Author Contact Information: Erik Gross VISX Incorporated 3400 Central Expressway Santa Clara, CA, 95051

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1 Author Contact Information: Erik Gross VISX Incorporated 3400 Central Expressway Santa Clara, CA, Telephone: Fax:

2 Improvements in the Calculation and Visualization of Wavefront- Driven Point Spread Functions. Erik Gross, BS. George Dai, PhD Charles Campbell, PhD Purpose The Point Spread Function (PSF) allows physicians to see aberrations as the patient sees them. The standard methods for calculating a PSF are based on long-standing optical techniques. These methods are suited to astronomy and laser science, but do not capture the subtleties of the human visual system. This paper examines factors that alter perception of visual aberrations and proposes methods for incorporating these factors in the PSF calculation. Methods The following visual effects were simulated and analyzed: Single wavelength vs. multiple wavelengths Chromatic aberration Retinal resolution Wavelength-dependant visual response Stiles-Crawford effect Non-linearity of retinal response The impact of each effect on individual visual perception was characterized based on ocular physiology and the underlying associated physical principles. An algorithm was developed to improve the PSF to represent each effect more accurately. Results PSFs were notably altered by all of the effects. The changes were most noticeable for patients with significant high-order aberrations. The most dramatic changes in the PSF occurred when chromatic aberration and multiple wavelengths were added. Conclusion Standard methods for generating a PSF are inadequate because they do not reflect true visual experiences. By including major visual effects in the calculation, a more realistic PSF can be created. When these factors are combined, they affect vision sufficiently to justify adding them to the PSF.

3 Introduction Wavefront aberrations are not intuitively understood. Terms such as Zernike pentafoil, secondary coma, or peripherally retarded Wavefront are meaningless to the great majority of patients. The wavefront-generated Point Spread Function (PSF) is a more concrete concept that can easily be understood. The PSF quickly captures the scale and significance of wavefront aberrations. PSF shows the aberrations that affect vision and hides those which do not. Seeing the PSF can also be a validating experience for the patient who has lived with visual ghosting, halos or flares. Such patients can describe symptoms, but not truly convey what they see. The PSF offers objective confirmation by allowing the doctor to see what the patient sees. The purpose of this study was to calculate a PSF which more precisely predicts the patient s perception. Methods This method is based on a geometric model of the eye. The patient s wavefront is divided into several thousand small regions, and a beam of light is modeled passing through each region. The beam is deflected by the local first derivative of the wavefront, and is focused by the local second derivative. Each beam is traced to an impact on the retinal plane, and contributes its energy to the overall PSF. To generate a realistic PSF the following effects were added to the model: Polychromatic light source Chromatic aberration of the eye Wavelength-dependant visual response (photopic and scotopic conditions) Adjustable pupil size Stiles-Crawford effect Non-linear retinal response Each effect was tested independently, and in combination with other effects. All effects caused significant changes in the appearance of the PSF. The most significant change was caused by the combination of a polychromatic light source, the chromatic aberration, and wavelength-dependant visual response. By combining these effects with human color sensitivity (mapping wavelengths to Red, Green and Blue intensities) a color PSF can be generated. To determine if the PSF was affected the method of Wavefront reconstruction, a series of PSFs were generated using both a 6 th order Zernike reconstruction and a high resolution Fourier reconstruction.

