measurement of wave-front aberrations in soft contact lenses by use of a Shack Hartmann wave-front sensor

Transcription

1 Measurement of wave-front aberration in soft contact lenses by use of a Shack Hartmann wave-front sensor Tae Moon Jeong, Manoj Menon, and Geunyoung Yoon Lower- and higher-order wave-front aberrations of soft contact lenses were accurately measured with a Shack Hartmann wave-front sensor. The soft contact lenses were placed in a wet cell filled with lens solution to prevent surface deformation and desiccation during measurements. Aberration measurements of conventional toric and multifocal soft contact lenses and a customized soft contact lens have proved that this method is reliable. A Shack Hartmann wave-front sensor can be used to assess optical quality of both conventional and customized soft contact lenses and to assist in enhancing lens quality control Optical Society of America OCIS codes: , , Introduction Contact lenses are widely used to improve visual performance by correcting lower-order aberrations such as defocus and astigmatism. Most studies of contact lenses have focused on lens design, 1,2 optical performance of lenses, 3 and the effect of tear film on vision performance. 4 A ray tracing method was frequently used to evaluate the optical performance of the contact lens based on its design parameters. Since the first measurement by Liang et al. 5 of ocular wave-front aberrations with a Shack Hartmann wave-front sensor, it has been found that higher-order aberrations significantly degrade visual performance, especially when the eye s pupil is relatively large. 6 Therefore there has been an increasing interest in developing methods to correct higherorder aberrations. An adaptive optics system, 7 phase plates, 8,9 customized contact lenses, 10 and customized refractive surgery 11 have been proposed to correct higher-order aberrations. Customized contact lenses are considered a practical and nonsurgical correction method among the above techniques. The customization of contact lenses produces an irregular The authors are with the University of Rochester, Rochester, New York T. M. Jeong (tjeong@cvs.rochester.edu) is with the Center for Visual Science, M. Menon is with the Department of Biomedical Engineering, and G. Yoon is with the Center for Visual Science, the Department of Biomedical Engineering, and the Department of Ophthalmology. Received 5 November 2004; revised manuscript received 28 February 2005; accepted 28 February /05/ $15.00/ Optical Society of America surface profile, which is designed to compensate for higher-order aberrations in the eye. A conventional method for measuring contact lens power, namely, lensometry, cannot evaluate the higher-order aberration generated by the irregular surface profile. Therefore it is essential to develop a reliable method that can accurately measure both lower- and higher-order wave-front aberrations in customized contact lenses for more comprehensive assessment of optical performance of lenses. However, few studies have been made to evaluate the unpredictable lower- and higher-order aberrations induced by factors such as a manufacturing error and hydration. Unlike for phase plates and other solid optics, the measurement of wave-front aberrations in soft contact lenses is not straightforward because a conventional lensometer is incapable of measuring higher-order aberrations. Also, when one is measuring wave-front aberrations, especially in soft contact lenses, it is desirable to place the lenses in a wet cell to prevent surface deformation and desiccation 12 caused by the flexibility and the water content of lens material. For these reasons, Lopez-Gil et al. 10 measured the wave-front aberration of customized soft contact lenses in a wet cell by using an interferometer. Although the wet cell successfully prevents the problems described above, an interferometeric method cannot measure large amounts of wave-front aberrations because of its relatively narrow dynamic range. However, customized contact lenses with large amounts of wave-front aberrations are required for compensating for eyes with abnormal corneal conditions such as keratoconus and corneal transplants. To resolve this limitation, a Shack Hartmann wave- 20 July 2005 Vol. 44, No. 21 APPLIED OPTICS 4523

2 Fig. 1. Optical layout of a Shack Hartmann sensor for measuring wave-front aberrations in contact lenses. The contact lens is placed in a wet cell to prevent surface deformation and desiccation during the measurement. The radial ring and three straight lines allow more-precise alignment to the optical axis of the system. The image of a contact lens was taken from the pupil camera. front sensor was used to measure wave-front aberrations of soft contact lenses placed in a wet cell. In this paper we describe our use of a Shack Hartmann wave-front sensor to measure the lowerand higher-order wave-front aberrations in soft contact lenses. This method used a wet cell in which soft contact lenses were submerged to maintain their surface profiles and hydration. To compensate for the reduction in the measured magnitude of the aberration in the wet cell, a conversion factor was introduced. Features such as reliability and sensitivity of the performance of the wave-front sensor were investigated for the wave-front measurement of a soft contact lens in a wet cell. Finally, three different kinds of soft contact lenses, i.e., conventional toric, multifocal, and customized contact lenses, were measured, and the results were compared with designed values. 