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Femtosecond lasers can be used to write a variety of gradient index refractive devices. Writing devices with an arbitrary optical profile (i.e., freeform) requires knowing the functional dependence of the phase change that the wavefront will experience when passing through a region written under different exposure parameters. We measured this dependence as a function of writing speed and power in hydrogel-based contact lenses. Regions of constant refractive index change were written under different conditions and then the phase change was measured with a Mach-Zehnder interferometer and a phase retrieval algorithm. This functional dependence was tested by writing arbitrary Zernike polynomials with varying magnitudes.
© 2015 Optical Society of America
1. Introduction
Nonlinear absorption is the underlying working principle that has allowed the use of femtosecond lasers in the artificial creation of microstructures and different types of optical devices. Only at the focal volume of an optical system is the laser intensity large enough for a significant amount of nonlinear absorption to occur. This highly localized deposition of energy (within volume of λ3 order of magnitude) leads to highly localized material property changes inside of a material [1]. This high degree of control in energy deposition has allowed femtosecond laser technology to find applications in many different areas of science (e.g., [1–6]). One of these areas of science in which femtosecond lasers have been successfully used is in the field of visual correction. For instance, the possibility of using femtosecond lasers for tuning the focal length of intraocular lenses or for reducing the capsule opacification of intraocular lenses has been studied [7–9]. In 2011, our group showed the writing of gradient index (GRIN) lenses with cylindrical power in ophthalmic hydrogel materials [10]. Our group has also created a technique called intra-tissue refractive index shaping (IRIS), which consists of a surgical procedure in which the refractive index of the cornea is locally changed by different amounts by controlling the exposure parameters to achieve the desired corneal refractive correction [11–15]. In 2014, this technology was used to create a GRIN refractive structure that had −1.4 diopters (D) of cylinder and −2.0 D of defocus in live cat cornea, written in-vivo [15].
A GRIN lens is a structure that has a spatial variation in the local index of refraction. The local change induced in the refractive index by the femtosecond laser writing depends on the exposure parameters used [3, 4, 16]. Writing high quality GRIN refractive devices to specific prescriptions requires knowledge of the exposure parameters that will accurately yield the desired change in the refractive index. As such, writing a refractive structure in a pre-determined manner necessitates finding a function that relates the refractive index change to the exposure parameters. Then, given a specific refractive profile, this function is used to determine the exposure parameters at each point in the material as the beam scans across the sample. Henceforth, we will refer to this function as the “calibration function”.
Femtosecond lasers have been used to write GRIN refractive structures [17–21]. In these works, however, constant exposure parameters were used across the samples rather than changing the exposure parameters as the sample is being scanned. Using the same exposure parameters causes the exposed regions to experience the same change in refractive index, and so the GRIN structure is made by deciding which spatial region is exposed. Using this approach, it is possible to stack several layers of refractive index change and obtain a multi-level approximation to the refractive structure [18, 20]. With a multi-level approximation instead of a continuous refractive structure, only a fraction of the light will be focused where it is desired. In other words, multi-level structures do not have a diffraction efficiency of 100% and exhibit multifocality. To eliminate multifocality, a true continuous change in the refractive index is needed. Doing so involves changing the exposure parameters during scanning, which necessitates a calibration function.
In 2012, Watanabe, et al., studied the exposure parameter conditions necessary to see a change in the index of refraction versus sample damage for poly(dimethylsiloxane) [16]. This qualitative information is far from sufficient for refractive devices as a numerical value of the refractive index change is needed for each different set of exposure parameters used. In this work, we are focused on obtaining the change in the wavefront phase,
where λ is the incoming radiation wavelength and d is the length of the index change region parallel to the optical axis. Equation (1) gives the change in the wavefront phase in number of waves. Different points in the wavefront will accumulate different phases and the GRIN lens is a transfer function that modifies the phase of the wavefront. In visual applications, the quantity that is ultimately needed is the change in the wavefront phase.Commercially available hydrogel-based contact lenses (Acuvue2, Johnson&Johnson) were used in this study. These contact lenses are made of a material named etafilcon A [22]. According to Johnson&Johnson, etafilcon A is a “copolymer of 2-hydroxyethyl methacrylate and methacrylic acid cross-linked with 1,1,1-trimethylol propane trimethacrylate and ethylene glycol dimethacrylate” with a “a benzotriazole UV-absorbing monomer” to block UV radiation [22].
