**1. Introduction**

256 Soybean – Genetics and Novel Techniques for Yield Enhancement

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late blight disease in California, USA, using hyperspectral remote sensing. *International Journal of Applied Earth Observation and Geoinformation*, Vol. 4, No 4, pp. Light polarimetry is a useful tool by which to analyze the modification in the shape and orientation of the field vectors of the electromagnetic radiation which propagates through scattering medium. Among the methods available to analyze turbid media, the use of polarized light has attracted much attention recently, as it has been discovered that multiply scattered photons still maintain partial polarization. [1-4] A typical experiment entails launching a known polarization state in light into a turbid sample and measuring the polarization properties of the reemitted light. The detected signal depends on many variables, including the number and nature of scattering events, the incident polarization state, and the detection geometry. [5-7] In the past few years, several groups have shown how polarization sensitive scattering measurements can be used to measure certain properties of turbid medium such as the average particle size, [8] scattering coefficient, anisotropy factor of particle suspensions , [9] optical material characterization, [10-11] and the study of biological materials. [11-13] An optical polarizers and retarders are rotated to provide additional incident and analyzed polarization states to enable the reconstruction of the 2-D Mueller matrix of various biological sample [14-15]. It has also been shown that the benefits of using polarized light can be combined with different optical modalities. For example, the benefit of using of polarized light in optical coherence tomography (OCT) measurements can significantly improve image contrast. [16-17]

Furthermore, the measurement of polarization parameters of the light scattered benefits from a relatively simple, fast, and convenient data acquisition procedure, [18-19] which motivates the ongoing efforts aimed at further developing the scattering polarization imaging technology. If some of the light retained its polarization properties upon multiple scattering at 1800 transmittion mode and this effect could be quantified and exploited, potentially useful measurements could be made in almost any clinical situation. Since light in the visible and infrared regions of the electromagnetic spectrum is not harmful to biological tissues at moderate flounce levels, has a penetration depth of several millimeters, and has a reasonable chance of scattering out of the tissue and being detected, it would be ideal for making noninvasive measurements. Other practical reasons for studying the behavior of light at 180° would be for the possibility of spatial imaging to map out the locations of sample structures and compositions, and to gain a better general understanding of turbid systems. [20-22]

Polarization Sensitive Optical Imaging

are defined by:[30]

Mueller matrix approach to polarization and light scattering.

mathematically how these optical elements affect a light beam.

0

3

intensity *<sup>t</sup> <sup>I</sup>* incident on the sample and <sup>0</sup><sup>0</sup> *<sup>I</sup>* , <sup>900</sup> *<sup>I</sup>* , <sup>450</sup> *<sup>I</sup>*

*S*

**3. Stokes vector-Mueller matrix formulism**

and Characterization of Soybean Using Stokes-Mueller Matrix Model 259

any material. The necessary procedure is elegantly demonstrated by the Stokes-vector

The research of polarized scattered light deals with the entire scattering process in the context of Stokes-Mueller matrices and polarizations. [29] An introduction to optical polarization often starts with a description of the optical elements which physically act as polarizers and retarders. The Stokes vector-Mueller matrix- calculus is then used to show

A Stokes vector, a 4 x 1 vector, is a mathematical representation of the polarization state of light. [30] It can be represented as a set of six intensity measurements recorded through a set of various polarizing filters. The Stokes vector is composed of four elements, *I, Q, U*, and *V* and provides a complete description of the light polarization state. If the total irradiant

transmitted by a polarizer-retarders are focused to the detector, then, the Stokes parameters

0 0

Table 1. A matrix array showing the polarization measurements, necessary to measure each particular matrix element of the different configurations (polarizer and analyzer) setup.

*U S I I E E <sup>V</sup> <sup>S</sup> I I E E* 

*<sup>I</sup> E E <sup>I</sup> <sup>S</sup> I I Q S E E*

<sup>90</sup> 0 0 <sup>1</sup> <sup>0</sup> <sup>2</sup> 0 0 45 45

0 0 2 cos

*rc lc x y*

*t x y*

, <sup>450</sup> *<sup>I</sup>* 

2 2 0 0

2 2

*x y x y*

0 0

2 sin

, *rc I* , and *lc I* the irradiances

(2)

A comprehensive understanding of light propagation and scattering for the most general case of highly scattering media is yet to be attained. An analysis based on the Stokes vector and Mueller matrix approach provides a theoretical framework, which can be directly related to the experimentally measurable parameters [23-24]. The Stokes vector - Mueller matrix approach for scattering has been extended to characterization of spatially varying polarization patterns for scattered light. In this approach, determining 16 components of the Mueller matrix for the studied object gives a comprehensive description of scattering properties of a sample or a medium in the spatial domain. Rather then being just one number, each of the 16 components of the Mueller matrix is, in fact, a two-dimensional (2D) array of numbers, corresponding to different spatial locations across the surface of the object or medium.[25]

In this study, we consider experimental Mueller matrix of soybean oil (highly tissue like phantom) for their polarization and depolarization observations. The transmitted photons preserve their polarization memory and Mueller matrix represents this information in the form of matrix array and intensity patterns.
