Polarimetric systems design has seen recent utilization of linear systems theory for system descriptions. Although noise optimal systems have been shown, bandwidth performance has not been addressed in depth generally and is particularly lacking for Mueller matrix (active) polarimetric systems. Bandwidth must be considered in a systematic way for remote sensing polarimetric systems design. The systematic approach facilitates both understanding of fundamental constraints and design of higher bandwidth polarimetric systems. Fundamental bandwidth constraints result in production of polarimetric "artifacts" due to channel crosstalk upon Mueller matrix reconstruction. This dissertation analyzes bandwidth trade-offs in spatio-temporal channeled Mueller matrix polarimetric systems. Bandwidth is directly related to the geometric positioning of channels in the Fourier (channel) space, however channel positioning for polarimetric systems is constrained both physically and by design parameters like domain separability. We present the physical channel constraints and the constraints imposed when the carriers are separable between space and time. Polarimetric systems are also constrained by noise performance, and there is a trade-off between noise performance and bandwidth. I develop cost functions which account for the trade-off between noise and bandwidth for spatio-temporal polarimetric systems. The cost functions allow a systems designer to jointly optimize systems with good bandwidth and noise performance. Optimization is implemented for a candidate spatio-temporal system design, and high temporal bandwidth systems resulting from the optimization are presented. Systematic errors which impact the bandwidth performance and mitigation strategies for these systematic errors are also presented. Finally, a portable imaging Mueller matrix system is built and analyzed based on the theoretical bandwidth analysis and system bandwidth optimization. Temporal bandwidth performance is improved by 300% over a conventional dual rotating retarder Mueller matrix polarimeter. Reconstruction results from the physical instrument are presented, and issues with the implemented system design are discussed.

Nanostructured, porous materials offer great promise for application in areas such as energy storage, photovoltaics, and catalysis. These materials are often difficult to characterize because they are structurally and compositionally inhomogeneous, and disordered with features to small to be resolved by scanning probe techniques such as atomic force microscopy (AFM) and scanning electron microscopy (SEM). These shortcomings require that new techniques be developed that can be applied to real world systems to elucidate how the interplay of material composition and structure alters their performance. Towards this end, the development of a hybrid quartz crystal microbalance/ ellipsometric porosimetry (QCM/EP) technique is being pursued to facilitate the determination of a number of material parameters such as porosity, pore size distribution, and surface area. Additionally, the use of adsorbate probe molecules of varying polarity gives further information about adsorbate-surface interactions and surface chemistry characteristics. Simultaneous acquisition of both mass-based and refractive index based adsorption isotherms fosters mechanistic understanding about the behavior of adsorbates confined in mesopores while at the same time reducing the uncertainty in the analysis of the optical parameters acquired via ellipsometry. To highlight the power of this approach, studies of TiO₂ and TiC, electrode materials as model systems will be presented that have helped us validate measurement and modeling protocols for extracting physical properties. / text