This manuscript describes how the functional form of the phase change as a function of power and writing speed was determined. We also describe an interferometric technique for determining this calibration function. Once the calibration function was determined, different Zernike polynomials [23] representing arbitrary refractive corrections were written into the material. By adjusting power and writing speed, and by adding additional GRIN layers in the materials, larger phase variations can be induced.
2. Experimental setup
The femtosecond laser writing system is shown in Fig. 1(a). A Spectra-Physics Mai Tai HP produces 100 fs femtosecond pulses at a repetition rate of 80 MHz with 2.6 W of average power at 800 nm. The beam is attenuated by a half-wave plate and a linear polarizer, and is then focused into an acousto-optic modulator (AOM; M1133-aQ80L-1.5, Isomet) to provide power control with megahertz bandwidth. After the AOM, a lens recollimates the beam, and the beam then enters a 2-mirror galvanometer (SC2000 Digital Scanner, GSI Lumonics). The plane between the two mirrors of the galvanometer is then relayed through a 4f Keplerian telescope to the entrance pupil of a microscope objective. The sample is placed after the microscope objective and the focal volume is adjusted to be 63 μm below the sample surface.
Fig. 1 (a) A diagram showing the main elements of setup used for writing. The microscope objective, eyepiece, and tube lens can be used to see the written region while writing occurs. (b) Diagram of our Mach-Zehnder interferometer used for characterizing samples. Identical microscope objective are used in the sample arm and the reference arm.
We used a 40X microscope objective with NA 0.60 (LUCPlanFLN, Olympus). The microscope objective’s used field of view has a diameter of 340 μm, determined by the maximum field angle used and its effective focal length. The beam optimally filled the entrance pupil of the objective to maximize the effective numerical aperture of the focused beam. A CCD camera monitors the obliquely scattered light during the writing. The sample was sandwiched between two borosilicate glass #1.5 coverslips that were between 160 μm and 190 μm thick. The sample was mounted on a kinematic mount to remove sample tilt that was attached to a linear motor stage configuration, allowing motion in the X-, Y-, and Z-directions using three linear DC motorized stages (VP-25XA, Newport Corp.). The microscope objective was mounted on an Olympus IX70 manual stand. The Olympus IX70 manual stand has a tube lens and an eyepiece that allows the user to see the written region while the sample is mounted in place (see Fig. 1(a) below).
Given the nonlinear nature of the process, small misalignments in the writing system will affect the focal spot quality at the focal volume, and thus the efficiency of the nonlinear writing process. Some specific alignment considerations are as follows. Beam aberrations were minimized by using lenses at a working f-number larger than 50 (other than the microscope objective). Pupil matching was ensured by moving the galvo mirrors back and forth slightly, without rotating them, until vignetting was not observed for all the fields used.
The orthogonal galvanometer mirrors are controlled to create a raster pattern with 0.5 μm line spacings, which is smaller than the ~1 μm width of each line, resulting in a nearly continuous refractive index change. The AOM is used to control the laser power as the focal volume quickly scans the sample [24], which is synchronized with the galvanometer scanning.
For sample metrology, phase contrast microscopy photographs of the written region where taken with a 20X phase contrast microscope objective in an Olympus BX51 microscope system. Quantitative information was obtained by using a custom-built Mach-Zehnder interferometer to obtain 2D phase maps using a 633 nm HeNe laser, see Fig. 1(b). This interferometer has identical microscope objectives (Olympus objectives Plan N 40X, NA 0.65) in both the sample and the reference arms. The pattern plane is conjugate to the detector plane. The microscope objectives in both arms are located at the same distance with respect to the detector plane to ensure that no curvature in the measured interfered wavefront is induced.
3. Calibration function
The laser power through the writing microscope objective was calibrated and linearized based on the input voltage applied to the AOM. The contact lenses have a base curvature of 8.7 mm, a diameter of 14 mm, and −0.50 D of optical power from lot B00HM58. The samples were removed from their packages, carefully applanated so as not to damage them, and sandwiched between two #1.5 coverslips. While sandwiched between the coverslips, the samples were in contact with sufficient contact lens solution from their initial package such that the sample would stay hydrated during the writing and the reading process.
Care was taken to ensure that the normal of the applanated sample was parallel to the optical axis, ensuring minimal sample tilt. If tilt was present, the focal volume would be at different depths within the sample as we move the sample laterally to write in different regions. Patterns written at different depths will have different amounts of spherical aberration, altering the efficiency of the writing process. The objective used for writing has an adjustable collar to compensate for the spherical aberration introduced by writing at different depths inside the sample. This collar was set to minimize spherical aberration at ~63 μm below the sample surface, which was the nominal writing depth, and through the coverslip, which also introduces spherical aberration. Given sample size and objective field of view, many structures can be written inside a single sample since the XY stages can move the writing location to different regions in the sample.
