measured via multiplexing--readily provides a Jones matrix [15]. Jones matrix OCT relates the Jones matrix \(J_{meas}\) measured at each sample position to a reference matrix (e.g., \(J_{surface}\) at the surface of the sample), thereby yielding a unitary transformation of the sample matrix \(J_{sample}\)[15; 16; 75]  
\[\widetilde{J}_{sample}=J_{meas}\ J_{surface}^{-1}. \tag{9}\]  
Here the tilde denotes the unitary transformation.