Linda Lundstrom & Peter Unsbo Royal Institute of Technology (KTH), Sweden

1. Unwrapping Hartman-Shack Images from Highly Aberrated Eyes Using an Iterative B-spline Based Extrapolation Method Linda Lundstrom & Peter Unsbo Royal Institute of Technology (KTH), Sweden

2. Hartman-Shack Wavefront Sensor • Measures the aberrations of the eye, widely used to evaluate the optical quality of normal, abnormal and post-surgery eyes (JZ Liang et al.,JOSA A 1994) • Has the potential of doing objective refraction and giving prescription for patients in seconds (L Thibos et al., J of Vis 2004) • Is the key component for adaptive optics which can improve retinal image to the highest resolution (JZ Liang et al., JOSA A 1997)

3. Aberrations of the eye

4. Why are we interested in the aberrations of the eye? • To understand better how the eye transform optical information into biochemical and neuronal signals; • To improve the design of visual instrumentation (microscopes, telescopes, display systems…); • To improve the quality of visual corrections for people with visual problems (spectacles, contacts, laser refractive surgery, IOL implant…); • To understand better normal and abnormal eye development (emmetropization, myopia, anisometropia…) ; • To “see” what happens in the retina in vivo with high resolution retinal imaging systems.

5. Principle of wavefront sensing From Thibos, Principles of Hartmann-Shack Aberrometry, Wavefront Sensing Congress 2000

6. Principle of wavefront sensing From Thibos, Principles of Hartmann-Shack Aberrometry, Wavefront Sensing Congress 2000

7. Principle of wavefront sensing By comparing the reference pattern and the observed pattern, the offsets of the focus spots of the lenslets Δx and Δ y can be calculated. Then the wavefront W(x, y) can be computed with the following equations.

8. Wavefront sensor in ophthalmic instruments

9. Limitations of SH WF sensing • Can’t measure chromatic aberration; • Light scatter and other noises affect the precision of the measurement; • In the case of big distortion of wavefront, focus spots might overlap, and ambiguity exists for the reconstruction. As a result, the measurable aberrations are relatively small. (Two approaches to this problem: optical manipulations and software-based algorithms)

10. The purpose and the results • Purpose: To extend the dynamic range of Hartman-Shack wavefront sensor using B-spline based extrapolation • The results: The dynamic range of a typical HS sensor increases 3.5 to 13 times compared with a simple unwrapping algorithm

11. Methods Inputs HS spot positions in the HS image Positions of the projected lenslet centers B-spline basis functions used

15. Results Simulations showed that compared with direct method, the proposed algorithm can unwrap 3.5 – 13 times more aberrations. Successful examples form human eyes

16. Disadvantages and future work • Error propagation. One wrong assignment at the early stage will affect all following solutions. • Continuity assumption. The algorithm depends on the assumption that aberrations are continuous over the whole pupil, but for some dramatically abnormal eyes, the sampling can cause huge discontinuity.