Measurement of wave-front aberration in soft contactlenses 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 aShack–Hartmann wave-front sensor. The soft contact lenses were placed in a wet cell filled with lenssolution to prevent surface deformation and desiccation during measurements. Aberration measure-ments of conventional toric and multifocal soft contact lenses and a customized soft contact lens haveproved that this method is reliable. A Shack–Hartmann wave-front sensor can be used to assess opticalquality of both conventional and customized soft contact lenses and to assist in enhancing lens qualitycontrol. © 2005 Optical Society of America

OCIS codes: 170.3890, 170.4460, 330.4460.

1. Introduction

Contact lenses are widely used to improve visual per-formance by correcting lower-order aberrations suchas defocus and astigmatism. Most studies of contactlenses have focused on lens design,1,2 optical perfor-mance of lenses,3 and the effect of tear film on visionperformance.4 A ray tracing method was frequentlyused to evaluate the optical performance of the con-tact lens based on its design parameters.

Since the first measurement by Liang et al.5 ofocular wave-front aberrations with a Shack–Hartmann wave-front sensor, it has been found thathigher-order aberrations significantly degrade visualperformance, especially when the eye’s pupil is rela-tively large.6 Therefore there has been an increasinginterest in developing methods to correct higher-order aberrations. An adaptive optics system,7 phaseplates,8,9 customized contact lenses,10 and custom-ized refractive surgery11 have been proposed to cor-rect higher-order aberrations. Customized contactlenses are considered a practical and nonsurgical cor-rection method among the above techniques. The cus-tomization of contact lenses produces an irregular

surface profile, which is designed to compensate forhigher-order aberrations in the eye. A conventionalmethod for measuring contact lens power, namely,lensometry, cannot evaluate the higher-order aberra-tion generated by the irregular surface profile. There-fore it is essential to develop a reliable method thatcan accurately measure both lower- and higher-orderwave-front aberrations in customized contact lensesfor more comprehensive assessment of optical perfor-mance of lenses. However, few studies have beenmade to evaluate the unpredictable lower- andhigher-order aberrations induced by factors such as amanufacturing error and hydration.

Unlike for phase plates and other solid optics, themeasurement of wave-front aberrations in soft con-tact lenses is not straightforward because a con-ventional lensometer is incapable of measuringhigher-order aberrations. Also, when one is measur-ing wave-front aberrations, especially in soft contactlenses, it is desirable to place the lenses in a wet cellto prevent surface deformation and desiccation12

caused by the flexibility and the water content of lensmaterial. For these reasons, Lopez-Gil et al.10 mea-sured the wave-front aberration of customized softcontact lenses in a wet cell by using an interferome-ter. Although the wet cell successfully prevents theproblems described above, an interferometericmethod cannot measure large amounts of wave-frontaberrations because of its relatively narrow dynamicrange. However, customized contact lenses with largeamounts of wave-front aberrations are required forcompensating for eyes with abnormal corneal condi-tions such as keratoconus and corneal transplants.To resolve this limitation, a Shack–Hartmann wave-

The authors are with the University of Rochester, Rochester,New York 14627. T. M. Jeong (tjeong@cvs.rochester.edu) is withthe Center for Visual Science, M. Menon is with the Department ofBiomedical Engineering, and G. Yoon is with the Center for VisualScience, the Department of Biomedical Engineering, and the De-partment of Ophthalmology.

Received 5 November 2004; revised manuscript received 28 Feb-ruary 2005; accepted 28 February 2005.

0003-6935/05/214523-05$15.00/0© 2005 Optical Society of America

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front sensor was used to measure wave-front aberra-tions 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 lower-and higher-order wave-front aberrations in softcontact lenses. This method used a wet cell in whichsoft contact lenses were submerged to maintain theirsurface profiles and hydration. To compensate for thereduction in the measured magnitude of the aberra-tion in the wet cell, a conversion factor was intro-duced. Features such as reliability and sensitivity ofthe performance of the wave-front sensor were inves-tigated for the wave-front measurement of a soft con-tact lens in a wet cell. Finally, three different kinds ofsoft contact lenses, i.e., conventional toric, multifocal,and customized contact lenses, were measured, andthe results were compared with designed values.

