Data on near infrared polarization spectroscopy measurements to evaluate the potential of the Mueller matrix elements in characterization of turbid liquid samples

In this article, a set of 50 turbid liquid samples with different levels of absorption and scattering properties were prepared and measured at various orientations of polarizers and analyzers to obtain the 16 elements of the complete Muller matrix. Partial Least Square (PLS) was used to build calibration models in order to assess the potential of polarization spectroscopy through the elements of Muller matrix to predict chemical and physical parameters.


Data
Several measurements on 50 turbid liquid samples with different level of concentration in scatterers and absorbers were made (Fig. 1). In parallel, diffuse reflectance spectra in different states of polarized light in visible and near-infrared wavelength range were measured with Polarized Light System (Fig. 2). From these spectral raw data, linear combination of these different polarization states were calculated to obtain the complete Mueller matrices (Fig. 3) for each 50 turbid liquid samples corresponding to the processed data set. The details of all databases are given in part 3. With a Partial Least Square (PLS) algorithm, an example of predicting models were obtained for the concentration of absorbers (Fig. 4a) and scatterers (Fig. 4b) for element M 22 of the Muller matrix.

Liquid phantom
Turbid liquid samples were composed of methylene blue (MB), Intralipid 20% solution (IL) and distilled water used as absorbing, scattering and dilution material respectively [2]. IL is an intravenous fat emulsion that contains fat globules which act as scattering particles. MB is a water-soluble nonscattering dye that presents two peaks absorption at 668 nm and 609 nm due to monomer and dimmer forms in aqueous solutions [3]. In contrast, the absorption by water and IL is minimal in the wavelength range. Hence, MB and IL are well-adapted in the considered wavelength range to interpret and to discriminate the effects of scattering and absorption on the measured polarized reflectance spectra.

Polarization spectroscopy system
The experimental setup for studying the diffuse reflectance of polarized light is presented in Fig. 2. This system was the same Polarized Ligth Spectroscopy system (PoLiS) that we used in previous study [4]. The PoLiS system integrates a polarization state generator (PSG) and polarization state analyzer (PSA). Both the PSG and PSA consisted of a rotating broad-band (400e800 nm) linear polarizer (LP) (NT52-557, Edmunds Optics) and a rotating quarter-wave plate (QWP) (AQWP05M À 600, Thorlabs) in order to generate and to select the various polarization states that are needed. Spectral data were collected with a spectrometer (MMS1, Zeiss) in the 350e1100 nm wavelength range at 3 nm intervals.   [5]. A two letter combination corresponds to one measurement. For example, the combination (VP) means that the PSG is adjusted to obtain linear polarization along the vertical axis (y axis) for incoming light and PSA is adjusted to recover linear polarization with a þ 45 offset for reflected light.

Mueller matrix
The Mueller matrix provides the most general and complete description of the response of a medium to excitation by polarized light in either reflection or transmission configurations. Fig. 3 lists the necessary measurements and combinations in order to determinate each matrix element [5]. To obtain the 16 elements of the complete Mueller matrix, it was necessary to measure 7 configurations respectively for both the PSG and PSA: From these 49 configurations in total corresponding to 49 reflectance spectral measurements (7 for incoming polarized light x 7 for reflected polarized light), each matrix element was calculated by the corresponding linear combinations. For example, the M 12 element is obtained by measuring the total reflected intensity for an incident light linearly polarized along the horizontal axis and subtracting from this the total reflected intensity for an incident light linearly polarized along the vertical axis. Finally, except for the first element, each other element of the Muller matrix corresponding to physical properties of the medium considered such as polarization, depolarization or birefringence.

Spectral acquisition
For each turbid liquid samples, diffuse reflectance spectra of polarized light was measured for each of the 49 configurations from the both PSG and PSA. Moreover, for each of these 49 configurations, white diffuse standard (Spectralon®, SRS-99-010. Labsphere) was measured in order to standardize spectra from non-uniformities of all components of the PoLiS system.

PLS algorithm
All computations and multivariate data analysis were performed with Matlab software v. R2015b (The Mathworks Inc., Natick, MA, USA). A Partial Least Square (PLS) algorithm was used to model the physical and chemical parameters of the turbid liquid media. A general PLS model was built using the whole calibration set (two third of the sample) and a predicting set (one third of the sample). The number of Latent Variables (LV) was determined by comparing performances by leave-one-out cross validation method. Two basic statistical parameters including the determination coefficient (R 2 ) and the standard error of cross-validation (SECV) were calculated. These parameters were used to assess the performance of each calibration model for predicting absorbers and scatterers concentration. An example of predicting models for element M 22 of the Muller matrix is presented for the concentration of absorbers (Fig. 4a) and scatterers (Fig. 4b).