This dissertation is comprised of two separate topics within the domain of polarization optical engineering. The first topic is a Mueller matrix roots decomposition, and the second topic is polarization computer generated holography. The first four chapters of the dissertation are on the topic of the Mueller matrix roots decomposition. Recently, an order-independent Mueller matrix decomposition was proposed in an effort to organize the nine depolarization degrees of freedom. Chapter 1 discusses relevant Mueller matrix decomposition prior art and the motivation for this work. In chapter 2, the critical computational issues involved in applying this Mueller matrix roots decomposition are addressed, along with a review of the principal root and common methods for its calculation. The choice of the pth root is optimized at p = 10⁵, and computational techniques are proposed which allow singular Mueller matrices and Mueller matrices with a half-wave of retardance to be evaluated with the matrix roots decomposition. A matrix roots algorithm is provided which incorporates these computational results. In chapter 3, the Mueller matrix roots decomposition is reviewed and a set of Mueller matrix generators are discussed. The parameterization of depolarization into three families, each with three degrees of freedom is explained. Analysis of the matrix roots parameters in terms of degree of polarization maps demonstrates that depolarizers fall into two distinct classes: amplitude depolarization in one class, and phase and diagonal depolarization in another class. It is shown that each depolarization family and degree of freedom can be produced by averaging two non-depolarizing Mueller matrix generators. This is extended to provide further insight on two sample measurements, which are analyzed using the matrix roots decomposition. Chapter 4 discusses additional properties of the Mueller matrix roots generators and parameters, along with a pupil aberration application of the matrix roots decomposition. Appendix C, adapted from a conference proceedings paper, presents an application of the matrix roots depolarization parameters for estimating the orientation of a one-dimensionally textured object. The last two chapters are on the topic of polarization computer generated holography. In chapter 5, an interlaced polarization computer-generated hologram (PCGH) is designed to produce specific irradiance and polarization states in the image plane. The PCGH produces a tangentially polarized annular pattern with correlated speckle, which is achieved by a novel application of a diffuser optimization method. Alternating columns of orthogonal linear polarizations illuminate an interlaced PCGH, producing a ratio of polarization of 88% measured on a fabricated sample. In chapter 6, an etched calcite square-wave retarder is designed, fabricated, and demonstrated as an illuminator for an interlaced polarization computer generated hologram (PCGH). The calcite square-wave retarder enables alternating columns of orthogonal linear polarizations to illuminate the interlaced PCGH. Together, these components produce a speckled, tangentially polarized PCGH diffraction pattern with a measured ratio of polarization of 84% and a degree of linear polarization of 0.81. An experimental alignment tolerance analysis is also reported.

<p> </p><p> </p><p> </p><p><p>The main</p><p>objective of this thesis is to study the polarization effects of the beetle <em>Cetonia aurata </em>using Mueller-matrix ellipsometry. The outer shell of the beetle consists of complex microstructures which control the polarization of the reflected light. It has metallic appearance which originates from helicoidal structures. When these microstructures are exposed to polarized or unpolarized light, only left-handed circularly polarized light is reflected. Moreover, the exo-skeleton of the beetle absorbs right-handed polarized light. Multichannel Mueller-matrix ellipsometer or dual rotating compensator ellipsometer, called RC2, from J.A.Woollam is used to measure the polarization caused by different parts of beetle’s body. The 16 Mueller matrix elements are measured in the spectral range 400-800 nm at multiple angles of incidencein the range 40⁰-70⁰. An Optical model is developed to help us understand the nature and type of microstructure which only reflects the green colour circularly polarized light. With the help of multiparametric modeling, we were able to find optical properties and structural parameters. The parameters are: the number of layers, the numbers of sub-layers, their thicknesses, and the orientation with respect to optical axes. This optical model describes the nanostructures which provide the reflection properties similar to the nanostructure found in the beetle <em>Cetonia aurata. </em>The model is also useful for analysis of the optical response data of different materials with multilayer structures.</p></p><p> </p>

The main objective of this thesis is to study the polarization effects of the beetle Cetonia aurata using Mueller-matrix ellipsometry. The outer shell of the beetle consists of complex microstructures which control the polarization of the reflected light. It has metallic appearance which originates from helicoidal structures. When these microstructures are exposed to polarized or unpolarized light, only left-handed circularly polarized light is reflected. Moreover, the exo-skeleton of the beetle absorbs right-handed polarized light. Multichannel Mueller-matrix ellipsometer or dual rotating compensator ellipsometer, called RC2, from J.A.Woollam is used to measure the polarization caused by different parts of beetle’s body. The 16 Mueller matrix elements are measured in the spectral range 400-800 nm at multiple angles of incidencein the range 400-700. An Optical model is developed to help us understand the nature and type of microstructure which only reflects the green colour circularly polarized light. With the help of multiparametric modeling, we were able to find optical properties and structural parameters. The parameters are: the number of layers, the numbers of sub-layers, their thicknesses, and the orientation with respect to optical axes. This optical model describes the nanostructures which provide the reflection properties similar to the nanostructure found in the beetle Cetonia aurata. The model is also useful for analysis of the optical response data of different materials with multilayer structures.