2. Shack–Hartmann Wave-Front Sensor for SoftContact Lenses

Figure 1 shows an optical layout for measuring thewave-front aberrations of soft contact lenses. The sys-tem consists of a wet cell in which a soft contact lensis submerged, an image relay system, a pupil camera,and a Shack–Hartmann wave-front sensor. The wetcell is a chamber that has transparent optical win-dows on its top and bottom and is filled with lenssolution (0.9% normal saline). The contact lens isplaced on the bottom optical window of the wet cell.An XYZ translational stage and a rotational stage areattached to the wet cell to align the soft contact lenswith the optical axis of the wave-front sensor and toadjust the rotational orientation of the contact lens.

The image relay system consists of two achromaticlenses that have an identical 20 cm focal length. The

image relay system transfers the wave-front aberra-tions of the soft contact lens to the lenslet array in theShack–Hartmann wave-front sensor. The lenslet ar-ray has a center-to-center lenslet spacing of 400 �mand a focal length of 24 mm. A relatively long focallength was chosen to increase the sensitivity. Withthis lenslet array, the dynamic range was �12 diopt-ers (D) for a 6 mm pupil with the lens in the wet cell.

A light source from a laser diode with a wavelengthof 635 nm was coupled into a fiber and collimated.This collimated reference beam passed through a con-tact lens, and the wave front was distorted by aber-rations included in the contact lens. The spot arraypattern formed with the lenslet array was recordedwith a CCD camera and used to reconstruct wave-front aberrations. Contact lenses that were measuredhad radial rings and three straight lines representingthe optical zone and orientation of the contact lens, asshown in Fig. 1. A pupil camera was used to align thecontact lenses to the optical axis by monitoring theseradial rings and straight lines. The wave-front aber-ration was measured for a 7.09 mm pupil, and wecomputed Zernike coefficients up to the 10th order.The measured Zernike coefficients were mathemati-cally renormalized for a 6 mm pupil.

3. Conversion Factor

Because a soft contact lens was submerged in a wetcell to prevent surface deformation and desiccation,the measured wave-front aberrations of the contactlens are fewer than those that would be measured inair. This result is simply due to the smallerrefractive-index difference between the contact lensmaterial and the lens solution than between the con-tact lens material and air. Therefore the aberrationsmeasured in the wet cell need to be rescaled to yieldthe aberrations of the contact lens in air. Figure 2shows a schematic diagram of the reduction of wave-front aberrations of the contact lens when it is placedin a contact lens solution. If a contact lens is placed ina contact lens solution that has refractive indexnmedium, the total phase delay ��solution�x, y�� at coordi-nates �x, y� in passing through the lens may be writ-ten as13

�solution(x, y) � kWsolution(x, y)� nmediumk[h � �(x, y)] � nlensk�(x, y)� nmediumkh � (nlens � nmedium)k�(x, y),

(1)

Wsolution(x, y) � nmediumh � (nlens � nmedium)�(x, y), (2)

where k is the wave number, nlens is the refractiveindex of the lens, h is the height of the lens at thecenter position, and ��x, y� and Wsolution�x, y� are thelens thickness and the wave-front aberration at co-ordinates �x, y�, respectively.

If the same contact lens is placed in air, the totalphase delay ��air�x, y�� in air �nmedium � 1� may bemodified as follows:

Fig. 1. Optical layout of a Shack–Hartmann sensor for measuringwave-front aberrations in contact lenses. The contact lens is placedin a wet cell to prevent surface deformation and desiccation duringthe measurement. The radial ring and three straight lines allowmore-precise alignment to the optical axis of the system. The imageof a contact lens was taken from the pupil camera.

