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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
21

Atmospheric Turbulence Characterisation Using Scintillation Detection and Ranging

Mohr, Judy Lynette January 2009 (has links)
Astronomical images taken by ground-based telescopes are subject to aberrations induced by the Earth's atmosphere. Adaptive optics (AO) provides a real-time solution to compensate for aberrated wavefronts. The University of Canterbury would like to install an AO system on the 1-m McLellan telescope at Mount John University Observatory (MJUO). The research presented in this thesis is the first step towards this goal. To design an effective AO system it is important to understand the characteristics of the optical turbulence present at a site. Scintillation detection and ranging (SCIDAR) is a remote sensing method capable of measuring the refractive index structure constant, Cn2(h), and the wind velocity profile, V(h). The dominant near ground turbulence (NGT) at MJUO required the use of both pupil-plane and generalised SCIDAR. A purpose-built SCIDAR system was designed and constructed at low cost, using primarily off-the-shelf components. UC-SCIDAR saw first light at MJUO in 2003, and has since undergone several revisions. The current version employs two channels for simultaneous pupil-plane and generalised SCIDAR measurements, and is very portable. Through the use of a different mounting plate the system could be easily placed onto any telescope. Cn2(h) profiling utilised standard analysis techniques. V(h) profiling using data from a 1-m telescope is not common, and existing analysis techniques were extended to provide meaningful V(h) profiles, via the use of partial triplet analysis. Cn2(h) profiling between 2005 and 2007 indicate strong NGT and a weak turbulent layer located at 12 - 14 km above sea level, associated with the tropopause region. During calm weather conditions, an additional layer was detected at 6 - 7 km above sea level. V(h) profiles suggest that the tropopause layer velocity is nominally 12 - 30 m/s, and that NGT velocities range from 2 m/s to over 20 m/s, dependent on weather. Little seasonal variation was detected in either Cn2(h) or V(h) profiles. The average coherence length, $r_0$, was found to be 12+-5 cm and 7+-1 cm for pupil-plane and generalised measurements respectively, for a wavelength of 589 nm. The average isoplanatic angle, $\theta_0$, was 1.5+-0.5 arcseconds and 1.1+-0.4 arcseconds for pupil-plane and generalised profiles respectively. No seasonal trends could be established in the measurements for the Greenwood frequency, $f_G$, due to gaps present in the V(h) profiles obtained. A modified Hufnagel-Valley (HV) model was developed to describe the Cn2(h) profiles at MJUO. The estimated $r_0$ from the model is 6 cm for a wavelength of 589 nm, corresponding to an uncompensated angular resolution, $\theta_{res}$, of 2.5 arcseconds. $\theta_0$ is 0.9 arcseconds. A series of V(h) models were developed, based on the Greenwood wind model with an additional Gaussian peak located at low altitudes, to encompass the various V(h) profiles seen at MJUO. Using the modified HV model for Cn2(h) profiles and the suggested model for V(h) profiles in the presence of moderate ground wind speeds, $f_G$ is estimated at 79 Hz. The Tyler frequency, $f_T$, is estimated at 11 Hz. Due to financial considerations, it is suggested that the initial AO design for MJUO focuses on the correction of tip/tilt only, utilising self-guiding, as it is unlikely that any suitable guide stars would be sufficiently close to the science object. The low $f_T$ suggests that an AO system with a bandwidth in the order of 60 Hz would be adequate for tip/tilt correction.
22

The microwave opacity of ammonia and water vapor: application to remote sensing of the atmosphere of Jupiter

Hanley, Thomas Ryan January 2008 (has links)
Thesis (Ph.D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Dr. Paul G. Steffes; Committee Member: Dr. Gregory D. Durgin; Committee Member: Dr. Robert D. Braun; Committee Member: Dr. Thomas K. Gaylord; Committee Member: Dr. Waymond R. Scott
23

DGPS em Rede: desenvolvimento e implantação via internet utilizando a Rede GNSS do Estado de São Paulo

