title: Modal estimation of wavefront phase from slopes over elliptical pupils.
abstract: OBJECTIVE
  Measuring the off-axis optical quality of the eye with a Shack-Hartmann wavefront sensor requires methods for reconstructing wavefront from the gradient data defined within an elliptical pupil. Such methods for modal estimation of wavefront aberrations are sensitive to pupil shape.
  
  
  METHODS
  We develop a conceptual framework that reconciles two published, but apparently dissimilar, methods for reconstruction over an elliptical pupil based on Zernike analysis. Our unified treatment shows that the two methods have different interpretations but the vectors of Zernike coefficients they produce are related linearly. Two novel methods based on Fourier series are also introduced for a model of gradient sensors based on Southwell geometry.
  
  
  RESULTS
  All four methods were evaluated numerically with three test-cases: a defocus wavefront (1), a spherocylindrical wavefront (2), and a random-generated wavefront (3). Under noise-free conditions, all four methods reconstructed the tested wavefronts accurately. The reconstruction error is negligible at the level of numerical computation. Furthermore, the Monte-Carlo simulation with test case 2 revealed small differences in sensitivity to noise between the two Zernike methods but no difference between the two Fourier methods. Because of the smoothing effects, the two Zernike-based methods are more robust to noise than are the two Fourier methods. However, Fourier methods are computationally faster.
  
  
  CONCLUSIONS
  All four modal methods are validated methods to reconstruct wavefronts from the gradients over the elliptical pupil. The choice of these methods is application dependent.
authors.affiliation: School of Optometry, Indiana University, Bloomington, Indiana 47405, USA. weix@indiana.edu
authors.forename: Xin
authors.initials: X
authors.lastname: Wei
authors.forename: Larry N
authors.initials: LN
authors.lastname: Thibos
mesh_terms: D003198:Computer Simulation; D005583:Fourier Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods; D011680:Pupil