4524 APPLIED OPTICS � Vol. 44, No. 21 � 20 July 2005

�air(x, y) � kWair(x, y) � k[h � �(x, y)] � nlensk�(x, y)� kh � (nlens � 1)k�(x, y), (3)

Wair(x, y) � h � (nlens � 1)�(x, y). (4)

Wave-front aberrations of the same lens in differentmedia can be expressed with refractive indices of thecontact lens material and the medium. Finally, wesolve for ��x, y� in Eq. (2) and substitute the resultinto Eq. (4) to obtain

Wair(x, y) � (nlens � 1)�(nlens � nmedium)� Wsolution(x, y) � C, (5)

C � h � (nlens � 1)�(nlens � nmedium) � nmediumh.(6)

In Eq. (5), C is the constant phase shift across the lensdetermined by the height of the lens (h) and the re-fractive indices �nlens, nmedium�. The value of C is neg-ligible because it does not affect the measured wave-front profile. Thus the conversion factor (CF) forwave-front aberrations between the contact lens so-lution and air can be defined as follows:

Wair(x, y) � CF � Wsolution(x, y), (7)

CF � (nlens � 1)�(nlens � nmedium). (8)

We can recalculate the wave-front aberrations of

soft contact lenses in air from the measured wave-front aberrations in the wet cell simply by multiply-ing the measured aberrations by this conversionfactor. Refractive indices 1.332 (Ref. 14) and 1.423 at635 nm were used for the saline solution and thecontact lens material in this study, respectively. Inthis case the conversion factor is 4.63.

4. Measurement of Wave-Front Aberrations in SoftContact Lenses

A. Reliability and Sensitivity of Shack–HartmannWave-Front Sensor

For assessing the reliability of the wave-front sensor,a calibration optic, called a phase plate, that has bothlower- and higher-order aberrations up to fifth orderwas fabricated. The wave-front aberrations of thephase plate measured with our Shack–Hartmannwave-front sensor were compared with those mea-sured with a commercial interferometer (ZYGOModel GPI-XP). Figure 3 shows the Zernike coeffi-cients measured with the Shack–Hartmann sensorand with the commercial interferometer. For simplic-ity, a single index scheme established by the VisionScience and Its Applications Standards Taskforceteam15 was used to label the Zernike coefficients. Themeasurements demonstrated good agreement in thetwo sets of Zernike coefficients. The root-mean-square (rms) value of the difference in Zernike coef-ficients between the two instruments was 0.065 �m,which is only 1.4 times larger than the diffraction-limited rms, defined as �14 (0.045 �m at � 0.633 �m). From this comparison it is shown thatthe Shack–Hartmann wave-front sensor used in thisstudy is as reliable as the ZYGO system in measuringthe wave-front aberrations.

For the reason that the conversion factor can am-plify a measurement error induced by noise, we in-vestigated the measurement sensitivity to calculatethe smallest amount of wave-front aberration that

Fig. 2. Parameters used to compute the conversion factor de-scribed in the equations in the text.

Fig. 3. Comparison of Zernike coefficients measured with aShack–Hartmann sensor and with the commercial interferometer.The rms value of the difference in Zernike coefficients for the twoinstruments was 0.065 �m. This value is 1.4 times higher thanthat of a diffraction-limited rms. Thus the wave-front sensor is soreliable as to measure the wave-front aberrations in a contact lens.

20 July 2005 � Vol. 44, No. 21 � APPLIED OPTICS 4525

the Shack–Hartmann wave-front sensor can reliablymeasure. Twenty-five successive measurements ofthe system aberrations were taken under normalwave-front measurement conditions without a con-tact lens in the wet cell. The rms of the difference ineach Zernike coefficient between the individual mea-sured wave fronts and an average wave front wascalculated. The rms of the difference was 0.014 �mfor a 7.09 mm pupil. If the conversion factor is 4.63,the measurement sensitivity worsened to 0.065 �m�0.014 �m � 4.63�. This indicates that wave-frontaberrations that have rms values smaller than0.065 �m cannot be accurately measured with oursystem. However, this minimum level of the aberra-tion that the Shack–Hartmann wave-front sensor canmeasure is only 1.4 times larger than the diffraction-limited rms. Again, from this comparison, the Shack–Hartmann wave-front sensor used in this study isstill sensitive enough to measure the wave-front ab-errations of a contact lens.

