Optics is perhaps the most precisely mathematicized of the physical sciences, with a pedigree stretching from Newton to Maxwell. The only comparable field of study with such an elegant and rigorous basis is quantum mechanics, whose history is much shorter. Unlike quantum mechanics, classical optics suffers from none of the phenomenological complications of the "problem of measurement, " yet like quantum mechanics the application of simple principles to complex real situations leads very quickly to mathematical difficulties that are well beyond current analytical and computational methods. For a situation as complex as the interaction of light with living tissue, approximate methods are required. The simplifications made in such approximations may at first sight seem so dramatic as to render the resultant model unrealistic, even though the computational complexity may still be high. It is thus of fundamental importance to compare and contrast such methods and to validate against experimental results.
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