Dalbelo, Luiz Fernando Antonio [UNESP] 26 February 2010 (has links) (PDF)
Made available in DSpace on 2014-06-11T19:22:25Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-02-26Bitstream added on 2014-06-13T19:07:52Z : No. of bitstreams: 1 dalbelo_lfa_me_prud.pdf: 1258749 bytes, checksum: 413bf515eb63448ca76790ba3eb43c75 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Atualmente é cada vez mais presente na comunidade civil a utilização do Global Positioning System (GPS). Um dos métodos de posicionamento GPS de grande destaque é o Differential GPS (DGPS). Esse método utiliza dois receptores, um como base e outro como móvel. O DGPS tem como princípio básico considerar a alta correlação dos erros provocados pela ionosfera, troposfera e órbita dos satélites. No entanto, com o afastamento entre o usuário e a estação base, a eficiência do método diminui, pois a correlação dos erros é reduzida. Mas, quando se utiliza uma rede de estações de referência, pode-se ter uma melhor modelagem dos erros na área de abrangência da rede. Surge então o conceito de DGPS em Rede (DGPSR). Alguns experimentos realizados com o DGPSR em modo pós-processados apontaram acurácia da ordem de 50 cm. Portanto, nesta pesquisa foi proposta a implementação do DGPSR em tempo real. As correções DGPSR são calculadas em tempo real por meio dos dados obtidos via Internet utilizando o protocolo Ntrip (Networked Transport of RTCM via Internet Protocol). Para isso, foram introduzidas várias alterações no software BNC, software este que foi desenvolvido pelo BKG e realiza a função do NtripClient. No que concerne às estações de referência GPS, foram utilizados dados da rede GNSS do oeste do estado de São Paulo (Rede GNSS/SP). A rede está composta, até o momento, por 10 receptores de alta tecnologia que podem ser conectados diretamente a Internet. Com relação aos resultados pode-se observar que o DGPSR utilizando 4 estações de referência apresentou melhorias de até 32% em planimetria e de 28% em altimetria, quando comparados ao DGPS utilizando somente uma estação de referência. Com relação a avaliação da latência pode-se verifica que latências de até 12 segundos parecem não causar influência nos resultados. / Nowadays, the Global Positioning System (GPS) has been very used by the civil community. One of the GPS positioning methods that have been emphasized is the Differential GPS (DGPS). In this method, two receivers are used. One of them as base and the other as rover station. The DGPS has the basic concept of considering high correlation of the errors caused by ionosphere, troposphere and satellite orbits. However, with the baseline growth the method efficiency decreases, because the errors correlation is reduced. But, using a reference station network it is possible to obtain an error modeling in the area of the network, using the network DGPS concept. Some experiments accomplished with DGPSR post processed mode presented promising results. Accuracy better than 50 cm was obtained. Therefore, in this research the goal is to implement the DGPS in real time. The corrections will be computed through data received by Internet using the Ntrip (Networked Transport of RTCM via Internet Protocol). In order to accomplish that, it was implemented several modifications in the BNC software. This software was developed by BKG and make the function of a NtripClient. It will be used a GPS network that is set up in the west of São Paulo State. This network is composed by 10 receivers of high technology that can be directly connected by Internet. Regarding the results, the DGPSR using 4 reference stations showed improvements of up to 32% in planimetry and 28% in altimetry when compared to pure DGPS. Regarding the assessment of latency it was noted that latencies of up to 12 seconds seems not to cause influence the results.
24

Petrographic and geochemical characterization of the micrometeorite collection from the Sør Rondane Mountains: Nature and origin of the extraterrestrial flux to Earth