To determine the calibration function that characterizes the induced optical phase shift as a function of scanning speed and laser power, we measured the change in phase corresponding to a given power and speed using the Mach-Zehnder interferometer. For each data point of a phase change at a given writing speed and power, we wrote five to eight different rectangles of about 114 μm by 38 μm written at the corresponding speed and power. Figure 2(a) shows a phase contrast image of some of these rectangular patterns, while Fig. 2(b) shows an interferogram from the Mach-Zehnder interferometer of a region containing two rectangles. The interferometer has sufficient tilt induced to obtain about eight fringes across the narrow dimension of the written rectangles. Figure 2(b) also shows the phase discontinuity induced by the writing process at the edges of the written rectangles. We obtained 2D phase maps from this data using carrier fringe methods [25]. Once extracted, the phase was unwrapped using the Goldstein’s branch cut unwrapping algorithm [26, 27].
Fig. 2 (a) Written rectangles of constant phase. (b) Fringes taken with the interferometer to measure the induced phase change.
Preferably, the phase map in a written region should be measured before and after the writing takes place. By subtracting the phase before the writing takes place, the only phase left should be the changes induced by the writing itself. Performing this subtraction should remove any phase variation imperfections in the incoming wavefront and any phase variations inherently present in the sample. Furthermore, subtracting the background should remove any variations or errors introduced in the phase map by the interferometer itself because of small imperfections causing differences between the sample and reference arm. Doing so, however, was impractical given the location and number of samples needed for the study. Instead, we subtracted the local background and assumed there was little variation in the sample across neighboring regions, given that commercial contact lenses were used. The phase map from a region near each rectangle (~200 μm of separation) was used to subtract the local background phase. Figure 3 shows the phase map of the interferogram from Fig. 2(b) with the local background phase subtracted. It is clear there are two rectangular regions with a distinct phase shift from the base substrate.
Fig. 3 Retrieved phase map of region containing two rectangles of constant phase. The rectangles shown were written at 675 mW at 30 mm/s.
In addition to the background phase, some samples had residual tilt. Tilt was removed using a similar procedure to the background phase by performing a least-squares fit, as shown in Fig. 4.
A data point in the calibration function consists of the phase change corresponding to a given power and writing speed. We wrote a program that gives the average induced delta phase for a given rectangle in the written region by manually selecting the outer boundaries of the rectangular regions. Data points were collected at 3, 5, 10, 15, 20, 30, and 40 mm/s at power intervals of 48.2 mW. The lower power tested at each speed changed from speed to speed. We increased the power in the aforementioned power steps until we reached 675 mW or until sample damage was observed. The data points at which we observed sample damage were not measured and, therefore, not included in the calibration function.
The carrier fringe method [25] to obtain the phase map from the interference fringes does give sign information as it can recognize between elevations and depressions in the phase profile. However, we still confirmed the sign of the phase change. First, we nulled the tilt difference between the mirrors in both arms of the Mach-Zehnder interferometer. Then, a written rectangle was placed in the sample arm. This time, however, the sample was applanated with a cover slip to introduce wedge, as shown in Fig. 5. This re-introduced tilt fringes in the interferometer. In this configuration, the rays that cross the sample on the thicker side travel a longer optical path. By observing whether the fringes would shift towards the side with more optical path length or towards the side with less optical path length, the sign of the phase change can be determined. With this configuration, fringes inside the written rectangles shifted towards the thicker side of the sample. The relative refractive index change induced must be negative, as the fringes moved towards the side with more optical path length as to cancel the negative phase that they acquired from passing through the written region.
Fig. 5 Sample with cover glass introducing wedge. This was done to validate the sign of the induced phase change in the sample from the writing.
