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Abstract
The wavefront aberrations of hydrogel material were altered using a technique of femtosecond laser induced refractive index modification. Gradient-index Fresnel lenses ranging from −3.0 to +1.5 diopters (5.8 mm diameter) were written in contact lens material (Contaflex GM Advance 58). Optical quality was assessed in terms of wavefront aberrations, image contrast, and scatter. The spherical and cylindrical power writing errors were 0.05 D ± 0.07 D and 0.10 D ± 0.14 D respectively, and the lenses preserved almost all spatial frequency information relevant for human vision. The induced wavefronts were comprised of a mosaic of approximately 1400 stitched segments, leading to undesirable diffraction. This work demonstrates the capability of femtosecond laser induced refractive index modification to produce high quality optical devices for vision correction.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
One of the many uses of femtosecond laser writing lies in its ability to induce refractive index changes within biocompatible materials with micron-scale spatial resolution. A refractive index change may be locally induced by focusing femtosecond laser pulses within a material, where a non-linear absorption process leads to a localized chemical reaction within the focal volume. By controlling the exposure parameters of the delivery beam (e.g. power, speed, number of scans, line separation, exposure time, etc.), a refractive index pattern may be inscribed thereby inducing a wavefront aberration. The induced wavefront may be used to correct the eye’s refractive error or increase the eye’s depth of focus for presbyopia correction.
Several research groups have investigated ocular wavefront correction by locally changing the refractive index inside of a material rather than by changing the shape of its surface. Applying this technique to biocompatible materials opens the possibility of inscribing a wavefront correction directly into contact lenses and/or intraocular lenses [1–7]. Being able to inscribe a wavefront correction directly into a contact lens, or even in an intraocular lens that is already in a patient’s eye, enables this technique to address particular customization needs that are difficult or impractical to implement otherwise. Figure 1(a) illustrates the most common approach of creating optical devices through topographical changes, while Figs. 1(b) and 1(c) illustrate the concept of obtaining optical devices through a variation in refractive index.
Fig. 1 (a) Lens obtained by shaping the interface between materials with different refractive indices. (b) Gradient-index (GRIN) lens obtained by varying the refractive index spatially. (c) GRIN Fresnel lens. In the most general case, Δn can be positive or negative, and it is drawn in Figs. 1(b) and 1(c) as a negative quantity.
The induced wavefront is defined by the optical phase change caused by the femtosecond laser modification of refractive index. Optical phase change (Δϕ) is defined in Eq. (1):
where Δn is the refractive index change induced in the material, d is the axial thickness of the modified region, and λ is the wavelength of light of the wavefront [4, 8]. Equation (1) calculates the phase change induced in number of waves [4, 8].
The efficacy of the phase change depends on the pairing of the laser system parameters and material compatibility. Previous studies in this field have investigated the impact of material properties (e.g. chemical composition, water content) on the magnitude of available optical phase change [1-2, 5-6, 8-14]. If one wave of phase change can be obtained, it is possible to phase-wrap the wavefront to obtain Fresnel lenses, as shown in Fig. 1(c), while maintaining monofocality at the design wavelength [15-16]. However, the maximum phase change induced in a single layer can be smaller than one wave, requiring multiple layers to accumulate more phase [4, 7]. However, multiple layers results in longer writing time, potential registration errors, higher cost, and poor scalability. As such, it is desirable to write a complete device in just one single layer.
Recently, we reported the synthesis of custom hydrogels that led to phase changes significantly larger than one wave in the center of the visible spectrum in a single layer with femtosecond writing [8]. At the same time, it is advantageous to be able to induce large phase changes in materials from which optical devices are already being made. In this work, we report results of single-layer large phase changes close to the center of the visible spectrum (543 nm) with Contaflex GM Advance 58 (Contamac, Ltd.), a soft contact lens hydrogel material with 58% water content. No modifications were made to the material to enhance its compatibility with femtosecond writing as it has been reported elsewhere [2, 8].
In the current study, material characterization was carried out and Fresnel lenses were subsequently created over an area of 6 mm in diameter. The optical quality of these lenses was then assessed with a custom-developed Shack-Hartmann wavefront sensor and an optical bench test system.