Soens, Bastien 17 September 2021 (has links) (PDF)
The Antarctic continent has traditionally been a successful searching ground for meteoritic material due to its cold and dry climate. Meteorites, and their microscopic analogues micrometeorites, were originally sampled from Antarctic ice and snow. Recently, however, a large collection of micrometeorites was discovered in sedimentary traps and moraine deposits from the Transantarctic Mountains, where extraterrestrial dust particles have accumulated for a prolonged time span (ca. 3–4 Ma). Micrometeorites (or ‘cosmic dust’) show unique chemical and isotopic signatures, which originate from a large and diverse amount of asteroidal and cometary bodies within the Solar System. In addition, they document major events such as the origin and evolution of the Solar System, and provide insight into the source region of their precursor bodies. These sedimentary deposits consequently represent a valuable archive that documents the flux of extraterrestrial material to Earth and ancient meteoritic events over Antarctica.Yet, much of this information is lost during the atmospheric entry stage, where cosmic dust is subjected to frictional heating and is partially or completely molten down. This may significantly alter the original physicochemical and isotopic properties of extraterrestrial dust particles. A thorough understanding of these physicochemical processes is thus required to reconstruct the atmospheric entry of cosmic dust (but also larger objects) and interpret their chemical and isotopic data. During the course of this PhD research, multiple sedimentary deposits from the Sør Rondane Mountains (Dronning Maud Land, East Antarctica) were petrographically examined and chemically-isotopically characterized using state-of-the-art instruments. Furthermore, various experiments and numerical models were constructed to replicate the atmospheric entry stage of both small- and large-sized meteoritic material. This study has demonstrated that the Sør Rondane Mountains sedimentary deposits contain a rich and pristine variety of extraterrestrial- and impact-related materials, including micrometeorites, microtektites and meteoritic condensation spherules. Statistical analysis suggests that the Sør Rondane Mountains micrometeorite collection is representative of the contemporary flux of cosmic dust to Earth. Extraterrestrial material is subjected to a complex interplay of redox and volatilization processes during atmospheric entry heating, which allow to explain the chemical trends observed in cosmic dust. Isotopic studies also suggest that at least a minor fraction of the micrometeorite population has sampled new, unknown types of asteroidal and/or cometary bodies. Microtektites and meteoritic condensation spherules have been linked to major meteoritic events on Earth ca. 790 ka and ca. 430 ka ago, respectively, and underline the importance of the Earth’s atmosphere during their formation. The results of this PhD research emphasize the scientific value of Antarctic sedimentary deposits and provide more insight into the processes taking place during the atmospheric entry of extraterrestrial material. / Le continent antarctique a traditionnellement été un terrain de recherche fructueux pour le matériel extraterrestre en raison de son climat froid et sec. Les météorites et leurs analogues microscopiques, les micrométéorites, ont été à l'origine échantillonnés dans la glace et la neige de l'Antarctique. Plus récemment, une grande collection de micrométéorites a été découverte dans des pièges sédimentaires et des dépôts de moraine des montagnes transantarctiques, où des particules de poussière extraterrestres se sont accumulées pendant une période prolongée (environ 3-4 Ma). Les micrométéorites (ou « poussière cosmique ») présentent des signatures chimiques et isotopiques uniques, qui proviennent d'une quantité importante et diversifiée de corps astéroïdes et cométaires au sein du système solaire. En outre, elles documentent des événements majeurs tels que l'origine et l'évolution du système solaire et donnent un aperçu de la région source de leurs corps parents. Ces dépôts sédimentaires représentent par conséquent une archive précieuse qui documente le flux de matière extraterrestre vers la Terre et les événements météoritiques anciens au-dessus de l'Antarctique.Pourtant, une grande partie de cette information est perdue au cours de l'étape d'entrée dans l'atmosphère, où la poussière cosmique est soumise à un chauffage par friction et est partiellement ou complètement fondue. Cela peut altérer considérablement les propriétés physico-chimiques et isotopiques d'origine des particules de poussière extraterrestres. Une compréhension approfondie de ces processus physico-chimiques est donc nécessaire pour reconstituer l'entrée atmosphérique des poussières cosmiques (mais aussi des objets plus gros) et interpréter leurs données chimiques et isotopiques. Au cours de cette recherche de doctorat, plusieurs dépôts sédimentaires des montagnes Sør Rondane (Dronning Maud Land, Antarctique de l'Est) ont été examinés pétrographiquement et caractérisés chimiquement et isotopiquement. En outre, diverses expériences et modèles numériques ont été construits pour reproduire l'étape d'entrée dans l'atmosphère de matériaux météoritiques de petite et de grande taille.Cette étude a démontré que les dépôts sédimentaires des montagnes Sør Rondane contiennent une variété riche et peu altérée de matériaux extraterrestres et de cratères d’impacts, notamment des micrométéorites, des microtektites et des sphérules de condensation météoritique. L'analyse statistique suggère que la collection de micrométéorites des montagnes Sør Rondane est représentative du flux contemporain de poussière cosmique vers la Terre. La matière extraterrestre est soumise à une interaction complexe de processus d'oxydo-réduction et de volatilisation lors de l'entrée dans l'atmosphère, ce qui permet d'expliquer les tendances chimiques observées dans la poussière cosmique. Des études isotopiques suggèrent également qu'au moins une fraction mineure de la population de micrométéorites a échantillonné de nouveaux types inconnus d’astéroïdes et/ou de comètes. Les microtektites et les sphérules de condensation météoritiques ont été liées à des événements météoritiques majeurs sur Terre il y a ~790 ka et ~430 ka, respectivement, et soulignent l'importance de l'atmosphère terrestre lors de leur formation. Les résultats de cette recherche doctorale soulignent la valeur scientifique des dépôts sédimentaires de l'Antarctique et donnent un meilleur aperçu des processus qui se déroulent lors de l'entrée dans l'atmosphère de matière extraterrestre / Doctorat en Sciences / info:eu-repo/semantics/nonPublished
25

