Theoretical background

When polarized light is allowed to pass through micro-meter depth of the sample, the polarization state of the incoming light is distorted. Polarization analysis can be carried out by Jones calculus as well as Stokes algebra. Again, Jones calculus is limited to fully polarized light whereas Stokes algebra is applied to all polarization states (partially polarized, unpolarized and fully polarized). The polarization state of light can be described using the Stokes vector as follows,

Where, first parameter S₀ describes the total optical field intensity, S₁ describes the difference in intensity between 0⁰ and 90⁰ linearly polarized states, the intensity difference between 45⁰ and -45⁰ linearly polarized states are described by S₂ and the difference in intensity between the right and left-handed circularly polarized states are described by S₃. DOP, DOLP, DOCP and anisotropy (r) of light are defined by the following equations:

DOP represents the polarization property of the light, whose value ranges from 0 to 1. For perfectly polarized light, DOP = 1 and for unpolarized light, Stokes parameter, S₀ = 1, S₁ = S₂ = S₃ = 0 and DOP = 0. Depending on the degree of polarization, the DOP value ranges between 0 and 1 for partially polarized light. DOLP represents the crystalline alignment of molecules parallel to the linear polarization states and the value ranges between 0 and 1. Within the focal volume, the ability of molecules to flip the circularly scattered light is represented by DOCP and the value ranges between 0 and 1. The signal anisotropy is represented by ‘r’ and the value ranges between − 0.5 to 1. The Optical property of the sample responsible for the change in the polarization state of light after its interaction with an optical system can be described by the Mueller matrix [32, 33]. Input Stokes vector (Sin) and output Stokes vector (Sout) of light can be related as follows,

Then, sample Mueller matrix (M) can be measured as,

However, the cryptic nature of 16 element Mueller matrix, leaves behind an unclear understanding of polarization interactions [34]. Hence, it's necessary to decompose the Mueller matrix to gain insight into various properties such as diattenuation, retardance and depolarization. For turbid media such as biological tissue, ‘M’ can be decomposed using Lu-Chipman polar decomposition [35] into three basis matrices as

Where MΔ is depolarization matrix, MR is retardance matrix and MD is diattenuation matrix, respectively.