We revisited an empirical relationship between the integrated volume depolar- ization ratio, oacc, and the effective multiple scattering factor, -n, on the basis of Monte Carlo simulations of spaceborne lidar backscatter associated with homogeneous wa- ter clouds. The relationship is found to be sensitive to the extinction coefficient and to the particle size. The layer integrated attenuated backscatter is also obtained. Comparisons made between the simulations and statistics derived relationships of the layer integrated depolarization ratio, oacc, and the layer integrated attenuated backscatter, -n, based on the measurement by the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellite show that a cloud with a large effective size or a large extinction coefficient has a relatively large integrated backscatter and a cloud with a small effective size or a large extinction coefficient has a large integrated volume depolarization ratio. The present results also show that optically thin water clouds may not obey the empirical relationship derived by Y. X. Hu. and co-authors.

An adding-doubling method is employed to calculate the reflected Stokes parameters for cirrus cloud layers composed of different habits and effective sizes. The elements of the Mueller matrix are determined from the reflected Stokes parameters by considering four different incident polarization states. The sensitivity of these elements is observed by comparing different ice crystal habits, effective sizes, and optical depth. The Mueller elements are strongly dependent on habit. The three habits, aggregate, bullet rosette, and plate, are observed and the M12/M11,M43/M11 and M44/M11 elements are discussed. The wavelength used is 0.532µm, which is the lidar wavelength used on the CALIPSO satellite. The linear depolarization ratio is also discussed. The method of subtracting the two depolarization ratios, is noted as another way to possibly better distinguish ice crystal habits. The sensitivity of the Mueller matrix to effective size is also observed. For three size distributions, the Mueller elements indicate no strong dependence. This may be due to the assumption of randomly oriented ice. Also, using an absorbing wavelength might provide dependence. Finally, the Mueller elements are dependent on optical depth. For a greater optical depth, the strength of reflection increases while the polarization decreases. As the optical depth increases, any peak-like features become non-existent.

Over one million Americans are afflicted with skin cancer each year. Even though skin cancer has a 95% cure rate, approximately 10,000 people die in the United States each year of this disease. The current ABCDE(F) detection method is not sensitive enough to detect skin cancer in its early stages and requires a biopsy for any suspicious lesions. A lot of unnecessary biopsies, which are painful and costly to the patient, are taken. Therefore, a noninvasive technique is needed that can accurately detect the presence of skin cancer. In this thesis, an optical approach will be presented that has potential to be a noninvasive skin cancer detection technique. Several morphological and biochemical changes occur as tissue becomes cancerous, and therefore the optical properties of the tissue can be used to detect skin cancer. A Mueller matrix imaging system has been developed by our group that measures the 16 or 36-element Mueller matrix, which completely describes the optical properties of the tissue sample. The system is automated and can collect the Mueller matrix in less than one minute. This system will be used to image Sinclair swine, and data analysis techniques will be employed to determine if the system can distinguish between cancerous and noncancerous tissue. System software improvements will also be made, and a new calibration technique will be presented.