2. Methods
A diagram of the writing setup used in this study is shown in Fig. 2(a). A Spectra-Physics Mai Tai HP laser was used to create 100 femtosecond (fs) pulses with a repetition rate of 80 MHz, a central wavelength of 800 nm, and an average power of 3.0 W. A second harmonic generator (SHG) doubled the frequency of the laser to yield 400 nm pulses, which was the central wavelength used for the writing. A pulse compressor made of two prisms and a mirror directly followed the SHG to allow control of the time width of the individual pulses at the sample plane [17]. The pulse compressor corrected the dispersion introduced by the optics in the system and resulted in pulses at the sample plane of full width at half maximum (FWHM) of 178 fs as measured by a commercial TPA-UV autocorrelator using a sech2 best fit. The beam was then focused through an electronic shutter, which was used to allow the blocking or the passing of the beam as the writing takes place. An acousto-optic modulator (AOM) was used to control the intensity of the laser beam at high speeds, after which the beam was directed onto an integrated 2-axis galvanometer. The galvanometer was relayed with a unit magnification Keplerian telescope to the entrance pupil of an air-immersion microscope objective used to focus the light into the sample and perform the writing. A tube lens and eyepiece were set in place for the user to monitor the writing in progress, while a CCD camera monitored the light obliquely scattered from the sample during the writing.
Fig. 2 (a) Diagram of the femtosecond writing setup. (b) Diagram illustrating that the lenses were written with galvanometer scanning and aided by controlling the 3D location of the sample.
The field of view of the writing system was 245 μm by 88 μm. To write a refractive device over an optical zone 6 mm in diameter, the hydrogels were mounted on a kinematic stage whose location was controlled in 3D by a motorized XYZ translational stage. This allowed the lenses to be written as stitched mosaics containing approximately 1400 rectangles. The galvanometer mirrors scanned the sample and modified the material over the field of view of the optical system, and when done, the motorized stages moved the sample to the next part of the sample to be modified appropriately. This writing strategy is shown schematically in Fig. 2(b).
The scanning was achieved by moving the galvanometer mirrors in a way that created a raster scan pattern over the field of view with a 0.5 μm line spacing at a constant scanning speed of 25 mm/s. As the laser beam scanned the sample, the amount of energy deposited at each spot, and therefore the induced phase change in the wavefront at each spot, was controlled with the AOM according to the desired phase profile. The sample was hydrated at all times during the writing in a borate buffered saline (BBS) solution. The BBS solution had a standard concentration of 0.9% and a pH specification of 7.10 to 7.30. After the writing, the lenses were stored in a ReNu multipurpose solution from Bausch and Lomb Incorporated.
In order to know the correct amount of energy that needed to be deposited at each spot to yield the necessary phase change, we followed the interferometric calibration technique described elsewhere to measure the material response [4]. The material response is defined as the phase change induced in the material as a function of writing power. Figure 3 shows two squares written with 130 mW. The phase change induced at 130 mW represents one point in the material response. Figure 3(a) shows a bright field picture of the two squares, while Fig. 3(b) shows the interference fringes of the same region. The sign of the induced phase is deduced from the direction in which the fringes shift in the interferogram [4], while the magnitude is obtained from the relative shift of the fringes inside of the written region relative to the fringes in the unwritten region. The interferometer employed used a wavelength of 633 nm. The measured material response is shown in Section 3. Similarly, the bright field pictures can be used to measure the relative transmission of the written areas compared to the unwritten areas. This is done by comparing the intensity of the bright field image inside of the written areas to the intensity of the surrounding unwritten areas. The relative transmission of the written areas compared to the unwritten areas transmission as a function of writing power is also shown in Section 3.
Fig. 3 (a) Bright field picture of region with two small squares written with femtosecond writing with a power of 130 mW. (b) Interference fringes of the same region. Notice the clear phase change within the written squares. Interferometer wavelength is 633 nm.
