Wavefront aberration function from hard contact ...

Wavefront aberration function from hard contact lenses obtained with two different techniques. Angel S. Cruz Félix*, Estela López-Olazagasti, David Sánchez-de-la-Llave, Gustavo Ramírez,Zavaleta, Eduardo Tepichín-Rodríguez. Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis enrique Erro No. 1, Sta. Ma. Tonantzintla, Puebla, Mex. C.P. 72840. ABSTRACT The analysis and measurement of the wavefront aberration function are very important tools in the field of visual optics; they are used to understand the performance of the human eye in terms of its optical aberrations. In recent years, we have compared, through two different methods, the wavefront aberration function of a reference refractive surface of 5 mm in diameter and we have demonstrated its equivalence1. Now, we want to extend these results to a set of hard contact lenses. These hard contact lenses have been subjected to different laser ablation techniques which are typically used in refractive surgery. Our goal is to characterize the resultant ablation profile. We show our results obtained for both, a nonablated hard contact lens and the corresponding ablated samples. Keywords: wavefront aberration function, Mach-Zehnder, Hartmann-Shack, contact lenses, laser refractive surgery.

1. INTRODUCTION Wavefront sensing technology help us to understand the objective performance of the human eye in terms of its optical aberrations2,3,4,5 and is in this matter in which we focus our present work. By analyzing the wavefront aberration function of the human eye using this technology we can know the effects caused by laser refractive surgery procedures which are used to correct several kinds of ametropies that are present in the human eye. Particularly we are interested in the effects caused by two procedures that are commonly used in visual laser correction which are known as ASA (Advanced Surface Ablation) and PASA (Pseudoacommodative Surface Ablation)1,6. In order to analyze the effects caused by these two procedures they were applied directly over a set of hard contact lenses which would simulate the anterior face of the cornea and, as a result, we could obtained a static profile which would be equivalent to that from the human eye, then we applied analysis techniques to confirm the shift produced by these surface ablations over the contact lenses for several clinical cases6. In a previous work7, we used a Shack-Hartmann wavefront sensor and a Mach-Zehnder type interferometer to first obtain the wavefront aberration function from a reference refractive surface. The main purpose was to generalize this method and being able to fully characterize a set of hard contact lenses which have been subjected to different ablation techniques typically used in refractive surgery for vision correction. We have proved that both methods are equivalents despite of the scales on which the results are presented7. Now, in this work we present the resultant wavefront aberration function obtained from the ablation profile performed for several clinical cases. In the next section we give a brief and simple description of the optical devices used for this work.

Applications of Digital Image Processing XXXIV, edited by Andrew G. Tescher, Proc. of SPIE Vol. 8135, 813514 · © 2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.892919

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2. DESCRIPTION OF THE TECHNIQUES As mentioned before, two different methods were used to obtain the wavefront aberration function from a set of hard contact lenses. For the first method we obtained interference patterns of our contact lenses with a CCD mounted on the exit of a Mach-Zehnder type interferometer which is shown schematically in Fig. 1. This particular geometrical setup allows us to adjust different wavefronts as the reference beam, and gives us the capability to handle the refractive surface under test in several positions along the test arm8,9. Once we obtained the interference patterns, they were processed with an interferometric analysis software called APEX®, which is capable to analyze the static fringe patterns obtained in optical testing environments, and it performs a global least-square fit of the Zernike Polynomials to the data10, therefore, we could obtain directly from the fringe analysis the wave aberration function for the set of our contact lenses.

Figure 1.- Mach-Zehnder type interferometer.

For the second method we used a commercial Hartmann-Shack wavefront sensor from THORLABS® model WFS150, to obtain the wavefront aberration function. The wavefront sensor was placed in same position were the CCD was mounted for capturing the interference patterns just to ensure that the detection plane was the same. Fig. 2 shows the basic arrangement of a typical modern Shack-Hartmann WFS. The essential components of the device are an array of micro lenses (lenslet array), and a camera, in this case a CCD chip, which was used as a mean for recording the pattern of images formed by the micro lenses.

Figure 2.- Basic arrangement of a Shack-Hartmann wavefront sensor11.

We have proved that both methods are equivalents and we have choose to present both results in order to compare both methods and let others to decide which of them to use just by their own means.


3. RESULTS We analyze a set of 5 PMMA hard contact lenses with a diameter of 9.3 ± 0.05 mm and a curve base radius of 9.1 ± 0.05 mm. Two contact lenses were previously treated in a certified ophthalmology clinic for the correction of myopia and hyperopia with a surface ablation technique called ASA and a change in their optical power of +3.00 D and -3.00 D was introduced. Another two contact lenses were previously treated in a certified ophthalmology clinic for the correction of myopia and hyperopia with a surface ablation technique called PASA and a change in their optical power of +3.00 D and -3.00 D was introduced. The last one of the hard contact lenses has remained with no ablation at all in order to be kept as a reference for qualitative comparison between the others. We show in Table 1 some of their features. Table1.- Features of our lenses under test. Lens

Procedure

Treatment

Power [D]

1

No Ablation

---

---

2

ASA Positive

Hyperopia

+ 3.00

3

ASA Negative

Myopia

- 3.00

4

PASA Positive

Hyperopia

+ 3.00

5

PASA Negative

Myopia

- 3.00

In the next figures we show the interference patterns obtained with the CCD.

