A numerical method for decomposing discrete wavefront aberration data into their individual azimuthal orders is presented. The approach utilizes the multi-angle averaging method, where the wavefront error is averaged under m equally spaced angular positions. This angular averaging cancels out all those contributions that are not integer multiples of the number of angular positions. Generally, the sampling theorem gives the maximum angular order that can be resolved by the given discrete data set. By combining the multi-angle averaging method at different m with the sampling theorem one can extract not only any distinct azimuthal order including their harmonics but in particular also each fundamental angular order. The basic algorithm is explained and numerically demonstrated. It is also shown how this approach compares to other angular decomposition methods such as Fourier filtering and Zernike decomposition.

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Stephan Reichelt, "Decomposition of non-rotationally symmetric wavefront aberrations into their azimuthal orders," Proc. SPIE 11102, Applied Optical Metrology III, 111020B (Presented at SPIE Optical Engineering + Applications: August 13, 2019; Published: 3 September 2019); https://doi.org/10.1117/12.2528169.