The focus of this thesis is the improvement of acquisition and processing of Mueller matrix polarimetry using a confocal scanning laser ophthalmoscope (CSLO) and the application of Mueller matrix polarimetry to image the retina. Stepper motors were incorporated into a CSLO to semi-automate Mueller matrix polarimetry and were used in retinal image acquisition. Success rates of Fourier transform based edge detection filters, designed to improve the registration of retinal images, were compared. The acquired polarimetry images were used to reassess 2 image quality enhancement techniques, Mueller matrix reconstruction (MMR) and Stokes vector reconstruction (SVR), focusing on the role of auto-contrasting or normalization within the techniques and the degree to which auto-contrasting or normalization is responsible for image quality improvement of the resulting images. Mueller matrix polarimetry was also applied to find the retardance image of a malaria infected retinal blood vessel imaged in a confocal scanning laser microscope (CSLM) to visualize hemozoin within the vessel. Image quality enhancement techniques were also applied and image quality improvement was quantified for this blood vessel. The semi-automation of Mueller matrix polarimetry yielded a significant reduction in experimental acquisition time (80%) and a non-significant reduction in registration time (44%). A larger sample size would give higher power and this result might become significant. The reduction in registration time was most likely due to less movement of the eye, particularly in terms of decreased rotation seen between registered images. Fourier transform edge detection methods increased the success rate of registration from 73.9% to 92.3%. Assessment of the 2 MMR images (max entropy and max signal-to-noise ratio (SNR)) showed that comparison to the best CSLO images (not auto-contrasted) yielded significant average image quality improvements of 158% and 4% when quantified with entropy and SNR, respectively. When compared to best auto-contrasted CSLO images, significant image quality improvements were 11% and 5% for entropy and SNR, respectively. Images constructed from auto-contrasted input images were of significantly higher quality than images reconstructed from original images. Of the 2 other images assessed (modified degree of polarization (DOPM) and the first element of the Stokes vector (S0)), DOPM and S0 yielded significant average image quality improvements quantified by entropy except for the DOPM image of the RNFL. SNR was not improved significantly when either SVR image was compared to the best CSLO images. Compared to the best auto-contrasted CSLO images, neither DOPM nor S0 improved average image quality significantly. This result might change with a larger number of participants. When MMR were applied to images of malaria infected retinal slides, image quality was improved by 19.7% and 15.3% in terms of entropy and SNR, respectively, when compared to the best CSLO image. The DOPM image yielded image quality improvements of 8.6% and -24.3% and the S0 image gave improvements of 9.5% and 9.4% in entropy and SNR, respectively. Although percent increase in image quality was reduced when images were compared to initial auto-contrasted CSLO images, the final image quality was improved when auto-contrasting occurred prior to polarimetry calculations for max SNR and max entropy images. Quantitative values of retardance could not be found due to physical constraints in the CSLM that did not allow for characterization of its polarization properties and vibrational noise. Mueller matrix polarimetry used to find the retardance image of a malaria infected retina sample did yield visualization of hemozoin within the vessel but only qualitatively. In conclusion, improvements in the acquisition and registration of CSLO images were successful in leading to considerably shorter experimentation and processing times. In terms of polarimetric image quality improvement techniques, when compared to the best CSLO image. A large proportion of the improvement was in fact due to partially or completely stretching the pixel values across the dynamic range of the images within the algorithm of each technique. However, in general the image quality was still improved by the Mueller matrix reconstruction techniques using both entropy and SNR to generate the CSLO retinal images and the CSLM imaged malaria infected sample. In the malaria sample, retinal blood vessel visualization was also qualitatively improved. The images yielded from Mueller matrix polarimetry applied to a malaria infected retinal sample localized hemozoin within the blood vessel, but a quantitative image of the phase retardance could not be achieved.