For this study, six Fresnel GRIN lenses were created in plano hydrogels made of Contaflex GM Advance 58 using only one layer of induced phase change. This material is a non-ionic, hydrophilic polymer based on glycerol methacrylate, has a chemical formula of C34H51NO14, and is currently used in the manufacturing of soft lenses [18–20]. This polymer is also known as “Acofilcon A”, and its chemical name is “Diprop-2-enyl (2Z)-but-2-enedioate polymer with (2RS)-2,3-Dihydroxypropyl 2-methylprop-2-enoate, 1-Ethenylpyrrolidin-2-one, 2-hydroxyethyl 2-methylprop-2-enoate and Methyl 2-methylprop-2-enoate” as given by the U.S. National Center for Biotechnology Information [20]. The nominal designs of the lenses were as follows: five lenses with pure spherical power (−3.00 D, −1.50 D, −0.75 D, +0.75 D, +1.50 D) and one cylindrical lens (0.00 DS, −1.50 DC). The design wavelength for all of these lenses was 543 nm and the height of the phase wrapping between Fresnel zones was 2π radians. As such, one should expect no multifocality from the nominal design of these lenses at the design wavelength.
Several measurements were carried out on the finished lenses. While the lenses were written over a diameter of 6 mm, they were measured over a diameter of 5.8 mm to avoid edge artifacts. One of these measurements was imaging the lenses with a 20X differential interference contrast (DIC) microscopy system to evaluate the general quality of the lens written. The written wavefront in each lens was also measured with a custom-built Shack-Hartmann wavefront sensor. The wavefront from each sample was recorded before the writing and after the writing in the same orientation. Subtracting the pre-writing wavefront from the post-writing wavefront allows the calculation of the wavefront induced by the writing procedure. Using the spot pattern, the coefficients corresponding to the Zernike polynomials from 2nd to 10th order as specified by the Optical Society of America (OSA) convention were obtained [21]. The wavefront was calculated using the spots over a 5.8 mm diameter corresponding to the central part of the lens being measured. The lenslet array used in the wavefront sensor has a lenslet pitch of 188 μm, focal length of 7.96 mm, and a magnification between the sample and the lenslet array of 2:1, which yields 157 lenslets over the measurement zone.
Decomposition of the wavefront into Zernike polynomials allows the calculation of the root-mean-square (RMS) of the wavefront through the use of Eq. (2),
where is the coefficient corresponding to the Zernike polynomial specified by the n and m indices [22]. Higher-order RMS (HORMS) was calculated by applying Eq. (2) for . Furthermore, the Zernike coefficients can also be used to calculate the spherical power (S) and cylindrical power (C) of the measured lenses, in the negative sign convention, through the use of Eq. (3),where r is the pupil radius (2.9 mm in our case) and tan−1 is the arctangent function [23]. Equation (3) differs from the one derived by Dai as the goal here is to measure the power of the induced wavefront itself and not of the spectacle correction [23]. It has been reported before that measuring multifocal elements with a Shack-Hartmann wavefront sensor can result in the introduction of artifacts in the measured wavefront [24–28]. As such, all wavefront measurements collected with the Shack-Hartmann wavefront sensor were carried out at the design wavelength of 543 nm, at which the nominal design is purely monofocal. In theory, no multifocality and no artifacts should be seen at the design wavelength with a phase discontinuity between Fresnel zones of 2π radians [24-25].Furthermore, a custom built optical bench was used to collect the 543 nm modulation transfer function (MTF) of each lens at best focus [29]. A diagram of this custom built optical bench is shown in Fig. 4(a). The lenses were tested over the central diameter of 5.8 mm. The optical bench imaged a 1951 USAF resolution target, as shown in Fig. 4(b). The resolution target was illuminated with a white LED and the light was filtered with a green filter having a central wavelength at 543 nm and a FWHM of 10 nm. The vertical and horizontal edges from the square in the image collected were used to compute the vertical and horizontal edge spread function (ESF), from which the horizontal and vertical MTFs were calculated at best focus. Calculating a one-dimensional slice through the MTF from measurement of the ESF involves the intermediate step of calculating the line spread function (LSF), as described elsewhere in the literature [30-31]. The optical bench used a Badal optometer to induce defocus from −5 D to + 5 D while keeping the lens at a plane conjugate to the aperture stop plane. This plane conjugate to the aperture stop is referred to as pupil plane II and shown in Fig. 4(a). The area under the MTF (aMTF) curves from 0 lp/° to 60 lp/° was computed and normalized to the area of a diffraction limited lens as shown in Fig. 5. The integration was carried out up to 60 lp/° as this spatial frequency is the upper limit of human vision and information above this frequency yields no improvement in the perceived image in human vision [32–34].