Este estudo apresentou uma metodologia para inferir hidrometeoros a partir de medidas polarimétricas de um radar meteorológico de dupla polarização banda X. A metodologia consiste em uma abordagem teórica baseada em simulações numéricas com um modelo de espalhamento Mie (T M atrix e M ueller) e uma experimental pautada na aplicação de um algoritmo de classificação de hidrometeoros (Dolan and Rutledge [2009]). As si- mulações teóricas foram utilizadas para estudar os efeitos da distribuição de tamanho de gotas, temperatura dos hidrometeoros, ângulo de elevação e mistura de hidrometeoros a partir do fator de refletividade do radar (Z), refletividade diferencial (Z DR ), fase diferen- cial especifica (K DP ) e coeficiente de correlação( HV ). Os valores de Z DR são 0.5 dBZ maior para a frequência de banda X do que para um banda S. A partir de Z maior que 45 dBZ K DP começa a ficar maior que 0. Já HV começa a diminuir quando Z é maior que 25 dBZ. Não se observa variações significativas para o graupel, porém para granizo K DP é maior que 0 quando Z é maior que 15 dBZ, entretanto, para água, os valores são consideravelmente menores. Os efeitos de temperatura só são notados quando Z é maior que 60 dBZ. Ao analisar o efeito da elevação, observa-se que Z DR diminui com o aumento da elevação, sendo mais sensível para Z maiores, o mesmo efeito é observado para K DP e HV . Estas variações são mais sensíveis para água e granizo do que para o graupel. Comparando as distribuições exponencial e gama para considerar os efeitos da distribuição do tamanho de gotas para o caso da chuva, nota-se que a distribuição exponenciais é maior que a gama quando as gotas aumentam seu tamanho e diminui sua concentração, devido que na simulação teórica foi utilizado N 0 fixo.Ao analisar os efeitos da co-existência de água e graupel, temos que as gotas de água dominam o sinal de Z quando Z for maior que 30 dBZ, já K DP será positivo(negativo) quando Z for maior(menor) que 35 dBZ da água, desde que Z do graupel seja menor que 10 dBZ, já HV tende a ficar próximo de 1 quanto mais graupel é observado. Para a mistura de granizo e água, Z da água domina o do granizo quando Z é maior que 45 dBZ, K DP é maior(menor) que zero quando Z for maior (menor) que 25 dBZ desde que Z do granizo seja menor que 10 dBZ, já Z DR da água(granizo) domina o do granizo(água) quando Z for maior(menor) que 45 dBZ. Na parte experimental, dois casos observados durante o experimento de campo do Projeto CHUVA no Vale do Paraíba em 8 de Fevereiro e 22 de Março de 2012 foram utilizados. A classificação de hidrometeoros segundo Dolan and Rutledge [2009] indicaram a presença de chuva próximo da superfície proveniente de graupel e granizo. Acima dos 5 km foram identificados a presença de graupel,granizo e cristais de gelo. Ao examinar as regiões classificadas como granizo e graupel dentro da região de 0 e 15 C com os resultados teóricos, é possível explicar a presença concomitante de água e granizo e água e graupel nestas regiões. / This study presents a methodology for inferring hydrometeors from polarimetric mea- surements of a X band double polarization meteorological radar. The methodology consists of a theoretical approach based on numerical simulations with a Mie scattering model (T-Matrix and Mueller) and an experimental approach based on the application of a classification algorithm of hydrometeors (Dolan and Rutledge [2009]). The theoretical simulations were used to study the effects of droplet size distribution, hydrometeor tem- perature, elevation angle and mixture of hydrometeors from radar reflectivity factor (Z), differential reflectivity (Z DR ), specific differential phase (K DP ) and correlation coefficient ( HV ). The values of Z DR are 0.5 dBZ higher for the X band frequency than for the S band frequency. From Z greater than 45 dBZ, K DP starts to get higher than 0. When Z is greater than 25 dBZ, HV starts to decrease. No significant variations are observed for the graupel, however for hail, K DP is greater than 0 when Z is greater than 15 dBZ, but these values were much lower than for water. Temperature effects are only noticed when Z is greater than 60 dBZ. When analyzing the effect of elevation, it is observed that Z DR decreases with increasing elevation, being more sensitive to Z larger; the same effect is observed for K DP and HV . These variations are more sensitive to water and hail than to the graupel. Comparing the exponential and gamma distributions to consider the effects of droplet size distribution in the case of rain, it is noted that the exponential distribution is larger than the gamma when the droplets increase in size and decrease in concentration, due to the fact that in the simulation was used N 0 fixed. When analyzing the effects of co-existence of water and graupel, we have that the water droplets dominate the Z signal when Z is greater than 30 dBZ, K DP will be positive (negative) when Z is greater (lower) than 35 dBZ of water, since Z of the graupel is less than 10 dBZ and HV tends to be close to 1 when more graupel is observed. For the mixture of hail and water, Z of water dominates that of hail when Z is greater than 45 dBZ, K DP is larger (smaller) than zero when Z is larger (smaller) than 25 dBZ since Z of hail is less than 10 dBZ and Z DR of water (hail) dominates hail (water) when Z is greater (lower) than 45 dBZ. In the experimental part, two cases observed during the field experiment of the RAIN Project in Vale do Paraíba on February 8 and March 22, 2012 were used. The classification of hydrometeors according to Dolan and Rutledge [2009] indicated the presence of rain near the surface coming of graupel and hail. Above 5 km were identified the presence of graupel, hail and ice crystals. When examining the regions classified as hail and graupel within the region of 0 and 15 C with the theoretical results, it is possible to explain the concomitant presence of water and hail and water and graupel in these regions.