B. Toric Lens

A conventional toric soft contact lens was measuredwith our wave-front sensor. This lens had a designedrefraction of �4.5 D spherical power �1.75 D cylin-drical power. The measured dioptric powers of thislens were �4.6 D spherical and �1.6 D cylindrical fora 6 mm pupil, which showed a good agreement withthe design. Negative vertical coma ��0.20� 0.04 �m� was consistently observed in this toriclens owing to a vertical shift of the apexes of theanterior and posterior surfaces of this lens. The ver-tical shift of the apexes of the anterior and posteriorsurfaces came from the prismatic geometry of thislens. Other higher-order aberrations were negligiblysmall for this lens.

C. Multifocal Contact Lens

Figure 4(a) shows the measured Zernike coefficientsfor a multifocal lens with three different sphericalrefractions. Measured spherical aberrations (Z12, or12 in Zernike mode) for multifocal contact lenses withthe designed spherical refractions of 0, �3, and�5.25 D were �0.21, �0.28, and �0.37 �m, respec-tively, for a 6 mm pupil. Negative spherical aberra-tion, which increases the depth of focus forpresbyopia, was observed in the multifocal contactlenses. Except for spherical aberration, higher-orderaberrations were not significantly large. These mea-sured amounts of spherical aberration were similarto the theoretically calculated values from the contactlens design data, which were �0.23, �0.36, and�0.39 �m, respectively, for a 6 mm pupil. Because ofspherical aberration, multifocal contact lenses havedifferent spherical powers for different pupil sizes.The spherical power was calculated for several pupilsizes. Figure 4(b) shows the variation in dioptricpower of the multifocal contact lenses as a function ofpupil size. The dioptric powers in Fig. 4(b) were di-rectly calculated from defocuses at different pupilsizes. The negative power of multifocal contact lensesincreases with the pupil size, and the designed re-

fraction was obtained at a pupil size of approximately5 mm.

D. Wave-Front Aberration of a Customized Contact Lens

A customized soft contact lens for the human eye wasfabricated with a lathe to correct wave-front aberra-tions up to fifth order. Coma (Z7 and Z8), trefoil (Z6and Z9), and spherical aberration (Z12) were thedominant aberrations for this customized contactlens. The higher-order rms of this eye was 1.22 �mfor a 6 mm pupil. This amount of higher-order rms isat least two to three times larger than what we wouldexpect to see in a normal eye. The wave-front aber-rations of the customized contact lens were measuredin the same experimental setup. Figure 5(a) showsthe designed and measured wave-front aberrationmaps for the higher-order aberrations for a 6 mmpupil. In Fig. 5(a), the two wave-front maps are quitesimilar. Figure 5(b) shows the Zernike coefficients forthe designed and measured wave-front aberrationsfor a 6 mm pupil. Coma, trefoil, spherical aberration,and other higher-order aberrations [Fig. 5(b)] were

Fig. 4. (a) Zernike coefficients of three multifocal contact lensesfor a 6 mm pupil size. (b) Spherical power of three multifocalcontact lenses as a function of pupil size. The negative sphericalpower of the multifocal contact lenses increased with respect to thepupil size, and the designed refraction was obtained at a pupil sizeof approximately 5 mm.

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effectively generated in the customized contact lensfor compensating for higher-order aberrations in theeye. The higher-order rms difference between de-signed and measured Zernike coefficients was0.26 �m for a 6 mm pupil. Error in vertical coma (7 inZernike mode) was the main contributor to the dif-ference and is considered to be generated by a verticalshift of the apexes between the anterior and posteriorsurfaces of the contact lens.

