Polar decomposition of 3 x 3 Mueller matrix: a tool for quantitative tissue polarimetry

Abstract

The polarization properties of any medium are completely described by the sixteen element Mueller matrix that relates the polarization parameters of the light incident on the medium to that emerging from it. Measurement of all the elements of the matrix requires a minimum of sixteen measurements involving both linear and circularly polarized light. However, for many diagnostic applications, it would be useful if the polarization parameters can be quantified with linear polarization measurements alone. In this paper, we present a method based on polar decomposition of Mueller matrix for quantification of the polarization parameters of a scattering medium using the nine element (3 x 3) Mueller matrix that requires linear polarization measurements only. The methodology for decomposition of the 3 x 3 Mueller matrix is based on the previously developed decomposition process for sixteen element (4 x 4) Mueller matrix but with an assumption that the depolarization of linearly polarized light due to scattering is independent of the orientation angle of the incident linear polarization vector. Studies conducted on various scattering samples demonstrated that this assumption is valid for a turbid medium like biological tissue where the depolarization of linearly polarized light primarily arises due to the randomization of the field vector's direction as a result of multiple scattering. For such medium, polar decomposition of 3 x 3 Mueller matrix can be used to quantify the four independent polarization parameters namely, the linear retardance (delta ), the circular retardance (psi), the linear depolarization coefficient (Delta) and the linear diattenuation (d) with reasonable accuracy. Since this approach requires measurements using linear polarizers only, it considerably simplifies measurement procedure and might find useful applications in tissue diagnosis using the retrieved polarization parameters.

Mueller polarimetric imaging for surgical and diagnostic applications: a review

“…The digital resolution of the system is dependent on the CCD camera used. The acquired 3 3 3 Mueller polarimetric images were interpreted using a similar method to polar decomposition for a complete Mueller matrix [204]. As a result, linear depolarization, retardance and linear diattenuation can be obtained to reconstruct images.…”

The polar decomposition method in the polarimetric study of light scattered by deterministic profiles and dense media

“…La segunda matriz por orden de actuación, , contiene el parámetro de retardo, (que representa la capacidad del sistema para introducir un desfase entre ambas componentes ortogonales o estados propios del retardador), un parámetro azimutal, (que representa el origen de orientación de los estados propios), y la rotación, [9]. MR puede ser expresada como [15] Particularmente, el retardo puede ser obtenido a través de una expresión polarimétrica general:…”

“…2-Medios densos en volumen, altamente difusores, despolarizadores y que presentan actividad óptica. Estos sistemas constituyen una muestra novedosa del potencial de la DP, tanto por su complejidad como por la similitud entre su análisis y el que puede ser llevado a cabo en tejidos biológicos "invivo" [9].…”

Mueller matrix decomposition of diffuse reflectance imaging in skeletal muscle

“…Theoretically, there are multiple possible decomposition families [19]. In this study, we applied the original method introduced by Lu and Chipman [8] and used by others [9][10][11] for tissue characterizations. The specific procedures applied in this study are described below.…”

“…Lu and Chipman [8] introduced the polar decomposition algorithm to derive the diattenuation, retardance, and depolarization matrices from a Mueller matrix. Swami et al [9] explored a simplified decomposition algorithm for use in a subset (3 × 3) of the Mueller matrix measured with only linearly polarized light. Manhas et al [10] and Ghosh et al [11] recently extended Lu and Chipman's original method by further decomposing the total retardance into linear retardance and optical rotation.…”