4 To test the PSF algorithm, a protocol was devised in which patients were asked to draw their own PSFs by looking at a small light against a ruled background. Results The retina demonstrates a logarithmic sensitivity to light that has usually not been included when generating PSFs. It was found that this effect significantly changed the appearance of the PSF and therefore decided that it should be modeled when practical.. When the theoretical pupil size was changed, both the size and shape of the PSF changed significantly. This expected result indicates that when showing a PSF, the pupil size should be included. The Stiles-Crawford effect was found to have the least impact. The effect was largest for patients with large pupils, but even in these cases it did not fundamentally alter the PSF image. The results of the wavefront accuracy tests indicated that 6 th order Zernike reconstruction is not sufficient to generate an accurate PSF. The general sizes and shapes were similar, but the Fourier-based images showed many features that were not visible in the Zernikebased images. Examples are shown in Figure 1. Figure 1 <<On the top row are PSFs for a patient with myopia. The image (a) was generated using a 6 th order Zernike Wavefront reconstruction. The image (b) was from the same Wavefront, but used a high-fidelity Fourier reconstruction. The bottom row shows the same images from a highly aberrated eye. (RMS=.89_) (c & d). Each image covers 25 arc minutes, and the letter E corresponds to the 20/20 line of a Snellen eye chart. The substantial differences between paired images implies that 6 th order Zernike reconstruction is not sufficient to generate and accurate PSF>> An example of the PSF testing protocol result is presented is Figure 2. The patient s drawings closely resembled the generated PSF in both scale and features.

5 Figure 2 <<Testing the PSF: A patient with significant aberration (4 days post-op PRK and re-epithelializing) was measured on a VISX WaveScan device. The data was used to calculate PSFs for OD (a) and OS (b). The patient was shown a light source set against a ruled background, and asked to draw what they saw for each eye. The close match in scale and shape indicates that the PSF is predicting the patients visual perception.>> Discussion Being able to generate a realistic PSF allows a variety of interesting analyses. Some of these applications include: Source-dependant PSF Using the model eye allows different light spectra to be used in generating the PSF. In this study, a white light solar spectrum was used most often, but PSFs were also tested using the spectra of halogen lights, tungsten lights, commercial LEDs, and common street lighting. Results showed that a patient s PSF can be significantly affected by the spectrum. A patient with a good PSF in white light may have a poor PSF if looking at a red LED. Each PSF can be convolved with an image of a traditional Snellen eye chart to estimate the patient s visual acuity under different lighting conditions. Photopic and Scotopic PSF The retinal wavelength response function shifts from photopic conditions (peak sensitivity = 555 nm) to scotopic conditions (peak sensitivity = 507 nm). A daytime and nighttime PSF can be calculated from the same wavefront by allowing the model to shift from one function to the other. Analysis shows that most patients experience a shift towards myopia under nighttime conditions. This myopic shift is explained by the scotopic eye s preference for blue light, which has a greater chromatic shift. This analysis may be useful for patients complaining of night myopia.

6 Partial PSF Typically, a PSF is calculated by simulating light over the entire pupil. However, by using a geometric eye model, a one-to-many relationship is established between each point on the patient s wavefront and the components of the PSF. In one mode of the model, a user is presented with an eye image of the patient s pupil. The user can point a curser at a portion of the pupil and immediately see which part of the PSF is generated by that part of the wavefront. This technique is useful when the eye is highly aberrated eye. In effect, it is possible to isolate features in the PSF and relate the cause of a particular flare or ghost to a specific area on the eye. Volumetric PSF The PSF captures an image at the patient s retina. By extending the model, it is possible to calculate a PSF at theoretical locations before and beyond the retina. By arranging a series of these images into a three-dimensional array, the PSF can be viewed as an extended three-dimensional structure called the Volumetric Point Spread Function (VPSF). The VPSF can be used to study a patient s depth of focus, and to see the interaction of the patient s defocus and high-order aberrations. Figure 3 shows how the VPSF can be used to analyze depth of focus preoperatively and postoperatively for a patient participating in a presbyopia ablation clinical trial. The VPSF it clearly shows that the patient s depth of focus has increased to include a larger reading range, up to 2 diopters.

7 Figure 3. <<The Volumetric Point Spread Function (VPSF) is generated by calculating the PSF at many points through focus, and arranging them to simulate a focused cone of light. The Pre-Op VPSF on the left is from a patient with presbyopia. The patient received a multi-focal ablation, and the Post-Op VPSF shows an improved depth of focus, extending the patient reading range to almost 2 diopters>> Conclusion The patient PSF is a powerful, but currently under-utilized diagnostic. Making PSFs more realistic and providing an easy method with which to produce them in a clinical setting will be of great benefit to both patients and doctors.