2. Shack Hartmann Wave-Front Sensor for Soft Contact Lenses Figure 1 shows an optical layout for measuring the wave-front aberrations of soft contact lenses. The system consists of a wet cell in which a soft contact lens is submerged, an image relay system, a pupil camera, and a Shack Hartmann wave-front sensor. The wet cell is a chamber that has transparent optical windows on its top and bottom and is filled with lens solution (0.9% normal saline). The contact lens is placed on the bottom optical window of the wet cell. An XYZ translational stage and a rotational stage are attached to the wet cell to align the soft contact lens with the optical axis of the wave-front sensor and to adjust the rotational orientation of the contact lens. The image relay system consists of two achromatic lenses that have an identical 20 cm focal length. The image relay system transfers the wave-front aberrations of the soft contact lens to the lenslet array in the Shack Hartmann wave-front sensor. The lenslet array has a center-to-center lenslet spacing of 400 m and a focal length of 24 mm. A relatively long focal length was chosen to increase the sensitivity. With this lenslet array, the dynamic range was 12 diopters (D) for a 6 mm pupil with the lens in the wet cell. A light source from a laser diode with a wavelength of 635 nm was coupled into a fiber and collimated. This collimated reference beam passed through a contact lens, and the wave front was distorted by aberrations included in the contact lens. The spot array pattern formed with the lenslet array was recorded with a CCD camera and used to reconstruct wavefront aberrations. Contact lenses that were measured had radial rings and three straight lines representing the optical zone and orientation of the contact lens, as shown in Fig. 1. A pupil camera was used to align the contact lenses to the optical axis by monitoring these radial rings and straight lines. The wave-front aberration was measured for a 7.09 mm pupil, and we computed Zernike coefficients up to the 10th order. The measured Zernike coefficients were mathematically renormalized for a 6 mm pupil. 3. Conversion Factor Because a soft contact lens was submerged in a wet cell to prevent surface deformation and desiccation, the measured wave-front aberrations of the contact lens are fewer than those that would be measured in air. This result is simply due to the smaller refractive-index difference between the contact lens material and the lens solution than between the contact lens material and air. Therefore the aberrations measured in the wet cell need to be rescaled to yield the aberrations of the contact lens in air. Figure 2 shows a schematic diagram of the reduction of wavefront aberrations of the contact lens when it is placed in a contact lens solution. If a contact lens is placed in a contact lens solution that has refractive index n medium, the total phase delay solution x, y at coordinates x, y in passing through the lens may be written as 13 solution (x, y) kw solution (x, y) n medium k[h (x, y)] n lens k (x, y) n medium kh (n lens n medium )k (x, y), (1) W solution (x, y) n medium h (n lens n medium ) (x, y), (2) where k is the wave number, n lens is the refractive index of the lens, h is the height of the lens at the center position, and x, y and W solution x, y are the lens thickness and the wave-front aberration at coordinates x, y, respectively. If the same contact lens is placed in air, the total phase delay air x, y in air n medium 1 may be modified as follows: 4524 APPLIED OPTICS Vol. 44, No July 2005

3 Fig. 3. Comparison of Zernike coefficients measured with a Shack Hartmann sensor and with the commercial interferometer. The rms value of the difference in Zernike coefficients for the two instruments was m. This value is 1.4 times higher than that of a diffraction-limited rms. Thus the wave-front sensor is so reliable as to measure the wave-front aberrations in a contact lens. Fig. 2. Parameters used to compute the conversion factor described in the equations in the text. air (x, y) kw air (x, y) k[h (x, y)] n lens k (x, y) kh (n lens 1)k (x, y), (3) W air (x, y) h (n lens 1) (x, y). (4) Wave-front aberrations of the same lens in different media can be expressed with refractive indices of the contact lens material and the medium. Finally, we solve for x, y in Eq. (2) and substitute the result into Eq. (4) to obtain W air (x, y) (n lens 1) (n lens n medium ) W solution (x, y) C, (5) C h (n lens 1) (n lens n medium ) n medium h. (6) In Eq. (5), C is the constant phase shift across the lens determined by the height of the lens (h) and the refractive indices n lens, n medium. The value of C is negligible because it