**5. Error analysis of Mueller matrix polarimeter**

For the retardations close to 00 or 900 the background noise on the detectors introduces a significant and systematic error of 150 at a signal to noise ratio of 10 dB. [35] The coherent detection scheme which calculates the Stokes parameters has better immunity to the system. in the calculation of the *Q* parameter the spectral density in one polarization channel is subtracted from the spectral density in the orthogonal polarization channel, thus eliminating constant background noise terms, and the *U* and *V* parameters are calculated from the cross correlation between the orthogonally polarized channels, eliminating autocorrelation noise. Noise will decrease the degree of polarization, since it will be present as autocorrelation noise in the Stokes parameter I. In the incoherent detection scheme only *V* is measured and the error in the phase retardation is introduced by the decrease of the amplitude of oscillations with increasing depth. In the coherent detection scheme, the Stokes parameters *Q, U*, and V can be renormalized on DOP, restoring the amplitude of the oscillations, and thus eliminating the systematic error.

We have analyzed system errors introduced by the extinction ratio of polarizing optics and chromatic dependence of wave retarders, and errors due to dichroism, i.e., the differences in

Polarization Sensitive Optical Imaging

**6. Experimental results**

the diagonal components.

and Characterization of Soybean Using Stokes-Mueller Matrix Model 263

The experimental setup for Mueller matrix polarimetry is shown schematically in Fig. 1. A light source with spot size is less than 2 mm passes through a Polarizer (P1) and quarter wave-plate (QWP1) and impinges on the sample. The scattered light which emerges from the sample passes through a analyzer (P2) and quarter wave-plate(QWP2), and is then recorded by the detector connected to lock in amplifier or CCD camera system (Pico Star, Lab Vision). The CCD resolution is 12 bit and the lab view software is used for data analysis. The scattering medium (soybean oil) is placed in a cylindrical thin-walled quartz cell (3x2 cm). Soybean oil is an inexpensive, non-toxic liquid with dielectric properties similar to very

In this study the soybean oil is used as tissue like phantom. We recovered optical information by selectively detecting a transmitted component of the scattered photon flux that has its initial polarization state preserved. These photons transmitted through or reemitted from a multiply scattering medium by using relatively inexpensive Mueller matrix polarimeter provides the basis for several potential applications. The measurement technique is based upon an operational principle, which involves the modulation of a polarization state. The resulting modulated light signal is collected by the detector/CCD camera and is analyzed pixel by pixel to calculate individual intensity patterns, which correspond respectively to the 16 components of the scattering Mueller matrix. In brief, the two polarizers and quarter-wave plates inserted in the probing and analyzing beam paths, are generate a periodic signal, this signal carries information about the properties of the medium which induces the transformation of the polarization state of the modulated probing light. The experimental procedure requires collecting of 16 intensity images at various orientations of the polarizing components. The described procedure provides the

The Stokes parameter I of the system in Fig.2 represents the magnitude of the intensity of the scattered light. Thus, any abrupt change in the detected signal indicates strong discontinuity in the refractive index of the specimen. Along with I, other Stokes parameters, *Q, U* and *V* can be used to detect structural changes that are not simply detected from I. Other Stokes parameter images of *U* and *V* show supplement information that there is no apparent level of stress inside the scatterer. Therefore, by analyzing the corresponding series of the polarization patterns one can trace scattering events of different order. Specifically, the data analysis of Fig. 3, suggests several interesting observations regarding the general properties of the scattering Mueller matrix. First, the magnitude of the off-diagonal components of the scattering Mueller matrix is significantly smaller than the magnitude of

In the present experiments, we are able to trace the polarization patterns and to verify that the existing magnitude distributions are preserved. The magnitude and the sign of most of the spatial extent of the matrix components for Fig. 3, 4 closely resemble the form of the Mueller matrix for scattering medium. The next important observation is that the experimental results clearly display several symmetry properties of certain matrix components for homogeneous scattering medium. The seven out of sixteen are independent and other can be calculated through symmetry relation. [39] By comparing the images of Fig. 3, 4, and 5, one can identify the unique features of the Mueller matrix for scattering medium. The axial symmetry of the system provides relation between all the Mueller matrix

low-water-content fatty tissue. For this reason, it is used as the tissue phantom. [38]

possibility to calculate the scattering Mueller matrix for a given sample.

the absorption and scattering coefficients for polarized light in soybean oil. System errors can be kept small by careful design of the system with achromatic elements, but can never be completely eliminated. Dichroism is a more serious problem when interpreting the results as solely due to birefringence. However, Mueller matrix polarimetry measurements have shown that the error due to dichroism is relatively small. [36] The variance in the computed Stokes vectors of transmitted light (excluding effect of birefringence) is due to multiple scattering, speckles, and shot noise (i.e., optimized system). At some depth, the detected signals are limited by shot noise. At shallower depths (i.e., before the shot noise limit) variance in the Stokes parameters is primarily due to the effects of multiple scattering and speckle. Multiple scattering scramble the polarization mainly in a random manner and this offers some means to distinguish it from birefringence. Thus, birefringence induced changes are relatively slow, and the Stokes parameters change according to the Mueller matrix of a linear retarder. [37] However, an optic axis that varies with depth will give changes in the polarization state that will be difficult to distinguish from the random manner of multiple scattering. More research is necessary on this complex problem. We use coherent light source and standard optical filters to minimize these errors for our Mueller matrix polarimeter.

Fig. 1. Experimental setup for measurements of transmitted Mueller matrix elements. A He-Ne laser beam with an output power of 5 mW at a wavelength of 632.5 nm is used as the light source. The laser light is focused on polarizer P1 for obtaining linearly polarized light. The circularly polarized light is generated, by inserting a quarter mica retardation plates behind the linear polarizer. The output polarized light is focus to soybean oil and again pass through linear polarizer, quarter wave plate and recorded on photodiode detector/CCD camera, which is controlled and operated with Lab software. The soybean oil is used as scattering phantom.

The experimental setup for Mueller matrix polarimetry is shown schematically in Fig. 1. A light source with spot size is less than 2 mm passes through a Polarizer (P1) and quarter wave-plate (QWP1) and impinges on the sample. The scattered light which emerges from the sample passes through a analyzer (P2) and quarter wave-plate(QWP2), and is then recorded by the detector connected to lock in amplifier or CCD camera system (Pico Star, Lab Vision). The CCD resolution is 12 bit and the lab view software is used for data analysis. The scattering medium (soybean oil) is placed in a cylindrical thin-walled quartz cell (3x2 cm). Soybean oil is an inexpensive, non-toxic liquid with dielectric properties similar to very low-water-content fatty tissue. For this reason, it is used as the tissue phantom. [38]