By analogy with the electron-hole density generation rate in a semiconductor under illumination of laser light [28, 29], we proposed a calibration function of the form
where E is the deposited energy and γ and κ are constants. By presuming that all of the non-linear absorption is entirely due to absorption of a given order, and that all of the non-linear absorption occurs at an infinitesimally thin layer, Eq. (2) becomeswhere P is the power [mW], v is the scan speed [mm/s], and the fitting parameters are α, β, and N. We found the fitting parameters to be α ( = 0.3837), β ( = 2.169e-10 [mm/(s·mWN)]), and N ( = 4). The phase is in number of waves at 633 nm, which was the metrology wavelength used for all the measurements reported in this manuscript.The fitting parameters in Eq. (3) were found by using a root least square fitting method using 43 different data points. Each one of these data points represents a different power/speed combination at which we obtained a measurable change in the phase but we did not inflict sample damage. Each one of these individual data points was obtained from averaging the phase change from five to eight rectangles that were written with the same power/speed combination. Each measurement of the written rectangle was the result of averaging the induced phase change of the pixels inside the region in which we wrote a rectangle, generating its own statistical spread. This can be seen visually in Fig. 3. Each written and measured rectangle is not an individual measurement but a large set of data. Each rectangle in the phase maps collected is made of tens of thousands of pixels, and each individual pixel already carries the phase information that we are interested in obtaining. The phases provided by individual pixels, and not the individual rectangles, are the individual measurements. Figure 6 shows the histograms of the number of pixels counted in Δϕ intervals outside and inside of the rectangle shown to the right in Fig. 3. The variance assigned to a power/speed combination is the average of the variances obtained for the rectangles written at that power/speed combination. To illustrate this explanation visually, Fig. 7 shows the results of the measured rectangles that we obtained for one of the data points out of the 43 data points used in the fitting (including an amplitude scalar of −1). Figure 7 shows the results from eight rectangles written at 675 mW and 30 mm/s. The phase data point used in the fitting for Eq. (3) for 675 mW and 30 mm/s is the average of these eight rectangles, and the variance of this data point is the average of the variance of these rectangles.
Fig. 6 (a) Distribution of pixels providing Δϕ in area surrounding the rectangle at the right in Fig. 3. The lower Δϕ contained in each column is (−0.0661 waves) + (0.005 waves)*(Column Number-1) while the upper Δϕ contained in each column is (−0.0661 waves) + (0.005 waves)*(Column Number). (b) Distribution of pixels providing Δϕ in area inside the rectangle at the right in Fig. 3. The lower Δϕ contained in each column is (−0.3815 waves) + (0.005 waves)*(Column Number-1) while the upper Δϕ contained in each column is (−0.3815 waves) + (0.005 waves)*(Column Number).
The 43 collected data points collected are shown in Fig. 8 compared to the calibration function at best fit for the entire calibration function (including an amplitude scalar of −1). Figure 8 also shows the standard deviation of each data point. The red sections of the fitting in Fig. 8 represent writing conditions over which damage was observed. These 43 data points are shown in 3D in Fig. 9 with the fitted calibration function surface map. This fitting process yielded a value of R2 = 0.98.
Fig. 8 Delta phase measured for different powers at (a) 3 mm/s, (b) 5 mm/s, (c) 10 mm/s, (d) 15 mm/s, (e) 20 mm/s, (f) 30 mm/s, and (g) 40 mm/s. The red part of the fitting represents exposure parameters over which we observed sample damage.
4. Arbitrary refractive structures
Once the calibration function was determined, the writing speed and power can be scaled to write arbitrary refractive structures. To demonstrate this, the Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, and Z10 Zernike polynomials were written in the hydrogel samples over a 150 μm diameter, as defined in the standard Zernike polynomial convention given by Born and Wolf [23]. A list of the explicit form of the first 37 polynomials in this convention, which is unit amplitude normalized, is given by Doyle, et al. [30]. Four identical copies of each Zernike polynomial were written in the sample. Figure 10 shows a phase contrast image of some of these written Zernike polynomials. When writing a given Zernike polynomial, we also had to add the correct amount of piston to ensure that the absolute value of the phase change would range from zero to the maximum desired value.
The squares and crosses in the images are fiducials for registration. We also wrote a description of the sample below the circular Zernike structure. After writing each polynomial set, the samples were measured using the previously described method and a Zernike decomposition of each pattern was obtained. These Zernike polynomials were written at 15 mm/s with a power corresponding to the desired phase change within the image based on the calibration function. In the current system, each Zernike polynomial device took ~1 minute to write. This is limited by data handling between the galvanometer, stages, and software, which was not optimized. In practice, we will use the calibration function and large area scanning system [24] to generate structures of suitable size for ophthalmic applications.