La estructura y componentes del ojo humano hacen que los cambios que se producen sobre el estado de polarización de la luz que emerge de él, tras realizar un doble paso y sufrir una reflexión en la retina, sean complejos y a priori poco predecibles. Esos cambios pueden influir en los resultados obtenidos con dispositivos que analizan la luz reflejada en la retina. Para conocer mejor los cambios que el ojo origina sobre un haz que lo atraviesa y los fenómenos a los que da lugar, se ha llevado a cabo un estudio de la calidad de imagen retiniana en función de los estados de polarización, así como un estudio espacial de los distintos parámetros de polarización a partir del cálculo de matrices de Mueller. Teniendo como base el método de doble paso, se ha diseñado y construido un polarímetro de imagen que utiliza retardadores variables de cristal líquido en los brazos generador y analizador. Con este dispositivo se han registrado series de dieciséis imágenes de doble paso correspondientes a las combinaciones independientes de estados de polarización de entrada y salida. Los resultados para varios sujetos muestran que la calidad de imagen depende en gran medida del estado de polarización de salida. Sin embargo, la influencia de la polarización de entrada, calculada usando matrices de Mueller espacialmente resueltas, juega un papel poco significativo. Por otra parte, el estudio polarimétrico de las imágenes de doble paso muestra que (1) la parte central de las imágenes tiene un grado de polarización del 80% frente a un 25% en la periferia; (2) el retardo introducido depende del observador, aunque la birrefringencia que presenta el ojo es lineal; (3) el dicroísmo es coherente con la longitud de onda empleada y (4) el valor de la polarizancia indica la existencia de cierta birrefringencia circular. / The structure and components of the human eye make changes produced on the polarization state of the light emerging from it after a double-pass through ocular media and a reflection in the retina be complicated and hardly predectible. Those changes can influence on the results obtained with any device analyzing the light reflected in the retina. A study of the retinal image quality as a function of the polarization state has been performed. A spatially resolved polarimetric study of different polarization parameters using Mueller-matrices was also performed. An imaging polarimeter adapted to an ophthalmoscopic double-pass apparatus using two ellectronically controlled liquid-crystal variable retarders has been developed. Series of sixteen double-pass images corresponding to independent combinations generator-analyzer have been recorded. Results obtained for several subjects show that the estimation of the image quality depends strongly on the polarization state in the exit pathway. However, the influence of the entrance polarization, calculated using spatially resolved Mueller-matrices is nearly negligible. On the other hand, the polarimetric study of double-pass images shows that (1) the light forming the central part of the images presents a degree of polarization of 80% while this is reduced to around 25% for the light in the skirts; (2) the retardation introduced by the eye in a double-pass is quite dependent on observers, although the birefringence is linear; (3) the dicroism is coherent with the wavelength used, and (4) the value of the polarizance indicates the existency of circular birrefringence.

The polarization behaviour for six species of Scarab beetles from the Chrysina genus is investigated with Mueller Matrix Spectroscopic Ellipsometer (MMSE). The m41 element of the matrix, which is related to the circular polarization behaviour, is analysed. The ellipticity, degree of polarization and azimuth angle are also presented to get a better understanding of the polarization effect. The measurements were done with a dual rotating compensator ellipsometer. The measured wavelength region was from 240 to 1000 nm and the angle of incidence from 25° to 75° in most of the cases. In general very high ellipticities (near circular) are reported. All specimens studied reflect both right- and left-handed polarized light. Depending on the species, two general types of polarization behaviour were observed. Chrysina macropus and Chrysina peruviana showed m41 values close to 0. Green stripes on Chrysina gloriosa showed similar polarization behaviour whereas gold stripes on the same beetle had much more pronounced m41 variations. Large m41 variations were also observed for Chrysina argenteola, Chrysina chrysargyrea and Chrysina resplendens. Four specimens of Chrysina resplendens show different m41 patterns suggesting differences in their structures.

Light reflected from the scarab beetles Cetonia aurata (C. aurata) and Chrysina gloriosa (C. gloriosa) has left-handed polarization. In this work the polarizing properties and structural characteristics of the cuticles of these two beetles are investigated with two different techniques: scanning electron microscopy (SEM) and Mueller-matrix spectroscopic ellipsometry (MMSE). SEM is used to get cross section images of the epicutucle and the endocuticle. Thicknesses around 18 μm were measured for both layers for C. aurata and between 12 and 16 μm for C. gloriosa. A layered structure is observed in both beetles. In addition, a cusp-like structure is also observed in C. gloriosa. MMSE showed left-handed near-circular polarization of light reflected on both beetles. For C. aurata this is observed in a narrow wavelength range (500-600 nm) and for C. gloriosa in a wider wavelength range (400-700 nm) when measured on golden areas of the cuticle. C. gloriosa also has green areas where the reflected light was linearly polarized. The results are used in regression modelling. A good model approximation was found for C. aurata for angles up to 60 whereas a good starting point for future work was reached for C. gloriosa.