Lens No. 1 Fig. 3.- Interference patterns obtained by means of a Mach-Zehnder type interferometer for the contact lens which has no ablation at all.

Lens No.2

Lens No.3

Fig. 4.- Interference patterns obtained by means of a Mach-Zehnder type interferometer from two contact lenses to which were applied the technique known as ASA. In the left a treatment for +3.00 D was applied and in the right a treatment of -3.00 D was applied.


Lens No.4

Lens No.5

Fig. 5.- Interference patterns obtained by means of a Mach-Zehnder type interferometer from two contact lenses to which were applied the technique known as PASA. In the left a treatment for +3.00 D was applied and in the right a treatment of -3.00 D was applied.

First of all we can note that all of the interferograms they exhibit important differences between them as they are the difference in the number of the rings in Lens No. 2 and Lens No. 3, and the evident irregularities in Lens No. 4 and Lens No. 5 which indicates us that the performed ablation made to each of them is affecting their surfaces with respect to the one which has no ablation at all. As for Lens No. 2, we see that the amount of number of rings is less with respect to the amount of the number of rings for Lens No. 3 which indicates us that the lens is suffering a change in the curvature of its surface having as a result a shift in the focal distance due to the applied ablation. The interferograms respectively shown in Fig. 3, Fig. 4 and Fig. 5 were processed with an interferometric analysis software called APEX® in order to obtain their corresponding wavefront aberration and the next figures we show their respective cross-section graphics.

Lens No.1 Fig. 6.- Cross-sections from the wavefront aberration functions obtained from the APEX® for the reference lens.

Lens No.2

Lens No.3

Fig.7.- Cross-sections from the wavefront aberration functions obtained from the APEX® analysis software for two contact lenses to which were applied the technique known as ASA. In the left a treatment for +3.00 D was applied and in the right a treatment of -3.00 D was applied.


Lens No.5

Lens No.4

Fig. 8.- Cross-sections from the wavefront aberration functions obtained from the APEX® analysis software from two contact lenses to which were applied the technique known as PASA. . In the left a treatment for +3.00 D was applied and in the right a treatment of -3.00 D was applied.

In the next figures we show the wavefront aberration functions obtained from the Hartmann-Shack wavefront sensor starting from the lens with no ablation at all. We can see important differences in the essential form of the presented wavefront maps for every each of the lenses. In Lens No. 2 the Hartmann-Shack wavefront sensor detected a convergence wavefront in comparison with Lens No. 3 where a divergence wavefront was detected.

Lens No.1 Fig. 9.- Wavefront aberration function obtained through means of the wavefront sensor of the contact lens which has no ablation at all.

Lens No.2

Lens No.3

Fig. 10.- Wavefront aberration function obtained by means of the wavefront sensor from two contact lenses to which were applied the technique known as ASA. . In the left a treatment for +3.00 D was applied and in the right a treatment of -3.00 D was applied.


Lens No.5

Lens No.4

Fig. 11.- Wavefront aberration functions obtained from the Hartmann-Shack wavefront sensor from two contact lenses to which were applied the technique known as PASA. . In the left a treatment for +3.00 D was applied and in the right a treatment of -3.00 D was applied.

As we observe a change in the essential form of the wavefront aberration function, which is due to the change of curvature produced by the surface ablation on every each of the lenses, then we can calculate the shift in the focal distance that was introduced by the procedure. 3.1 Shift in the focal distance. We used the fact that the wavefront sensor was placed at a distance of 14.1 cm., also we employed the obtained data directly from the wavefront sensor and we used the scheme of the sign convention shown in Fig. 7, which was taken from the user's manual11. In Table 2 we show the calculated focal distances for every each of the lenses.

Fig. 7.- Scheme of the sign convention used to calculate the shift in the focal distance introduced by the surface ablation(ref) in every one of our contact lenses.

Table 2.- Focal distances for all of the lenses with data obtained directly from the wavefront sensor. Lens

Procedure

Power [D]

RoC [cm]

Focal Distance [cm]

1

No ablation

----

318.8

-304.76

2

ASA Positive

+ 3.00

-123.97

-138.07

3

ASA Negative

- 3.00

147.53

-133.43

4

PASA Positive

+ 3.00

1150

-1135.9

5

PASA Negative

- 3.00

288.82

-274.72


From Table 2 we see indeed a significant shift in the focal distance for the lenses that have been subjected to different ablation techniques with respect to our reference which has no ablation at all, and this is in accordance to the expected results in which an specific ablation technique would introduce a shift in the focal distance when applied directly over the cornea, for example we can see that the calculated focal distances of Lens No. 2 and Lens No. 3 are pretty close to each other with their respective sign and this is related to the fact that if we combine a +3.00 D lens with a -3.00 D lens it would result on a combined power of 0.0 D. We also note that the calculated focal distance of the Lens No. 4 tells us that there has been an inaccuracy in the application of the procedure.

4. CONLUSIONS From the comparison of the obtained results through two different techniques, we can say that the ablation procedures that are commonly used in laser refractive surgery for visual correction applied directly over hard contact lenses, they do produce a change in the surface and a shift in their focal distance, and this changes should be different from those expected in the human cornea due to the differences in the index of refraction and the biological tissue interactions with the ablations.

ACKNOWLEDGMENTS The authors would like to thank to the national council of science and technology (CONACyT), in Mexico, for their support given with the project number py98777.

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