Fig. 4 (a) Diagram of the optical bench used for measurement of the MTF. The system images a resolution target while the tested lens is placed conjugate to the aperture stop plane. The Badal optometer brings the image to best focus. (b) Image of resolution target collected with an unwritten plano hydrogel. The green arrow added to this image points at the square whose edges were used to calculate the horizontal and vertical MTFs. The element surrounded by the red rectangle corresponds to 31 lp/°. Note that 30 lp/° corresponds to the clinical guideline of adequate resolution (i.e. 20/20 Snellen visual acuity).
Fig. 5 MTF plot of a theoretical diffraction limited lens and of a theoretical aberrated GRIN lens, both over the same aperture. The aMTF for this aberrated GRIN lens is the green area divided by the sum of the green and the blue areas.
Finally, two weak diffraction streaks were observed when a laser is shone through the written lenses. The intensity as a function of diffracted angle from the observed two diffraction streaks was measured for the +1.5 D lens from −90° to +90° with a collimated 633 nm continuous-wave (CW) laser. These measurements were carried out with a power meter mounted on a computer-controlled rotational scanning stage. This was used to detect the diffracted light over a 180° arc, 75 mm away, above the sample. A thin slit placed in front of the power meter head made the integration step for each measurement to be 0.21°. The metrology beam used in this setup creates a signal of FWHM over an angle of 0.55° even when there is no sample being tested. The intensity as a function of diffracted angle was also measured for an unwritten plano hydrogel for comparison [1].
3. Results
The experimental data for the material response is shown in Fig. 6. A least-square fit was applied as
where P is the writing power in mW, is the induced phase in number of waves at 632.8 nm, and the fitting parameters are α, ζ, and N [4]. The fitting parameters were found to be α = 1.2975, ζ = 6.56025e-05 [1/mW(N)], and N = 2. The fitting yielded a coefficient of determination of R2 = 0.9986. The best fit obtained for the material response is shown in Fig. 6.Figure 7 shows the relative transmission of the written areas compared to the unwritten areas transmission as a function of writing power. The relative transmission did not change significantly as a function of induced optical phase change. The average normalized transmission was 0.96 ± 0.20 and was poorly correlated with optical phase change (R2 = 0.14). Therefore, the written areas did not significantly attenuate the light nor affect transparency.
Fig. 7 Relative transmission of the written areas compared to the unwritten areas as a function of writing power. The horizontal black line highlights the relative transmission value of 1.0.
Assuming negligible material dispersion between 633 nm and 543 nm, the material response found at 633 nm, shown in Fig. 6, can be multiplied by a factor of (633/543) to obtain the material response at 543 nm. This factor can be derived by applying Eq. (1) for the two wavelengths and then dividing one equation by the other. Therefore, the induced phase of −0.94 waves at 633 nm, written with 140 mW of power, corresponds to an induced phase of −1.10 waves at 543 nm.
With knowledge of the material response, we proceeded to write the Fresnel lenses with nominal designs described in Section 2. Figure 8 shows a picture of one of these lenses under a DIC microscope. In this picture, the phase discontinuities at the edge of each Fresnel zone can be clearly discerned. Furthermore, the edges of each individual writing zone in the stitched mosaic can also be seen as a grid. The size of each one of these individual elements corresponds to the field of view of the galvanometer-relay-objective scanning system shown in Fig. 2(a). This stitching grid created weak diffraction orders that will be described later in this section.
In Fig. 8 the short edges of each individual writing zone (as determined by the scanner’s field of view) are more visible than the long edges. This may be an indication of higher refractive index change, which may have came from the fact that the writing beam lingered a bit along these locations, as they were the return points for the writing beam. DIC microscopy highlights the regions with large phase gradients, which makes phase discontinuities or jumps very noticeable [35], thus the stitched interfaces and Fresnel zone interfaces are easily visible.
