1. Paraxial Curvature WFS algorithms Curvature WFS AOS Review Tucson, Arizona Sep 10, 20131 Assuming a paraxial beam propagating along the z-axis, we have the transport of intensity equation (TIE):  Iterative FFT: C. Roddier and F. Roddier, J Opt Soc Am A 10, 2277-87 (1993)  Series expansion: T. E. Gureyev and K. A. Nugent, J. Opt. Soc. Am. A 13, 1670-1682 (1996)  Wavefront compensation:  Both the Iterative FFT and the Series Expansion algorithms are first order approximations valid only highly defocused images.  The accuracy of the WCS algorithm can be improved by iteratively compensating the effect of the estimated aberrations on the defocused images. (C. Roddier and F. Roddier, J Opt Soc Am A 10, 2277-87 (1993) )

2. Algorithmic Challenges for LSST Curvature WFS AOS Review Tucson, Arizona Sep 10, 20132 LSST WFS challenges & algorithmic modifications Large Central Obscuration (61%) Fast f/number (f/1.23) Off-axis Distortion and Vignetting (~1.7 o ) Split Sensor Design (covering 1.51° to 1.84°)

3. Tests using PhoSim Images Curvature WFS AOS Review Tucson, Arizona Sep 10, 20133 telescope perturbations and atmospheric turbulence turned off Phosim V3.2.6 April 2013 Field=(1.185,1.185) Field=(1.237,1.237)

4. Tests of WFS with Perturbed LSST Model Curvature WFS AOS Review Tucson, Arizona Sep 10, 20134

5. Algorithmic Linearity Curvature WFS AOS Review Tucson, Arizona Sep 10, 20135 Z7 on M1M3 (in wave)

6. Algorithmic Noise Curvature WFS AOS Review Tucson, Arizona Sep 10, 20136 (Algorithmic + atmospheric) Covariance matrix (Algorithmic + atmospheric) Correlation coefficients Variance Singular values