Experimental collection of laser beam irradiance data at Kennedy Space Center to support fade statistics based on the gamma-gamma distribution

Stalder, John 01 January 2004 (has links)
No description available.
26

Détection des zones d'ombre par les couleurs photométriques invariantes : application aux données IKONOS de Sherbrooke / Detection of shadow areas by the use of invariant photometric colors : application to IKONOS data of Sherbrooke

Akif, Said January 2007 (has links)
Résumé : L’ombre sur l’imagerie satellitaire à très haute résolution spatiale a suscité relativement peu de travaux de recherche en télédétection. La présente étude a pour objectif la détection des zones d’ombre sur l’imagerie IKONOS via l’exploitation des caractéristiques des couleurs de l’ombre. Ces caractéristiques découlent des couleurs photométriques invariantes issues des transformées couleurs. L’approche proposée a pour but d’évaluer dans un premier temps, le potentiel des transformées RGB normalisé, IHS (Intensity, Hue, Saturation), HSV (Hue, Saturation, Value), C[indice inférieur 1] C[indice inférieur 2] C[indice inférieur 3], L[indice inférieur 1] L[indice inférieur 2] L[indice inférieur 3] et M[indice inférieur 1] M[indice inférieur 2] M[indice inférieur 3] (Gevers and Smeulders, 1999) à discriminer les zones d’ombre. Cette évaluation s’est effectuée sur deux images simples dont la première est une image d’extérieur affectée par les effets atmosphériques, et la deuxième est une image d’intérieur, illuminée par une source de lumière artificielle. Les effets atmosphériques, notamment la dispersion, conduisent à la saturation maximale des zones d’ombre sur l’image d’extérieur. Cette conclusion a été vérifiée sur l’image IKONOS et exploitée pour développer une approche pour la détection de l’ombre sur ce genre de données. La transformée IHS a été retenue pour générer les couleurs photométriques H et S respectivement la teinte et la saturation. Deux dérivées I-S et H+l/I+1 ont été calculées. Ces dernières permettent le rehaussement des zones d’ombre sur l’image IKONOS. Trois méthodes de seuillage ont été appliquées sur les deux dérivées afin de particulariser les régions d’ombre. Les deux images finales issues du seuillage ont été fusionnées. La dernière étape de la recherche a consisté en une validation des résultats. Cette opération a démontré la robustesse de l’approche avec une précision globale moyenne de 80%. La confusion entre les zones d’ombre et les régions sombres est la principale faiblesse de l’approche proposée. Cependant, son amélioration est possible grâce à l’intégration d’autres types d’informations comme la texture et la prise en compte du voisinage. // Abstract : The shadow phenomena on the satellite imagery with very high spatial resolution has been the subject of a few research tasks in remote sensing. The aim of the present study is the detection of the shadow’s areas on IKONOS imagery with the use of the shadow’s colors characteristics. These characteristics were derived from the invariant photometric colors. The purpose of the suggested approach is to evaluate initially, the potential of normalized color RGB, IHS (Intensity, Hue, Saturation), HSV (Hue, Saturation, Value), C[subscript 1] C[subscript 2] C[subscript 3], L[subscript 1] L[subscript 2] L[subscript 3] et M[subscript 1] M[subscript 2] M[subscript 3] (Gevers and Smeulders, 1999) transform colors to discriminate shadow’s areas. This evaluation was carried out on two simple images whose first is an outside scene affected by the atmospheric effects, and the second is an interior one illuminated by artificial light source. The atmospheric effects, in particular dispersion, lead to the maximum saturation of shadow’s zones on the outside image. This conclusion was checked on IKONOS image and exploited to develop a method to detect the shadow on this kind of data. IHS transform was retained to generate the photometric colors hue (H) and saturation (S). Two derived images I-S and H+l/I+1 were calculated. They allow the raising of the shadow’s areas on IKONOS image. Three methods of thresholding were applied to the two derived images in order to differentiate the areas of interest. The two final images resulting from the thresholding were joined. The last stage of research consisted of a validation of the results. This operation showed the robustness of the approach with 80% of precision. Confusion between the shadow’s areas and the dark ones is the principal weakness of the suggested approach. However, this new technique can be improved by introducing other information like texture and nearest neighbor analysis.
27

