25 October 2011 Improving the quantitative testing of fast aspherics surfaces with null screen using Dijkstra algorithm
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Abstract
The null screen is a geometric method that allows the testing of fast aspherical surfaces, this method measured the local slope at the surface and by numerical integration the shape of the surface is measured. The usual technique for the numerical evaluation of the surface is the trapezoidal rule, is well-known fact that the truncation error increases with the second power of the spacing between spots of the integration path. Those paths are constructed following spots reflected on the surface and starting in an initial select spot. To reduce the numerical errors in this work we propose the use of the Dijkstra algorithm.1 This algorithm can find the shortest path from one spot (or vertex) to another spot in a weighted connex graph. Using a modification of the algorithm it is possible to find the minimal path from one select spot to all others ones. This automates and simplifies the integration process in the test with null screens. In this work is shown the efficient proposed evaluating a previously surface with a traditional process.
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Víctor Iván Moreno Oliva, Álvaro Castañeda Mendoza, Manuel Campos García, Rufino Díaz Uribe, "Improving the quantitative testing of fast aspherics surfaces with null screen using Dijkstra algorithm", Proc. SPIE 8011, 22nd Congress of the International Commission for Optics: Light for the Development of the World, 801125 (25 October 2011); doi: 10.1117/12.903399; https://doi.org/10.1117/12.903399
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