Análisis Teórico y Numérico de la Ecuación de Transporte de Irradiancia
The phase of a light wave that has been illuminated after striking a surface gives us information about the shape of the surface and with it the manufacturing quality of it. The techniques used to measure this phase can be divided into two main groups: interferometric techniques and geometric techni...
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| Format: | doctoral thesis |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2021 |
| Country: | México |
| Institution: | Instituto Nacional de Astrofísica, Óptica y Electrónica |
| Repository: | Repositorio Institucional del INAOE |
| Language: | Spanish |
| OAI Identifier: | oai:inaoe.repositorioinstitucional.mx:1009/2140 |
| Online Access: | http://inaoe.repositorioinstitucional.mx/jspui/handle/1009/2140 |
| Access Level: | Open access |
| Keyword: | info:eu-repo/classification/Inspec/Ecuación de Transporte de Irradiancia info:eu-repo/classification/Inspec/Frente de onda info:eu-repo/classification/Inspec/Pruebas ópticas info:eu-repo/classification/cti/1 info:eu-repo/classification/cti/22 info:eu-repo/classification/cti/2209 |
| Summary: | The phase of a light wave that has been illuminated after striking a surface gives us information about the shape of the surface and with it the manufacturing quality of it. The techniques used to measure this phase can be divided into two main groups: interferometric techniques and geometric techniques. However, interferometric techniques require that the instruments used are well aligned and that they have a highly coherent source, while geometrical techniques are limited by the Eikonal approach. Fortunately, there are also optical testing techniques that reconstruct the phase from the measurement of irradiance distributions in two or more planes perpendicular to the propagation direction of the wavefront. These techniques have their theoretical basis in the resolution of the irradiation transport equation (ITE). Previously, the propagation of the electromagnetic radiation in different regions of the spectrum and on different media has been studied. That is why there are different forms of the ITE. However, the equation presented by Teague in 1983 is the most widely used in the field of optics. In 1988 Ichicawa et al. They proposed for the first time a deterministic method of the resolution of the TIE, as well as an experimental demonstration of the recovery of the wavefront. To understand the validity interval of the ITE, it is necessary to know how this equation is deduced. It is important to note that the deduction of the ITE can be achieved both by concepts of physical optics and concepts of geometric optics. To arrive at the ITE by means of physical optics we start from the fact that light is an electromagnetic wave and that therefore it satisfies the wave equation. If we choose a monochromatic wave that has the form of a multiplication between two functions, spatial and temporal-harmonic, respectively, and substitute it in the wave equation, we will obtain a purely spatial differential equation that is known as the Hemholtz equation. |
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