Este estudo apresentou uma metodologia para inferir hidrometeoros a partir de medidas polarimétricas de um radar meteorológico de dupla polarização banda X. A metodologia consiste em uma abordagem teórica baseada em simulações numéricas com um modelo de espalhamento Mie (T M atrix e M ueller) e uma experimental pautada na aplicação de um algoritmo de classificação de hidrometeoros (Dolan and Rutledge [2009]). As si- mulações teóricas foram utilizadas para estudar os efeitos da distribuição de tamanho de gotas, temperatura dos hidrometeoros, ângulo de elevação e mistura de hidrometeoros a partir do fator de refletividade do radar (Z), refletividade diferencial (Z DR ), fase diferen- cial especifica (K DP ) e coeficiente de correlação( HV ). Os valores de Z DR são 0.5 dBZ maior para a frequência de banda X do que para um banda S. A partir de Z maior que 45 dBZ K DP começa a ficar maior que 0. Já HV começa a diminuir quando Z é maior que 25 dBZ. Não se observa variações significativas para o graupel, porém para granizo K DP é maior que 0 quando Z é maior que 15 dBZ, entretanto, para água, os valores são consideravelmente menores. Os efeitos de temperatura só são notados quando Z é maior que 60 dBZ. Ao analisar o efeito da elevação, observa-se que Z DR diminui com o aumento da elevação, sendo mais sensível para Z maiores, o mesmo efeito é observado para K DP e HV . Estas variações são mais sensíveis para água e granizo do que para o graupel. Comparando as distribuições exponencial e gama para considerar os efeitos da distribuição do tamanho de gotas para o caso da chuva, nota-se que a distribuição exponenciais é maior que a gama quando as gotas aumentam seu tamanho e diminui sua concentração, devido que na simulação teórica foi utilizado N 0 fixo.Ao analisar os efeitos da co-existência de água e graupel, temos que as gotas de água dominam o sinal de Z quando Z for maior que 30 dBZ, já K DP será positivo(negativo) quando Z for maior(menor) que 35 dBZ da água, desde que Z do graupel seja menor que 10 dBZ, já HV tende a ficar próximo de 1 quanto mais graupel é observado. Para a mistura de granizo e água, Z da água domina o do granizo quando Z é maior que 45 dBZ, K DP é maior(menor) que zero quando Z for maior (menor) que 25 dBZ desde que Z do granizo seja menor que 10 dBZ, já Z DR da água(granizo) domina o do granizo(água) quando Z for maior(menor) que 45 dBZ. Na parte experimental, dois casos observados durante o experimento de campo do Projeto CHUVA no Vale do Paraíba em 8 de Fevereiro e 22 de Março de 2012 foram utilizados. A classificação de hidrometeoros segundo Dolan and Rutledge [2009] indicaram a presença de chuva próximo da superfície proveniente de graupel e granizo. Acima dos 5 km foram identificados a presença de graupel,granizo e cristais de gelo. Ao examinar as regiões classificadas como granizo e graupel dentro da região de 0 e 15 C com os resultados teóricos, é possível explicar a presença concomitante de água e granizo e água e graupel nestas regiões. / This study presents a methodology for inferring hydrometeors from polarimetric mea- surements of a X band double polarization meteorological radar. The methodology consists of a theoretical approach based on numerical simulations with a Mie scattering model (T-Matrix and Mueller) and an experimental approach based on the application of a classification algorithm of hydrometeors (Dolan and Rutledge [2009]). The theoretical simulations were used to study the effects of droplet size distribution, hydrometeor tem- perature, elevation angle and mixture of hydrometeors from radar reflectivity factor (Z), differential reflectivity (Z DR ), specific differential phase (K DP ) and correlation coefficient ( HV ). The values of Z DR are 0.5 dBZ higher for the X band frequency than for the S band frequency. From Z greater than 45 dBZ, K DP starts to get higher than 0. When Z is greater than 25 dBZ, HV starts to decrease. No significant variations are observed for the graupel, however for hail, K DP is greater than 0 when Z is greater than 15 dBZ, but these values were much lower than for water. Temperature effects are only noticed when Z is greater than 60 dBZ. When analyzing the effect