Example written Zernike polynomials Z4, Z5, and Z9 are shown in Fig. 11. The top row of Fig. 11 shows the phase retrieved when we attempted to write only a given Zernike polynomial. The bottom row shows the ideal phase for each of the respective Zernike polynomials. Figure 12 shows the absolute value (in waves) of the coefficients obtained in the Zernike decomposition of when we attempted to write only one Zernike polynomial (Z4, Z5, and Z9). Figure 12 averages the coefficients of the four copies of each Zernike polynomial that we wrote. The error bars in Fig. 12 are the standard deviations of the coefficients found for each Zernike polynomial over the four phase maps corresponding to the four copies. Based on these results, the average absolute value of the coefficient of the Zernike polynomial that we were trying to write was at least 4.7 times higher than the absolute value of the second largest coefficient present among the first 20 polynomials (without including piston).
Fig. 11 (a) Phase map obtained when Z4 and piston were written. (b) Phase map obtained when Z5 and piston were written. (c) Phase map obtained when Z9 and piston were written. (d) Ideal structure containing only Z4 and piston. (e) Ideal structure containing only Z5 and piston. (f) Ideal structure containing only Z9 and piston.
Fig. 12 Zernike decomposition (absolute value) of the structures written intended to have only Z4, Z5, and Z9 polynomials.
Another way in which we quantified the Zernike structure writing process was by using the signal to noise ratio of the structure. We defined the signal of the written structure be the largest coefficient found in the Zernike decomposition of the measured phase map (piston excluded). The average of the signals from the fours copies is what is shown in Table 1. Furthermore, for each structure we wrote, we obtained the phase map of the noise of such structure. The phase map of the noise was obtained from subtracting the largest Zernike present (i.e., the Zernike polynomial from the signal) and piston from the measured phase map. The ideal structure would consist of only the Zernike polynomial from the signal and piston. As such, subtracting such Zernike polynomial and piston from the measured phase map is equivalent to removing the ideal phase map from the measured phase map. The result of this subtraction is the noise phase map. The noise for each structure was taken to be the standard deviation of its corresponding noise phase map. Based on the Zernike convention used, this calculation is mathematically equivalent to calculating the standard deviation of each phase map by using Eq. (4) with the residual Zernike error terms of that phase map [30, 31]. In this case, the residual Zernike error terms are all the Zernike polynomials other than the Zernike polynomial from the signal and piston. In Eq. (4), the “n” and “m” indices are the indices that each Zernike polynomial gets in the Born and Wolf convention, δ is the Kronecker delta function, and Ci is the coefficient of the “ith” Zernike polynomial [23, 30]. The average of the noises from the fours copies is what is shown in Table 1. The expression in Eq. (4) gives standard deviation, rather than RMS, since the coefficient for piston is not included in the summation [31, 32].
Table 1. Signal and noise for the set of four copies of each written Zernike polynomial. (λ = 633 nm)
Using the calibration curve, we also tested our capacity to write an arbitrary amount of a given Zernike polynomial. We did this by writing four copies of the Z10 polynomial. Z10 was chosen because it has a refractive profile that is not likely to be in the background of the contact lenses. The maximum change in phase for these four copies was close to the maximum we can achieve in a single layer. These patterns use the moniker “Z10-100”, since they comprised the Z10 polynomial and the coefficient value was 100% of the maximum value set for this experiment. Similarly, four refractive structures were written at Z10-75 or 75% of the maximum value set for this experiment, as well as four structures each at Z10-50 and Z10-25. Each of these refractive structures were written at 25 mm/s and the calibration function was used to adjust the power locally during writing to generate the refractive structures.
Table 2 shows the results of this experiment for writing scaled phase structures for Z10 at 100%, 75%, 50%, and 25% of the maximum value. The structures can be written with good reproducibility, as the maximum standard deviation in the Z10 coefficient was ≤0.0063 waves and the deviation from the desired structures was <11%.
Table 2. Coefficient for Z10 of structures with different amounts of phase change
Until now, all of the studies involved using only a single layer of writing. The final experiment we did was to write four structures of Z10, but using three layers instead of only one. This was done to study the effects of writing multiple layers on the measured phase change. The first layer was written 81 μm below the interface of coverslip and sample, the second one was written 63 μm below the interface, and the third layer was written 45 μm below the interface. Each layer was a copy of the Z10-100 structures, and as such, the expected coefficient should be three times higher than the coefficient for a single layer Z10-100 structure.
Figure 13 shows a phase map obtained for one of the three-layered Z10-100 structures. Clearly, Z10 (trefoil) can be seen, along with some higher frequency residual phase errors. Figure 14 shows the Zernike decomposition of these three-layered structures, along the standard deviation of the coefficients over the four copies. The average Z10 coefficient for these structures was 0.358 waves (at 633 nm), and the average of the noises (as defined for Table 1) was 0.050 waves. This gives a SNR of 7.2 for the three-layered structures. When a single layer of Z10 was written, the Z10 coefficient found was 0.125 waves, meaning that tripling the number of layers yielded an increase in the Z10 coefficient by a factor of ~2.9.
