Unwrapping Hartman-Shack Images from Highly Aberrated Eyes Using

an Iterative B-spline Based Extrapolation Method

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

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)

Aberrations of the eye

Why are we interested in the aberrations of the eye?

1. To understand better how the eye transform optical information into biochemical and neuronal signals;

2. To improve the design of visual instrumentation (microscopes, telescopes, display systems…);

3. To improve the quality of visual corrections for people with visual problems (spectacles, contacts, laser refractive surgery, IOL implant…);

4. To understand better normal and abnormal eye development (emmetropization, myopia, anisometropia…) ;

5. To “see” what happens in the retina in vivo with high resolution retinal imaging systems.

Principle of wavefront sensing

From Thibos, Principles of Hartmann-Shack Aberrometry, Wavefront Sensing Congress 2000

Principle of wavefront sensing

From Thibos, Principles of Hartmann-Shack Aberrometry, Wavefront Sensing Congress 2000

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.

Wavefront sensor in ophthalmic instruments

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)

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

MethodsInputs

HS spot positions in the HS image

Positions of the projected lenslet centers

B-spline basis functions used

Results

Simulations showed that compared with direct method, the proposed algorithm can unwrap 3.5 – 13 times more aberrations.

Successful examples form human eyes

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.