of elevation, it is observed that Z DR decreases with increasing elevation, being more sensitive to Z larger; the same effect is observed for K DP and HV . These variations are more sensitive to water and hail than to the graupel. Comparing the exponential and gamma distributions to consider the effects of droplet size distribution in the case of rain, it is noted that the exponential distribution is larger than the gamma when the droplets increase in size and decrease in concentration, due to the fact that in the simulation was used N 0 fixed. When analyzing the effects of co-existence of water and graupel, we have that the water droplets dominate the Z signal when Z is greater than 30 dBZ, K DP will be positive (negative) when Z is greater (lower) than 35 dBZ of water, since Z of the graupel is less than 10 dBZ and HV tends to be close to 1 when more graupel is observed. For the mixture of hail and water, Z of water dominates that of hail when Z is greater than 45 dBZ, K DP is larger (smaller) than zero when Z is larger (smaller) than 25 dBZ since Z of hail is less than 10 dBZ and Z DR of water (hail) dominates hail (water) when Z is greater (lower) than 45 dBZ. In the experimental part, two cases observed during the field experiment of the RAIN Project in Vale do Paraíba on February 8 and March 22, 2012 were used. The classification of hydrometeors according to Dolan and Rutledge [2009] indicated the presence of rain near the surface coming of graupel and hail. Above 5 km were identified the presence of graupel, hail and ice crystals. When examining the regions classified as hail and graupel within the region of 0 and 15 C with the theoretical results, it is possible to explain the concomitant presence of water and hail and water and graupel in these regions.

Au cours des dernières vingt années, le domaine de l'imagerie biomédicale a été largement développé. Dans ce cadre, cette thèse vise à la conception et à la réalisation d'un nouveau dispositif exploitant la longueur d'onde et l'état polarimétrique d'un faisceau lumineux. L'objectif final de cette méthode optique est l'application au diagnostic biomédical précoce, et plus particulièrement dans le domaine de la dermatologie. Il est important de rappeler que le milieu analysé ne subit ni biopsie ni injection d'agent de contraste. Ainsi, cette technique est non invasive et s'effectue sans contact. Par ailleurs, comme souvent en ce qui concerne l'optique visible, ce système est à faible coût et la calibration demeure relativement accessible; ce qui en fait un dispositif très bien adapté à l'utilisation en routine médicale a l'instar des sondes optiques qui équipent les saturomètres actuels. Dans une première partie de ce manuscrit, les méthodes mathématiques dites de "Stokes" et de "Mueller" sont présentées. Ceci nous permet d'introduire aisément la description de notre système polarimétrique ainsi que le calcul du degré de polarisation (DOP). Nous réservons tout un chapitre du manuscrit à la calibration du dispositif, à l'évaluation de ses possibilités ainsi qu'à ses limites théoriques et expérimentales. Ce protocole permet donc la mesure du degré de polarisation linéaire, circulaire et elliptique de tout système en rétrodiffusion. Ajoutons que cette mesure s'effectue en multispectrale suivant trois canaux bien définies (rouge, vert et bleu) et le tout en quasi temps-réel, c'est-à-dire a un rythme d'environ 12 images par seconde en pleine résolution. Le DOP, défini comme la différence normalisée des composante orthogonales du champ électrique, est étudiée et corrélé aux propriétés optique de diffusion des systèmes étudiés. Dans un premier temps, en nous appuyant sur une simulation de type Monte Carlo, le dispositif est validé sur de classiques solutions de billes de latex. Nous présenterons ensuite nos premiers résultats sur des images de peau effectuées in-vivo et ceci, sur un échantillon d'une trentaine d'individus. Nous dégageons ainsi les applications potentielles ainsi que les limites de ce dispositif concernant par exemple les signatures de différents phénomènes tels que brulures, cicatrices et naevus. Enfin, une conclusion et les perspectives de ce travail sont énoncées / (…) The domain of the biomedical imaging was widely developed. In this context, this thesis aims at the conception and at the realization of a new plan exploiting the wavelength and the state polarimétrique of a beam of light. The final goal of this optical method is the application in the early biomedical diagnosis, and more particularly in the field of the dermatology. It is important to call back that the analyzed environment does not undergo either biopsy or agent's injection of contrast. So, this technique is not invasive and is made without contact. Besides, as often as regards the visible optics, this system is low-cost and the calibration remains relatively accessible; What makes a device very well adapted to the use in medical routine has the instar of the optical probes which equip the current saturomètres. In a first part of this manuscript, the mathematical methods said about "Stokes" and about "Mueller" are presented. This allows us to introduce easily the description of our system polarimétrique as well as the calculation of the degree of polarization (DOP). We reserve a whole chapter of the manuscript for the calibration of the plan, for the evaluation of its possibilities as well as for his theoretical and experimental limits. This protocol thus allows the measure of the degree of linear, circular and elliptic polarization of any system rétrodiffusion. Let us add that this measure is made in multispectral according to three channels defined well (red, green and blue) and quite there almost time - reality, that is has a rhythm about 12 images per second in full resolution. The DOP, defined as the difference normalized of component orthogonal of the electric field, is studied and correlated in the properties optics of distribution of the studied systems

Measuring the Mueller matrix with optical coherence tomography (OCT) makes it possible to acquire the complete polarization properties of scattering media with three-dimensional spatial resolution. We first proved that the measured degree-of-polarization (DOP) of the backscattered light by OCT remains unity-a conclusion that validated the use of Jones calculus in OCT. A multi-channel Mueller-matrix OCT system was then built to measure the Jones-matrix, which can be transformed into a Mueller matrix, images of scattering biological tissues accurately with single depth scan. We showed that when diattenuation is negligible, the round-trip Jones matrix represents a linear retarder, which is the foundation of conventional PS-OCT, and can be calculated with a single incident polarization state although the one-way Jones matrix generally represents an elliptical retarder; otherwise, two incident polarization states are needed. We discovered the transpose symmetry in the roundtrip Jones matrix, which is critical for eliminating the arbitrary phase difference between the two measured Jones vectors corresponding to the two incident polarization states to yield the correct Jones matrix. We investigated the various contrast mechanisms provided by Mueller-matrix OCT. Our OCT system for the first time offers simultaneously comprehensive polarization contrast mechanisms including the amplitude of birefringence, the orientation of birefringence, and the diattenuation in addition to the polarization-independent intensity contrast, all of which can be extracted from the measured Jones or the equivalent Mueller matrix. The experimental results obtained from rat skin samples, show that Mueller OCT provides complementary structural and functional information on biological samples and reveal that polarization contrast is more sensitive to thermal degeneration of biological tissues than amplitude-based contrast. Finally, an optical-fiber-based multi-channel Mueller-matrix OCT was built and a new rigorous algorithm was developed to retrieve the calibrated polarization properties of a sample. For the first time to our knowledge, fiber-based polarization-sensitive OCT was dynamically calibrated to eliminate the polarization distortion caused by the single-mode optical fiber in the sample arm, thereby overcoming a key technical impediment to the application of optical fibers in this technology.

