AOS Review • Tucson, Arizona • Sep 10, 2013 1

Paraxial Curvature WFS algorithms

Curvature WFS

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) )

AOS Review • Tucson, Arizona • Sep 10, 2013 2

Algorithmic Challenges for LSST

Curvature WFS

• LSST WFS challenges & algorithmic modifications

• Large Central Obscuration (61%)

• Fast f/number (f/1.23)

• Off-axis Distortion and Vignetting (~1.7o)

• Split Sensor Design (covering 1.51° to 1.84°)

AOS Review • Tucson, Arizona • Sep 10, 2013 3

Tests using PhoSim Images

Curvature WFS

telescope perturbations and atmospheric turbulence turned off

PhosimV3.2.6April 2013

Field=(1.185,1.185) Field=(1.237,1.237)

AOS Review • Tucson, Arizona • Sep 10, 2013 4

Tests of WFS with Perturbed LSST Model

Curvature WFS

AOS Review • Tucson, Arizona • Sep 10, 2013 5

Algorithmic Linearity

Curvature WFS

Z7 on M1M3 (in wave) Z7 on M1M3 (in wave)

AOS Review • Tucson, Arizona • Sep 10, 2013 6

Algorithmic Noise

Curvature WFS

(Algorithmic + atmospheric)Covariancematrix

(Algorithmic + atmospheric)Correlationcoefficients

Variance

Singular values