The imaging performance of the created lenses is as follows. The wavefront data collected with the Shack-Hartmann wavefront sensor and analyzed with Eq. (2) and Eq. (3) are given by Table 1 and shown graphically in Fig. 9 and Fig. 10. The wavefront results yield a spherical power writing error of 0.05 D ± 0.07 D, a cylindrical power writing error of 0.10 D ± 0.14 D, and a HORMS of 0.14 μm ± 0.03 μm. Figure 11 shows the MTF curves of three of the written lenses, collected with the optical bench, as well as images of the resolution target created with these same lenses at best focus. The aMTF data measured for all the written spherical lenses are shown in Table 2. The MTF curves yield an average aMTF of 0.86 ± 0.08 for the spherical lenses written.
Table 1. Wavefront data from each of the written Fresnel lenses.
Fig. 9 Wavefront, as measured by the Shack-Hartman sensor, of the written lens with nominal design of (a) −3.0 D, (b) −1.5 D, (c) −0.75 D, (d) 0.00 DS, −1.50 DC, (e) + 0.75 D, and (f) +1.50 D.
Fig. 10 (a) Obtained spherical power versus the intended spherical power. The dashed line illustrates the ideal case in which the obtained and intended spherical powers are equal. (b) Obtained error in the cylindrical power versus the intended spherical power. The dashed line illustrates the ideal case in which the obtained error in the cylindrical power is zero. (c) Obtained HORMS versus the intended spherical power. The dashed line illustrates the ideal case in which the obtained HORMS is zero.
Fig. 11 (a) Collected horizontal and vertical MTF curves for the lenses with intended spherical powers of −0.75 D, −1.50 D, and −3.00 D respectively. The MTF curve of a diffraction-limited lens is also shown for reference. (b) Images of the resolution target created by each lens. The area surrounded by the green square is zoomed in (c). (c) The central part of each image, which contains the elements with higher spatial frequencies. The element surrounded by the magenta rectangle corresponds to 35 lp/°, while the element surrounded by the yellow rectangle corresponds to 62 lp/°. Note that 30 lp/° corresponds to the clinical guideline of adequate resolution (i.e. 20/20 Snellen visual acuity), while 60 lp/° is the Nyquist limit as determined by retinal photoreceptor sampling.
Table 2. aMTF data of the spherical lenses.
As mentioned before, the grid created by the stitching mosaic acts as a 2D diffraction grating. This phenomenon can be seen in Fig. 12(a). In this figure, individual orders of diffraction are seen after a CW 633 nm laser beam passes through the lens with nominal design of +1.50 D of spherical power. The direction, θ, in which each diffractive order is diffracted is given by the diffraction equation
where m is the order of diffraction, λ is the metrology wavelength (633 nm in our case), and p is the period of the grid [1]. As shown in Fig. 12(a), the stitching grid creates two streaks. For ease of reference, these streaks are labeled as “streak 1” and “streak 2”. Streak 1 has higher number of orders discernable, as well as having a smaller angular separation between the different orders of refraction, as this streak corresponds to the direction in which each element in the mosaic appears every 245 μm. Streak 2 corresponds to the direction in which each element in the mosaic appears every 88 μm.Fig. 12 (a) Picture of diffraction streaks created when a 633 nm laser goes through the lens with nominal design of +1.50 D of spherical power. (b) Same picture as in (a) but with an attenuation filter of optical density of 3.9 in front of the sample.
Each individual diffracted order is much weaker than the undiffracted (zeroth order) beam. Even the lower diffracted orders with more power have an intensity of about 400 times weaker than the intensity of the undiffracted beam from power meter measurements. While the diffraction streaks can be clearly seen in Fig. 12(a), note that both Fig. 12(a) and 12(b) were taken with oversaturated pixels at the undiffracted order. Figure 12(b) was taken with an additional attenuation filter in front of the sample.