does not affect the measured wavefront profile. Thus the conversion factor (CF) for wave-front aberrations between the contact lens solution and air can be defined as follows: W air (x, y) CF W solution (x, y), (7) CF (n lens 1) (n lens n medium ). (8) We can recalculate the wave-front aberrations of soft contact lenses in air from the measured wavefront aberrations in the wet cell simply by multiplying the measured aberrations by this conversion factor. Refractive indices (Ref. 14) and at 635 nm were used for the saline solution and the contact lens material in this study, respectively. In this case the conversion factor is Measurement of Wave-Front Aberrations in Soft Contact Lenses A. Reliability and Sensitivity of Shack Hartmann Wave-Front Sensor For assessing the reliability of the wave-front sensor, a calibration optic, called a phase plate, that has both lower- and higher-order aberrations up to fifth order was fabricated. The wave-front aberrations of the phase plate measured with our Shack Hartmann wave-front sensor were compared with those measured with a commercial interferometer (ZYGO Model GPI-XP). Figure 3 shows the Zernike coefficients measured with the Shack Hartmann sensor and with the commercial interferometer. For simplicity, a single index scheme established by the Vision Science and Its Applications Standards Taskforce team 15 was used to label the Zernike coefficients. The measurements demonstrated good agreement in the two sets of Zernike coefficients. The root-meansquare (rms) value of the difference in Zernike coefficients between the two instruments was m, which is only 1.4 times larger than the diffractionlimited rms, defined as 14 (0.045 m at m). From this comparison it is shown that the Shack Hartmann wave-front sensor used in this study is as reliable as the ZYGO system in measuring the wave-front aberrations. For the reason that the conversion factor can amplify a measurement error induced by noise, we investigated the measurement sensitivity to calculate the smallest amount of wave-front aberration that 20 July 2005 Vol. 44, No. 21 APPLIED OPTICS 4525

4 the Shack Hartmann wave-front sensor can reliably measure. Twenty-five successive measurements of the system aberrations were taken under normal wave-front measurement conditions without a contact lens in the wet cell. The rms of the difference in each Zernike coefficient between the individual measured wave fronts and an average wave front was calculated. The rms of the difference was m for a 7.09 mm pupil. If the conversion factor is 4.63, the measurement sensitivity worsened to m m This indicates that wave-front aberrations that have rms values smaller than m cannot be accurately measured with our system. However, this minimum level of the aberration that the Shack Hartmann wave-front sensor can measure is only 1.4 times larger than the diffractionlimited rms. Again, from this comparison, the Shack Hartmann wave-front sensor used in this study is still sensitive enough to measure the wave-front aberrations of a contact lens. B. Toric Lens A conventional toric soft contact lens was measured with our wave-front sensor. This lens had a designed refraction of 4.5 D spherical power 1.75 D cylindrical power. The measured dioptric powers of this lens were 4.6 D spherical and 1.6 D cylindrical for a 6 mm pupil, which showed a good agreement with the design. Negative vertical coma m was consistently observed in this toric lens owing to a vertical shift of the apexes of the anterior and posterior surfaces of this lens. The vertical shift of the apexes of the anterior and posterior surfaces came from the prismatic geometry of this lens. Other higher-order aberrations were negligibly small for this lens. Fig. 4. (a) Zernike coefficients of three multifocal contact lenses for a 6 mm pupil size. (b) Spherical power of three multifocal contact lenses as a function of pupil size. The negative spherical power of the multifocal contact lenses increased with respect to the pupil size, and the designed refraction was obtained at a pupil size of approximately 5 mm. C. Multifocal Contact Lens Figure 4(a) shows the measured Zernike coefficients for a multifocal lens with three different spherical refractions. Measured spherical aberrations (Z12, or 12 in Zernike mode) for multifocal contact lenses with the designed spherical refractions of 0, 3, and 5.25 D were 0.21, 0.28, and 0.37 m, respectively, for a 6 mm pupil. Negative spherical aberration, which increases the depth of focus for presbyopia, was observed in the multifocal contact lenses. Except for spherical aberration, higher-order aberrations were not significantly large. These measured amounts of spherical aberration were similar to the theoretically calculated values from the contact lens design data, which were 0.23, 0.36, and 0.39 m, respectively, for a 6 mm pupil. Because of spherical aberration, multifocal contact lenses have different spherical powers for different pupil sizes. The spherical power was calculated for several pupil sizes. Figure 4(b) shows the variation in dioptric power of the multifocal contact lenses as a function