5. Conclusions

Both lower- and higher-order wave-front aberrationsin several soft contact lenses have been successfullymeasured with a Shack–Hartmann sensor. The softcontact lenses were placed in a wet cell to preventsurface deformation and desiccation during measure-ment. Reliable and repeatable measurements of thewave-front aberrations were demonstrated with the

wet cell. In view of the increasing interest in devel-oping customized optics that can correct most opticalaberrations in the eye, this diagnostic technique willplay an important role in improving lens design andmanufacturing to achieve better quality of both con-ventional and customized contact lenses and intraoc-ular lenses.

References1. G. Bauer, “Longitudinal spherical aberration of modern oph-

thalmic lenses and its effect on visua acuity,” Appl. Opt. 19,2226–2234 (1980).

2. D. Atchison, “Aberrations associated with rigid contact lenses,”J. Opt. Soc. Am. A 12, 2267–2273 (1995).

3. X. Hong, N. Himebaugh, and L. Thibos, “On-eye evaluation ofoptical performance of rigid and soft contact lenses,” Optom.Vis. Sci. 78, 872–880 (2001).

4. F. Lu, X. Mao, J. Qu, D. Xu, and J. He, “Monochromatic wave-front aberrations in the human eye with contact lenses,” Op-tom. Vis. Sci. 80, 135–141 (2003).

5. J. Liang, B. Grimme, S. Goelz, and J. Bille, “Objective mea-surement of wave aberrations of the human eye with the use ofa Hartmann–Shack wave-front sensor,” J. Opt. Soc. Am. A 11,1949–1957 (1994).

6. J. Liang and D. Williams, “Aberrations and retinal image qual-ity of the normal human eye,” J. Opt. Soc. Am. A 14, 2873–2883(1997).

7. J. Liang, D. Williams, and D. Miller, “Supernormal vision andhigh-resolution retinal imaging through adaptive optics,” J.Opt. Soc. Am. A 14, 2884–2892 (1997).

8. R. Navarro, E. Moreno-Barriuso, S. Bara, and T. Mancebo,“Phase plates for wave-aberration compensation in the humaneye,” Opt. Lett. 25, 236–238 (2000).

9. G. Yoon, T. M. Jeong, D. Williams, and I. Cox, “Vision improve-ment by correcting higher-order aberrations with phase platesin normal eyes,” J. Refract. Surg. 20, S553–S557 (2004).

10. N. Lopez-Gil, A. Benito, J. Castejon-Mochon, J. Marin, G. Lo-a-Foe, G. Marin, B. Fermigier, D. Joyeux, N. Chateau, and P.Artal, “Aberration correction using customized soft contactlenses with aspheric and asymmetric surfaces,” Invest. Oph-thalmol. Visual Sci. 43, 973–973 (2002).

11. S. MacRae, J. Schwiegerling, and R. Snyder, “Customized cor-neal ablation and super vision,” J. Refract. Surg. 16, S230–S235 (2000).

12. G. Bauer and H. Lechner, “Measurement of the longitudinalspherical aberration of soft contact lenses,” Opt. Lett. 4, 224–226 (1979).

13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill,1996), pp. 96–97.

14. L. Thibos, M. Ye, X. Zhang, and A. Bradley, “The chromaticeye: a new reduced-eye model of ocular chromatic aberration inhumans,” Appl. Opt. 31, 3594–3600 (1992).

15. L. Thibos, R. Applegate, J. Schwiegerling, R. Webb, and VisionScience and Its Applications Standards Taskforce members,“Standards for reporting optical aberrations of eyes,” in VisionScience and Its Applications, V. Lakshminarayanan, ed., Vol.35 of OSA Trends in Optics and Photonics Series (OpticalSociety of America, 2000), pp. 232–244.

Fig. 5. (a) Higher-order wave-front maps for designed and mea-sured Zernike coefficients of a customized contact lens. The inter-val between contour lines is 0.8 �m. (b) Higher-order Zernikecoefficients of a customized contact lens for a 6 mm pupil size. Thehigher-order rms difference between the designed and measuredZernike coefficients was 0.26 �m for a 6 mm pupil.

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