The diffracted energy as a function of angle for streak 1 and streak 2 is shown in Fig. 13. This figure also shows the measurement of an unwritten sample for reference. From these measurements, we obtained that the angular width between the two directions where the diffracted intensity decays to 1/1000 of its maximum value (i.e. full width 1/1000) is 2.67° for an unwritten lens, 9.45° for streak 1, and 3.73° for streak 2. The reason why individual diffraction orders can be seen in Fig. 12(a) but not in Fig. 13 is because Fig. 12(a) was taken after letting the beam propagate 84 cm after the sample, while Fig. 13 was taken at 75 mm after the sample, where the orders were still significantly spatially overlapping.
Fig. 13 The diffraction patterns of streak 1 and streak 2 are shown. The pattern from an unwritten sample is shown for reference. The intensity patterns as a function of angle were normalized in these plots to the highest intensity measured for the unwritten sample. The instrument noise floor in this plot is 2.9e-5.
An unexpected finding regarding the written lenses is as follows. We noticed that the written lenses have some degree of multifocality. The written lenses form the brightest images in the optical bench at the desired written optical power. However, the lenses also formed faint images of the resolution target at multiple integers of the intended power. This effect was seen by looking at the resolution target images created as the Badal optometer introduces defocus and it is an indication that the phase discontinuities between Fresnel zones were not exactly 2π radians at the design wavelength.
A Fresnel lens is a diffractive device. If the phase discontinuity between Fresnel zones is of 2π radians all of the energy goes into the + 1 order, which gives the desired image. However, if the phase jump is not an integer number of waves, more images will be created at multiples of the intended power, as no individual diffractive order has 100% diffraction efficiency anymore. Figure 14 shows the different images of the resolution target created with the +1.5 D lens as the Badal optometer introduces different amounts of power. Notice that the brightest image is created at the intended order, but sharp images for other orders can be clearly seen as well. All the pictures shown in Fig. 14 were taken with the same camera exposure time. Please notice that the multifocality diffractive effect shown in Fig. 14 is introduced by the phase wrapping of the Fresnel lens, and not by the stitching grid that creates the diffraction streaks shown in Figs. 12 and 13.
Fig. 14 Image of the resolution target created by the lens designed to have + 1.5 D of power at (a) −1.5 D corresponding to the −1 order, (b) 0.0 D corresponding to the 0 order, (c) +1.5 D corresponding to the +1 order, (d) +3.0 D corresponding to the + 2 order, and (e) +4.5 D corresponding to the +3 order.
By using the five images shown in Fig. 14, it was possible to roughly calculate how much light goes into each one of these five orders (i.e. their diffraction efficiency) for the + 1.5 D lens. This was done by quantifying the relative intensity in each image after subtracting the baseline created by the defocused light coming from the other orders. This approach also assumed negligible amounts of energy going into all other orders. The diffraction efficiencies for the different orders for the +1.5 D lens found this way are shown in Fig. 15.
Fig. 15 Diffraction efficiencies of each order for the +1.5 D lens calculated from the images shown in Fig. 14.
4. Discussion
The high quality of the created lenses can be appreciated qualitatively through the images they formed of the USAF resolution target at best focus. The high quality of the created lenses is also attested quantitatively by the high values of their MTF curves and their low values of higher order aberrations indicated by the wavefront measurements. These results are particularly interesting considering the fact that this material was engineered to have desirable mechanical properties, machining properties, and oxygen transport properties that make it suitable for visual device applications. The fact that this material happens to have desirable properties for clinical use as well as desirable femtosecond writing properties allows the use of femtosecond writing to aid in the manufacturing, customization, implementation of complicated corrections, and general enhancement of devices made from this material.
