ArticleOptics express2020
Average gradient of Zernike polynomials over polygons.
Article in Optics express, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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Who cites it
5 citing papers in PubMed, 11 citations in OpenAlex.
- Telecentric model eye for correction of image distortion in adaptive optics ophthalmoscopes.Biomedical optics express · 2025Article
- Dynamic wavefront distortion in resonant scanners.Applied optics · 2021Article
- Shack-Hartmann wavefront sensor optical dynamic range.Optics express · 2021Article
- Multi-layer Shack-Hartmann wavefront sensing in the point source regime.Biomedical optics express · 2021Article
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Authors and funding
2 authors at 1 institution in 1 country.
Funding
Abstract
Wavefront estimation from slope sensor data is often achieved by fitting measured slopes with Zernike polynomial derivatives averaged over the sampling subapertures. Here we discuss how the calculation of these average derivatives can be reduced to one-dimensional integrals of the Zernike polynomials, rather than their derivatives, along the perimeter of each subaperture. We then use this result to derive closed-form expressions for the average Zernike polynomial derivatives over polygonal areas, only requiring evaluation of polynomials at the polygon vertices. Finally, these expressions are applied to simulated Shack-Hartmann wavefront sensors with 7 and 23 fully illuminated lenslets across a circular pupil, with their accuracy and calculation time compared against commonly used integration methods.
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Registered trials
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