DGPS em Rede : desenvolvimento e implantação via internet utilizando a Rede GNSS do Estado de São Paulo /

Dalbelo, Luiz Fernando Antonio. January 2010 (has links)
Resumo: Atualmente é cada vez mais presente na comunidade civil a utilização do Global Positioning System (GPS). Um dos métodos de posicionamento GPS de grande destaque é o Differential GPS (DGPS). Esse método utiliza dois receptores, um como base e outro como móvel. O DGPS tem como princípio básico considerar a alta correlação dos erros provocados pela ionosfera, troposfera e órbita dos satélites. No entanto, com o afastamento entre o usuário e a estação base, a eficiência do método diminui, pois a correlação dos erros é reduzida. Mas, quando se utiliza uma rede de estações de referência, pode-se ter uma melhor modelagem dos erros na área de abrangência da rede. Surge então o conceito de DGPS em Rede (DGPSR). Alguns experimentos realizados com o DGPSR em modo pós-processados apontaram acurácia da ordem de 50 cm. Portanto, nesta pesquisa foi proposta a implementação do DGPSR em tempo real. As correções DGPSR são calculadas em tempo real por meio dos dados obtidos via Internet utilizando o protocolo Ntrip (Networked Transport of RTCM via Internet Protocol). Para isso, foram introduzidas várias alterações no software BNC, software este que foi desenvolvido pelo BKG e realiza a função do NtripClient. No que concerne às estações de referência GPS, foram utilizados dados da rede GNSS do oeste do estado de São Paulo (Rede GNSS/SP). A rede está composta, até o momento, por 10 receptores de alta tecnologia que podem ser conectados diretamente a Internet. Com relação aos resultados pode-se observar que o DGPSR utilizando 4 estações de referência apresentou melhorias de até 32% em planimetria e de 28% em altimetria, quando comparados ao DGPS utilizando somente uma estação de referência. Com relação a avaliação da latência pode-se verifica que latências de até 12 segundos parecem não causar influência nos resultados. / Abstract: Nowadays, the Global Positioning System (GPS) has been very used by the civil community. One of the GPS positioning methods that have been emphasized is the Differential GPS (DGPS). In this method, two receivers are used. One of them as base and the other as rover station. The DGPS has the basic concept of considering high correlation of the errors caused by ionosphere, troposphere and satellite orbits. However, with the baseline growth the method efficiency decreases, because the errors correlation is reduced. But, using a reference station network it is possible to obtain an error modeling in the area of the network, using the network DGPS concept. Some experiments accomplished with DGPSR post processed mode presented promising results. Accuracy better than 50 cm was obtained. Therefore, in this research the goal is to implement the DGPS in real time. The corrections will be computed through data received by Internet using the Ntrip (Networked Transport of RTCM via Internet Protocol). In order to accomplish that, it was implemented several modifications in the BNC software. This software was developed by BKG and make the function of a NtripClient. It will be used a GPS network that is set up in the west of São Paulo State. This network is composed by 10 receivers of high technology that can be directly connected by Internet. Regarding the results, the DGPSR using 4 reference stations showed improvements of up to 32% in planimetry and 28% in altimetry when compared to pure DGPS. Regarding the assessment of latency it was noted that latencies of up to 12 seconds seems not to cause influence the results. / Orientador: João Francisco Galera Monico / Coorientador: Milton Hirokazu Shimabukuro / Coorientador: Daniele Barroca Marra Alves / Banca: Eniuce Menezes de Souza / Banca: Eno Darci Saatkamp / Mestre
28