On top of the advantages mentioned so far, femtosecond laser writing on biocompatible materials also offers the possibility of overcoming some current limitations of contact lenses and intraocular lenses. For instance, contact lenses are aided by thin lens designs as this provides the necessary oxygen transfer to the corneal surface [36]. Femtosecond writing can increase the power of the structures without the need to increase the thickness of the lens, which allows keeping the necessary oxygen transfer without reducing the size of the optical zone used. Furthermore, astigmatism-correcting contact lenses use ballast designs for keeping lenses centered and at a fixed rotation angle. These ballast designs can be compromised by the thickness profile within the optical zone [36]. By inducing the necessary correction without altering the thickness profile, femtosecond writing can offer better comfort, fitting, and stability. Regarding intraocular lenses, one of their limitations consists of the fact that intraocular lens implantation in cataract patients commonly results in residual refractive errors that require additional vision correction. Barañano et al. reported that 45% of the eyes implanted with an intraocular lens presented visual impairment [37], and Zhou et al. reported that 26.8% of the operated eyes were not within ±1.0 D of the target refraction after surgery [38]. In these situations, femtosecond laser writing could be used to imprint the necessary wavefront correction on the implanted intraocular lens, and achieve improved visual performance.
While the results obtained are promising, the written lenses had some imperfections. As shown in Fig. 14, the written lenses were multifocal. This unexpected multifocality calls into question the veracity of the measured wavefronts. The reason for this is that multifocal optical devices can create artifacts in the measurement of the wavefront. As described elsewhere [24–28], these artifacts can be seen in the spot pattern collected with Shack-Hartmann sensors as spot splitting. As such, we cannot rule out the possibility of some artifacts being introduced in our wavefront measurements due to unintended multifocality and spot splitting observed. However, we believe that such artifacts had small impact on our wavefront measurements based on the following reasons. The first reason is that almost all of the light goes into creating the desired image as opposed to going into other orders as seen in Figs. 14 and 15. The second reason is that the majority of the spots seen in the spots pattern from the wavefront sensor show little to no spot splitting, even at the edge of the lenses where the Fresnel zones get narrower. The third reason is that even for those spots that do show some spot splitting, the secondary spots are much fainter than the primary spot. This causes the secondary spots to have little effect in shifting the spot centroid, which is the quantity ultimately used for retrieving the wavefront. The last reason is that the measured wavefronts are in excellent agreement with the designed wavefront.
As already stated, the grid created by the stitching mosaic created two diffractions streaks. These diffraction streaks do not seem to have affected the measured imaging quality at all. This is consistent with the observation that the strongest diffracted orders have intensities around 400 times smaller than that of the undiffracted order. As such, any image created by any of the diffracted orders created by the stitching grid was below the detectable threshold. Still, this diffraction streaks could potentially get cumbersome if a patient looking through one of these devices has a very bright source within his/her field of view. As such, a system creating visual devices with femtosecond writing should have a larger field of view to remove or at least reduce the necessary amount of stitching.
Although there is a possibility that the mentioned defects in the lenses were caused by material imperfections, it is far more likely that these defects were caused by assumptions made during material calibration and/or limitations in the writing system. One assumption made for the material calibration was the assumption that the written region has little material dispersion, which is what allows us to measure the material response at 633 nm and write devices with a design wavelength at 543 nm. A second assumption made was that the material calibration, measured within an hour after the writing, stays constant in time. However, as we mentioned elsewhere in the literature, preliminary observations seem to indicate that the magnitude of the phase change continues to increase even after one hour after the writing is done, stabilizing at a later point in time [8].
The effect of the induced phase change stabilizing after the material calibration was carried out can be seen in Fig. 16. Figure 16 shows the theoretical diffraction efficiency of the different orders created by a Fresnel lens as a function of the phase discontinuity between the Fresnel zones. The functional form of these curves is given by a sinc-squared function [15-16]. As seen in this figure, if the phase jump between Fresnel zones is minus one wave, the efficiency of the + 1 order is 100%, resulting in all of the light going into the desired image. However, if the magnitude of the induced phase shift continues to increase after the writing, the phase discontinuity between Fresnel zones will not be of minus one wave anymore, and some of the light will go into other orders. Using these curves, it was possible to find a value for the phase discontinuity between Fresnel zones that closely matches the diffraction efficiencies reported in Fig. 15. This value is −1.38 waves, and this value is shown in Fig. 16 as a dashed vertical black line. Figure 17 shows the excellent agreement between the theoretical efficiencies that a Fresnel lens wrapped at −1.38 waves would have and the measured diffraction efficiencies reported in Fig. 15. This result is a strong indicator that the induced phase finally stabilized at a value 38% higher in magnitude than what was measured immediately after the writing.