Fig. 13 (a) Phase map obtained when three layers of Z10 and piston were written. (b) Ideal structure containing only Z10 and piston.
Fig. 14 Zernike decomposition (absolute value) of the three-layered structure in which Z10 was written. The height of each column represents the average of that Zernike coefficient over the four copies that we wrote. The error bars represent the standard deviations of each Zernike coefficient over the four copies that we wrote.
5. Summary and conclusions
We measured the induced phase change that the wavefront experiences when it passes through regions written at different writing speeds and powers in Acuvue 2 contact lenses with ~100 fs laser pulses. To obtain this dependence, we wrote rectangles that had a constant index of refraction for different speed/power combinations. Using a Mach-Zehnder interferometer, we extracted and unwrapped the phase map from the interferograms. The phase change corresponding to a given speed and power was extracted from these phase map pictures by carrying out some further operations. These operations included subtracting the phase map from a neighboring non-written region (considered the background) and removing residual tilt through software. A program calculated the average induced delta phase for a given region by manually selecting the boundaries of such region.
The data points corresponding to a given delta phase for a given speed and power were fitted to a function based on an electron-hole density function. This function is dependent on the focal spot velocity and power, and it fits the data with an R2 value of 0.98. The sign of the delta phase was verified to be negative by placing one of the structures in the Mach-Zehnder in the null configuration while known wedge or tilt was introduced on top of the sample.
The calibration function was used to write the Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, and Z10 Zernike polynomials and these structures were shown to have a signal to noise ratio that was always equal or larger than 3.4. When we tested our ability to write an arbitrary amount of a Zernike, the maximum standard deviation measured in the desired Zernike coefficient was ≤0.0063 waves and the departure from the desired structures was <11%. Once we have a calibration function, we can use it to generate arbitrary refractive corrections. Given that the residual error of the written refractive structures is low, the calibration function found is appropriate.
When a single layer of Z10 was written into the sample, the coefficient corresponding to this polynomial was measured to be 0.125 waves. The Z10 coefficient was 0.358 waves when three layers of these structures were written on top of each other separated by 18 μm. This represents an increase in this coefficient by a factor of ~3, consistent with a tripling of the number of layers.
Furthermore, the experiments and data demonstrate that we can write an arbitrary Zernike structure at 15 mm/s and data points were collected at this speed for the calibration function. However, the experiments and calibration function also show that we can write an arbitrary magnitude Zernike term and multi-layer refractive structures at 25 mm/s. This is critical because this is a speed at which data was not collected to determine the calibration function. Thus, this clearly demonstrates that the calibration function does well at predicting the phase change at all the speeds within the minimum measured speed and maximum measured speed (3 mm/s and 40 mm/s respectively).
This work opens the possibility of femtosecond laser writing of freeform optics in hydrogel-based contact lenses. In 2003, Applegate et al. showed that if the residual root mean square (RMS) error of the wavefront is below 0.050 μm or less, the effect on low and high contrast visual acuity from the residual phase of the wavefront will be negligible [33]. This desired RMS error at 0.050 μm corresponds to 0.079 waves (λ = 633 nm) of error. This work demonstrates that this threshold is achievable for this arbitrary refractive correction writing process. This work opens the possibility of customization of commercially available contact lenses through femtosecond laser writing to correct for higher order aberrations, which is not currently available. We have not characterized the phase shift at other wavelengths yet, however this will be the subject of further investigation.
Acknowledgments
This research was supported in part by the Center for Emerging and Innovative Sciences, a New York State-supported (NYSTAR) Center for Advanced Technology (award C090130), in part by funds from the University of Rochester School of Medicine & Dentistry (SAC Incubator program), and in part by a sponsored research contract from Clerio Vision, Inc. (award 058149-002). The authors would like to thank Professors Gary W. Wicks and Krystel R. Huxlin, as well as Robert W. Gray, Leva McIntire, and Nicolas S. Brown for useful conversations and advice. Special thanks go to Daniel R. Brooks for his constant and insightful advice in matters of logistics and engineering.
The authors declare the following interests: W. H. Knox and J. D. Ellis have founder’s equity in Clerio Vision, Inc., which partially supported this research. W. H. Knox and J. D. Ellis have no fiduciary responsibility in Clerio.
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