When the finite-difference time-domain (FDTD) method is applied to light scattering computations, the far fields can be obtained by either a volume integration method, or a surface integration method. In the first study, we investigate the errors associated with the two near-to-far field transform methods. For a scatterer with a small refractive index, the surface approach is more accurate than its volume counterpart for computing the phase functions and extinction efficiencies; however, the volume integral approach is more accurate for computing other scattering matrix elements. If a large refractive index is involved, the results computed from the volume integration method become less accurate, whereas the surface method still retains the same order of accuracy as in the situation of a small refractive index. In my second study, a fourth order symplectic FDTD method is applied to the problem of light scattering by small particles. The total-field/ scattered-field (TF/SF) technique is generalized for providing the incident wave source conditions in the symplectic FDTD (SFDTD) scheme. Numerical examples demonstrate that the fourthorder symplectic FDTD scheme substantially improves the precision of the near field calculation. The major shortcoming of the fourth-order SFDTD scheme is that it requires more computer CPU time than the conventional second-order FDTD scheme if the same grid size is used. My third study is on multiple scattering theory. We develop a 3D Monte Carlo code for the solving vector radiative transfer equation, which is the equation governing the radiation field in a multiple scattering medium. The impulse-response relation for a plane-parallel scattering medium is studied using our 3D Monte Carlo code. For a collimated light beam source, the angular radiance distribution has a dark region as the detector moves away from the incident point. The dark region is gradually filled as multiple scattering increases. We have also studied the effects of the finite size of clouds. Extending the finite size of clouds to infinite layers leads to underestimating the reflected radiance in the multiple scattering region, especially for scattering angles around 90 degrees. The results have important applications in the field of remote sensing.

Measuring the Mueller matrix with optical coherence tomography (OCT) makes it possible to acquire the complete polarization properties of scattering media with three-dimensional spatial resolution. We first proved that the measured degree-of-polarization (DOP) of the backscattered light by OCT remains unity-a conclusion that validated the use of Jones calculus in OCT. A multi-channel Mueller-matrix OCT system was then built to measure the Jones-matrix, which can be transformed into a Mueller matrix, images of scattering biological tissues accurately with single depth scan. We showed that when diattenuation is negligible, the round-trip Jones matrix represents a linear retarder, which is the foundation of conventional PS-OCT, and can be calculated with a single incident polarization state although the one-way Jones matrix generally represents an elliptical retarder; otherwise, two incident polarization states are needed. We discovered the transpose symmetry in the roundtrip Jones matrix, which is critical for eliminating the arbitrary phase difference between the two measured Jones vectors corresponding to the two incident polarization states to yield the correct Jones matrix. We investigated the various contrast mechanisms provided by Mueller-matrix OCT. Our OCT system for the first time offers simultaneously comprehensive polarization contrast mechanisms including the amplitude of birefringence, the orientation of birefringence, and the diattenuation in addition to the polarization-independent intensity contrast, all of which can be extracted from the measured Jones or the equivalent Mueller matrix. The experimental results obtained from rat skin samples, show that Mueller OCT provides complementary structural and functional information on biological samples and reveal that polarization contrast is more sensitive to thermal degeneration of biological tissues than amplitude-based contrast. Finally, an optical-fiber-based multi-channel Mueller-matrix OCT was built and a new rigorous algorithm was developed to retrieve the calibrated polarization properties of a sample. For the first time to our knowledge, fiber-based polarization-sensitive OCT was dynamically calibrated to eliminate the polarization distortion caused by the single-mode optical fiber in the sample arm, thereby overcoming a key technical impediment to the application of optical fibers in this technology.

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