Extraction of effective parameters of turbid media utilizing the Mueller matrix approach: study of glucose sensing

Abstract

Abstract. An analytical technique based on Stokes polarimetry and the Mueller matrix method is proposed for extracting the effective linear birefringence, linear dichroism, circular birefringence, circular dichroism, linear depolarization, and circular depolarization properties of turbid media. In contrast to existing analytical models, the model proposed extracts the effective parameters in a decoupled manner and considers not only the circular dichroism properties of the sample, but also the depolarization properties. The results show that the proposed method enables all of the effective parameters to be measured over the full range. Moreover, it is shown that the extracted value of the depolarization index is unaffected by the order in which the depolarizing Mueller matrix is decomposed during the extraction procedure. Finally, a method is proposed for calibrating the optical rotation angle of a polystyrene microsphere suspension containing dissolved D-glucose (C 6 H 12 O 6 ) powder in accordance with the distance between the sample and the detector. The experimental results show that the sensitivity of the resulting D-glucose measurement is equal to approximately 1.73 deg ∕M.

Mueller polarimetric imaging for surgical and diagnostic applications: a review

“…The Moore-Penrose pseudoinverse can be considered as computing the least squares solution of Equation (35). An oversampling system may contribute to a reduction of system noise (uncorrelated noise).…”

“…The average degree of polarization is thus obtained from the arithmetic mean of the DOP of emergent light corresponding to all of the possible SOPs of fully polarized incident light [33]. These depolarization parameters are useful tools to study depolarization [35][36][37] especially when it is not necessary to further invert the Mueller matrix for retardance and diattenuation information. …”

“…Both M PSG and M PSA entail at least four linear independent state vectors such that neither of the ranks of M PSG and M PSA are less than four to ensure this linear equation has a unique solution; that is, P should contain at least 16 the radiometric measurements to solve Equation (35). When M PSA and M PSG satisfy the minimal requirement for the matrices' ranks, but are not square matrices (i. e. P contains more than 16 radiometric measurements), this implies oversampling of the polarimetric system and their inverses should be replaced by Moore-Penrose pseudoinverse matrices M PSA and M PSG defined by…”

“…The intensity is sequentially sampled during the rotation of the retarders, resulting in a modulated signal, which can be Fourier analysed (Fourier series or Fourier transform), and all the Mueller matrix elements can be derived from the Fourier coefficients. Fourier analysis here serves as an alternative method to the general method based on matrix inverse or pseudoinverse in Equation (36) and (37) to solve Equation (35). The primary advantages of this dual-rotated-retarder configuration are fewer moving parts, reduced instrumentation cost, and that the calibration can be done without the need for reference samples the following assumptions: 1) both the linear retarders used in the PSG and PSA exhibit no diattenuation and depolarization; 2) the increment of rotation of both the linear retarders is highly reproducible [169,170].…”

“…As pivotal parts of a Mueller polarimeter, the PSG and the PSA are constructed to generate the required input SOPs and analyse the output SOPs so as to solve Equation (35) and obtain the Mueller matrix of the sample. The design of many passive polarization measurement devices like ellipsometers or Stokes vector polarimeters can be directly duplicated for the PSA and PSG.…”