Two bases (one biorthogonal and one orthonormal) are proposed for the expansion of strongly focused (high numerical aperture) scalar monochromatic fields. The performance of these bases is tested and compared, both with each other and with a similar basis proposed by Alonso et al. [Opt. Express14, 6894 (2006)]. It is found that the orthonormal basis proposed herein exhibits the lowest truncation error of these three bases for the same truncation order for the examples considered. Additionally, this basis is advantageous because it allows for the expansion of fields without rotational symmetry.
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Moore et al. (2009) studied this question.
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