of pupil size. The dioptric powers in Fig. 4(b) were directly calculated from defocuses at different pupil sizes. The negative power of multifocal contact lenses increases with the pupil size, and the designed refraction was obtained at a pupil size of approximately 5 mm. D. Wave-Front Aberration of a Customized Contact Lens A customized soft contact lens for the human eye was fabricated with a lathe to correct wave-front aberrations up to fifth order. Coma (Z7 and Z8), trefoil (Z6 and Z9), and spherical aberration (Z12) were the dominant aberrations for this customized contact lens. The higher-order rms of this eye was 1.22 m for a 6 mm pupil. This amount of higher-order rms is at least two to three times larger than what we would expect to see in a normal eye. The wave-front aberrations of the customized contact lens were measured in the same experimental setup. Figure 5(a) shows the designed and measured wave-front aberration maps for the higher-order aberrations for a 6 mm pupil. In Fig. 5(a), the two wave-front maps are quite similar. Figure 5(b) shows the Zernike coefficients for the designed and measured wave-front aberrations for a 6 mm pupil. Coma, trefoil, spherical aberration, and other higher-order aberrations [Fig. 5(b)] were 4526 APPLIED OPTICS Vol. 44, No July 2005

5 wet cell. In view of the increasing interest in developing customized optics that can correct most optical aberrations in the eye, this diagnostic technique will play an important role in improving lens design and manufacturing to achieve better quality of both conventional and customized contact lenses and intraocular lenses. Fig. 5. (a) Higher-order wave-front maps for designed and measured Zernike coefficients of a customized contact lens. The interval between contour lines is 0.8 m. (b) Higher-order Zernike coefficients of a customized contact lens for a 6 mm pupil size. The higher-order rms difference between the designed and measured Zernike coefficients was 0.26 m for a 6 mm pupil. effectively generated in the customized contact lens for compensating for higher-order aberrations in the eye. The higher-order rms difference between designed and measured Zernike coefficients was 0.26 m for a 6 mm pupil. Error in vertical coma (7 in Zernike mode) was the main contributor to the difference and is considered to be generated by a vertical shift of the apexes between the anterior and posterior surfaces of the contact lens. 5. Conclusions Both lower- and higher-order wave-front aberrations in several soft contact lenses have been successfully measured with a Shack Hartmann sensor. The soft contact lenses were placed in a wet cell to prevent surface deformation and desiccation during measurement. Reliable and repeatable measurements of the wave-front aberrations were demonstrated with the References 1. G. Bauer, Longitudinal spherical aberration of modern ophthalmic lenses and its effect on visua acuity, Appl. Opt. 19, (1980). 2. D. Atchison, Aberrations associated with rigid contact lenses, J. Opt. Soc. Am. A 12, (1995). 3. X. Hong, N. Himebaugh, and L. Thibos, On-eye evaluation of optical performance of rigid and soft contact lenses, Optom. Vis. Sci. 78, (2001). 4. F. Lu, X. Mao, J. Qu, D. Xu, and J. He, Monochromatic wavefront aberrations in the human eye with contact lenses, Optom. Vis. Sci. 80, (2003). 5. J. Liang, B. Grimme, S. Goelz, and J. Bille, Objective measurement of wave aberrations of the human eye with the use of a Hartmann Shack wave-front sensor, J. Opt. Soc. Am. A 11, (1994). 6. J. Liang and D. Williams, Aberrations and retinal image quality of the normal human eye, J. Opt. Soc. Am. A 14, (1997). 7. J. Liang, D. Williams, and D. Miller, Supernormal vision and high-resolution retinal imaging through adaptive optics, J. Opt. Soc. Am. A 14, (1997). 8. R. Navarro, E. Moreno-Barriuso, S. Bara, and T. Mancebo, Phase plates for wave-aberration compensation in the human eye, Opt. Lett. 25, (2000). 9. G. Yoon, T. M. Jeong, D. Williams, and I. Cox, Vision improvement by correcting higher-order aberrations with phase plates in normal eyes, J. Refract. Surg. 20, S553 S557 (2004). 10. N. Lopez-Gil, A. Benito, J. Castejon-Mochon, J. Marin, G. Loa-Foe, G. Marin, B. Fermigier, D. Joyeux, N. Chateau, and P. Artal, Aberration correction using customized soft contact lenses with aspheric and asymmetric surfaces, Invest. Ophthalmol. Visual Sci. 43, (2002). 11. S. MacRae, J. Schwiegerling, and R. Snyder, Customized corneal ablation and super vision, J. Refract. Surg. 16, S230 S235 (2000). 12. G. Bauer and H. Lechner, Measurement of the longitudinal spherical aberration of soft contact lenses, Opt. Lett. 4, (1979). 13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp L. Thibos, M. Ye, X. Zhang, and A. Bradley, The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans, Appl. Opt. 31, (1992). 15. L. Thibos, R. Applegate, J. Schwiegerling, R. Webb, and Vision Science and Its Applications Standards Taskforce members, Standards for reporting optical aberrations of eyes, in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2000), pp July 2005 Vol. 44, No. 21 APPLIED OPTICS 4527