Optical Turbulence Characterization for Ground-Based Astronomy

Hagelin, Susanna January 2010 (has links)
The optical turbulence, which creates perturbations of the wavefronts coming from the stars, is caused by small-scale fluctuations in the index of refraction of the atmosphere and is a problem for astronomers because it limits the maximum resolution of the ground-based telescopes. One way of identifying the best sites to build astronomical observatories, where the influence of the optical turbulence is as small as possible, is to use the standard meteorological parameters to get a first idea of the potential of a site. In the first part of this thesis the three sites on the Internal Antarctic Plateau that are the most interesting for astronomers (Dome A, Dome C and the South Pole) are investigated using the operational analyses of the ECMWF and a ranking of these three sites is presented. The second part of this thesis focuses on the ability of the mesoscale model Meso-NH to simulate the optical turbulence as well as the wind speed at Mt Graham (AZ, USA). A rich sample of measurements of the vertical distribution of the optical turbulence, the largest sample used in this type of study so far, is used to calibrate the Meso-NH model and to quantify its ability to simulate the optical turbulence. The measurements are distributed over different periods of the year thus making it possible to evaluate the performance of the model in different seasons. Both the vertical distribution of the optical turbulence and the astroclimatic parameters (seeing, wavefront coherence time and isoplanatic angle) are investigated. / Felaktigt tryckt som Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 708
29

The microwave opacity of ammonia and water vapor: application to remote sensing of the atmosphere of Jupiter

Hanley, Thomas Ryan 23 June 2008 (has links)
The object of this research program has been to provide a baseline for microwave remote sensing of ammonia and water vapor in the atmosphere of Jupiter through laboratory measurements of their microwave absorption properties. Jupiter is not only the largest planet in our solar system, but one of the most interesting and complex. Despite a handful of spacecraft missions and many astronomical measurements, much of Jupiter s atmospheric dynamics and composition remain a mystery. Although constraints have been formed on the amount of certain gases present, the global abundances and distributions of water vapor (H2O) and ammonia (NH3) are relatively unknown. Measurements of H2O and NH3 in the Jovian atmosphere to hundreds of bars of pressure are best accomplished via passive microwave emission measurements. For these measurements to be accurately interpreted, however, the hydrogen and helium pressure-broadened microwave opacities of H2O and NH3 must be well characterized, a task that is very difficult if based solely on theory and limited laboratory measurements. Therefore, accurate laboratory measurements have been taken under a broad range of conditions that mimic those of the Jovian atmosphere. These measurements, performed using a newly redesigned high-accuracy system, and the corresponding models of microwave opacity that have been developed from them comprise the majority of this work. The models allow more accurate retrievals of H2O and NH3 abundances from previous as well as future missions to Jupiter and the outer planets, such as the NASA New Frontiers class Juno mission scheduled for launch in 2011. This information will enable a greater understanding of the concentration and distribution of H2O and NH3 in the Jovian atmosphere, which will reveal much about how Jupiter and our solar system formed and how similar planets could form in other solar systems, even planets that may be hospitable to life.
30

Phase Statistics For a Lightwave Traveling Through Turbulent Media

Link, Donald J. 01 January 1985 (has links) (PDF)
A probability density function is developed for the phase of light that is the result of adding a signal to noise with K-distributed amplitude and uniform phase. The probability density function of the phase associated with the I-K distribution is also developed. In the process of deriving the probability density function of the phase much I as learned about the relationships between different probability density functions. Three different methods of deriving homodyned K statistics are shown to be equivalent. Two different methods of deriving I-K statistics are shown to be equivalent. Theoretical moments of the homodyned K distribution are compared with experimentally measured moments in order to determine the parameters of the model for different conditions of turbulence. An experiment is proposed for measuring the spatial structure function of the phase in a manner that will allow verifying the accuracy of the new probability density functions of the phase.

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