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Optimum
Shape of a Lens
How can the optimum shape of a lens be found? To do this a lens is
built by prisms, with each prism having the height h and the
widths d-i on the top and d-i+1 at the
base. The optimum shape is found if the dispersion of the light rays
is minimized. The dispersion, which is determined by the width of the
prisms, is the basis for the objective function for the optimization
problem.
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Genetic
Optimization
Optimum lens shape can easily be found by an evolutionary
algorithm. The algorithm generates new values (children) for
the d-i by varying the starting values (parents)
randomly. The child with the best value of the quality function
survives and is used as parent for the next iteration. After a few
generations, the optimum lens shape is found. The notebook shown
here demonstrates the process of evolutionary optimization. Each
graph shows the best child of a generation, with the algorithm
yielding the optimum shape for the lens.
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