The focus of this thesis is the improvement of acquisition and processing of Mueller matrix polarimetry using a confocal scanning laser ophthalmoscope (CSLO) and the application of Mueller matrix polarimetry to image the retina. Stepper motors were incorporated into a CSLO to semi-automate Mueller matrix polarimetry and were used in retinal image acquisition. Success rates of Fourier transform based edge detection filters, designed to improve the registration of retinal images, were compared. The acquired polarimetry images were used to reassess 2 image quality enhancement techniques, Mueller matrix reconstruction (MMR) and Stokes vector reconstruction (SVR), focusing on the role of auto-contrasting or normalization within the techniques and the degree to which auto-contrasting or normalization is responsible for image quality improvement of the resulting images. Mueller matrix polarimetry was also applied to find the retardance image of a malaria infected retinal blood vessel imaged in a confocal scanning laser microscope (CSLM) to visualize hemozoin within the vessel. Image quality enhancement techniques were also applied and image quality improvement was quantified for this blood vessel. The semi-automation of Mueller matrix polarimetry yielded a significant reduction in experimental acquisition time (80%) and a non-significant reduction in registration time (44%). A larger sample size would give higher power and this result might become significant. The reduction in registration time was most likely due to less movement of the eye, particularly in terms of decreased rotation seen between registered images. Fourier transform edge detection methods increased the success rate of registration from 73.9% to 92.3%. Assessment of the 2 MMR images (max entropy and max signal-to-noise ratio (SNR)) showed that comparison to the best CSLO images (not auto-contrasted) yielded significant average image quality improvements of 158% and 4% when quantified with entropy and SNR, respectively. When compared to best auto-contrasted CSLO images, significant image quality improvements were 11% and 5% for entropy and SNR, respectively. Images constructed from auto-contrasted input images were of significantly higher quality than images reconstructed from original images. Of the 2 other images assessed (modified degree of polarization (DOPM) and the first element of the Stokes vector (S0)), DOPM and S0 yielded significant average image quality improvements quantified by entropy except for the DOPM image of the RNFL. SNR was not improved significantly when either SVR image was compared to the best CSLO images. Compared to the best auto-contrasted CSLO images, neither DOPM nor S0 improved average image quality significantly. This result might change with a larger number of participants. When MMR were applied to images of malaria infected retinal slides, image quality was improved by 19.7% and 15.3% in terms of entropy and SNR, respectively, when compared to the best CSLO image. The DOPM image yielded image quality improvements of 8.6% and -24.3% and the S0 image gave improvements of 9.5% and 9.4% in entropy and SNR, respectively. Although percent increase in image quality was reduced when images were compared to initial auto-contrasted CSLO images, the final image quality was improved when auto-contrasting occurred prior to polarimetry calculations for max SNR and max entropy images. Quantitative values of retardance could not be found due to physical constraints in the CSLM that did not allow for characterization of its polarization properties and vibrational noise. Mueller matrix polarimetry used to find the retardance image of a malaria infected retina sample did yield visualization of hemozoin within the vessel but only qualitatively. In conclusion, improvements in the acquisition and registration of CSLO images were successful in leading to considerably shorter experimentation and processing times. In terms of polarimetric image quality improvement techniques, when compared to the best CSLO image. A large proportion of the improvement was in fact due to partially or completely stretching the pixel values across the dynamic range of the images within the algorithm of each technique. However, in general the image quality was still improved by the Mueller matrix reconstruction techniques using both entropy and SNR to generate the CSLO retinal images and the CSLM imaged malaria infected sample. In the malaria sample, retinal blood vessel visualization was also qualitatively improved. The images yielded from Mueller matrix polarimetry applied to a malaria infected retinal sample localized hemozoin within the blood vessel, but a quantitative image of the phase retardance could not be achieved.