May 2006
Volume 47, Issue 13
ARVO Annual Meeting Abstract  |   May 2006
Modal Estimation of Wavefront Aberrations for Irregularly–Shaped Pupils
Author Affiliations & Notes
  • X. Wei
    School of Optometry, Indiana University, Bloomington, IN
  • L. Thibos
    School of Optometry, Indiana University, Bloomington, IN
  • Footnotes
    Commercial Relationships  X. Wei, None; L. Thibos, None.
  • Footnotes
    Support  NEI–EY05109
Investigative Ophthalmology & Visual Science May 2006, Vol.47, 1201. doi:
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      X. Wei, L. Thibos; Modal Estimation of Wavefront Aberrations for Irregularly–Shaped Pupils . Invest. Ophthalmol. Vis. Sci. 2006;47(13):1201.

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      © ARVO (1962-2015); The Authors (2016-present)

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Purpose: : Conventional methods of wavefront reconstruction from measurements of wavefront slope (e.g. modal estimation with Zernike polynomials in a Shack–Hartmann aberrometer) are valid only for circular pupils. Therefore, there is a need for new methods to handle non–circular pupils (e.g. animal eyes, or human eyes for peripheral vision).

Methods: : Many inscribed rectangular domains were overlapped to cover the shape of a non–circular pupil. These rectangular domains are ideally suited for modal reconstruction using the complex exponential expansion of Fourier analysis. The estimated wavefronts of overlapping domains were combined to successively approximate the wavefront over the irregular domain of the pupil. The computational complexity of our algorithm was analyzed using the principles of computer science. Error propagation was analyzed using Monte Carlo simulation (500 repetitions) for a polynomial wavefront contaminated by additive Gaussian noise. The wavefront was defined over an elliptical pupil sampled at 625 points, from which wavefront slopes were computed using conventional (Hudgin) sampling geometry.

Results: : Complexity analysis indicated the algorithm is computationally feasible because it operates in polynomial time, which means the time to completion is proportional to the number of sample points raised to a fixed power. The algorithm successfully reconstructed the test wavefront over an elliptical pupil, which proves the applicability of the algorithm for non–circular pupils. The error propagation ratio (mean = 3.43, standard deviation of 2.01) was only 3 fold larger than expected for the ideal case of rectangular pupils (Freischlad & Koliopoulos, JOSA, 1986).

Conclusions: : Our new algorithm is robust, computationally feasible, non–iterative, and suitable for irregularly shaped pupils besides elliptical. The algorithm is also suitable for other difference–sampling geometries besides the one tested.

Keywords: optical properties • visual fields 

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