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YEAR BOOK |
Institute of Technology, Tralee
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Geometric optics and the space of oriented lines
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The classic model for the propagation of light is of light particles or photons, travelling along straight lines in space. The dual picture is of light propagating as a wavefront � a surface that is perpendicular to the straight lines and travels along these rays. This model is appropriate when the medium the light is travelling through is homogenous (i.e. the speed of light is constant in the medium).
Geometric optics is the study of light propagation through the investigation of the geometry of these rays and wavefronts. While this model is not suitable for some optical phenomena (e.g. interference, quantum aspects) it is an adequate description for many familiar everyday phenomena (e.g. reflection, refraction and diffraction).
The research being carried out by Dr Brendan Guilfoyle (IT Tralee), in collaboration with Dr Wilhelm Klingenberg (University of Durham, England), involves a careful study of the space of all rays and how subsets of these lines determine visual phenomena.
Reflection and refraction
The simplest interaction of light is that of the reflection off a surface. Given a reflective surface and an incoming wavefront, an outgoing wavefront is formed by reflection.
One of the results of the current research has been new methods for computing reflections. Thus, given the incoming wavefront and the surface, it has been possible to predict the outgoing wavefront. Similarly, given the incoming and outgoing wavefronts, it has been possible to reconstruct the reflective or refractive surface.
Various examples of this scattering of waves off surfaces have been computed analytically by the research team and the results have been encouraging. The range of applications of these new techniques includes 3-dimensional computer graphics, computer vision and radar and imaging technologies. In addition, the computations can be used to compute the geometric optics approximation to quantum forces.
Caustics
Places where light focuses give rise to higher intensity and hence bright patches. These caustics (from the Latin word meaning to burn) have been studied for centuries. An everyday example of a caustic is the coffee cup caustic: the bright heart-shaped patch commonly observed on the surface of a cup of coffee that is formed by reflection of light off the inside of the cup.
For a deep enough cup, a series of caustics are formed by multiple reflections off the inside of the cup. The new methods developed have allowed computation of these caustics in closed form. The caustics were then generated experimentally and compared with the theoretical predictions. The agreement between experiment and prediction was found to be very close.
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Contact: Dr Brendan Guilfoyle, Department of Mathematics and Computing,
IT Tralee, Clash, Tralee, County Kerry;
Tel: 066 7145600; E-mail: [email protected]