Fig. 16 Theoretical diffraction efficiencies of each order that Fresnel lenses have as a function of the optical phase at which the phase is wrapped. The vertical dashed line is at the phase value of −1.38 waves, which yields a good match with the experimentally found diffraction efficiencies.
Fig. 17 Comparison between the theoretical diffraction efficiencies for a Fresnel lens with phase wrapping of −1.38 waves and the ones measured with images of the resolution target.
It must be noted that ~15 months of time passed between the writing of the +1.5 D lens and the measurement of the diffraction efficiency corresponding to each of its orders. As such, we cannot predict how quickly the induced phase change stabilized after the writing. In the future, it will be crucial to carry out longitudinal studies for the induced phase change after the writing takes place to find out the time scale of this effect and to prevent the creation of undesired multifocal effects. A possible explanation for this time dependence on the induced phase shift is that the femtosecond writing depolymerizes the polymer into smaller fragments. These smaller fragments are likely to require additional time to diffuse out of the polymer background and leave behind a volume with increased water content [8]. To test this hypothesis directly will be the basis of future work.
Besides the assumptions made, the writing system used had multiple limitations that caused a writing time of three hours. Contributing factors included lossy optics, slow electronics, and the great amount of stitching necessary due to small field of view. Lossy optics in the writing system greatly limited the maximum amount of power available at the sample and resulted in the need to reduce the writing speed to achieve the necessary phase change [3-4]. This writing time may lead to phase imperfections such as astigmatism as it is possible to have small amounts of changes in the beam power or in the beam quality due to thermal effects in the SHG or the AOM. These undesirable thermal effects will affect more the last sections to get written in the lens. Some systems with superior specifications have been reported in literature elsewhere [7, 39-40].
Despite the system’s limitations mentioned above, we were successful in writing lenses that preserve almost all of the spatial frequency information relevant to the human eye, as attested by the high aMTF result of 0.86 ± 0.08 for the spherical lenses written. As such, these lenses create images of excellent quality for visual standards, as can be seen qualitatively in Fig. 11. These results open two possibilities from a manufacturing perspective. The first possibility is to use the material as it is with a femtosecond writing system that overcomes the limitations of our own system described earlier. The second is that it may be possible to enhance the femtosecond writing properties of this material even further while maintaining its attractive clinical properties. We have shown elsewhere in literature that it is possible to dramatically enhance a material’s femtosecond writing properties by changing a small percentage of its chemical composition [8]. To study such possibility should be the basis of future work.
In order to simplify the study, the Fresnel lenses were written in plano hydrogels. However, this technology may also be applied to curved surfaces with some extra considerations. It is always important to ensure that the energy is being focused inside of the sample at all times, and doing so increases in complexity with non-planar sample surfaces. Furthermore, when measuring the material response in a sample that already has a base power, the base power needs to be subtracted as to not interfere with the accuracy of the measurement of the phase induced by the femtosecond writing. These and other considerations will be addressed in future work.
The research described here shows great inherent potential for femtosecond writing in a material used for visual applications. However, any emergent technology striving to improve vision should be ultimately tested by its ability to yield satisfactory visual performance. As such, some of the lenses here described are being used in studies seeking to quantify visual acuity in participants looking through them. Initial results, presented elsewhere, indicate that visual performance on the newly perceived best focus when using these lenses is maintained with respect to a diffraction-limited control plate [41]. More studies of this nature will have to be performed in the future as this technology moves forward.
Finally, we mention that this research opens up a great many series of fundamental questions that still remain to be properly addressed. One of these questions is the reason behind the negative refractive index change induced in the material. By using Raman spectroscopy in a different hydrophilic material than the one used here, we recently showed a positive correlation of water concentration with optical phase change [8], leading to a negative refractive index change. Most likely, the explanation for the induced negative refractive index change in this material is also due to a local increase in water concentration, however, Raman studies in this material still have to be done to verify this. Additional pertinent questions to still be answered include the order of the nonlinearity responsible for the femtosecond writing, the chemical changes locally induced in the material in the affected and surrounding regions, and the molecular mechanism responsible for the change. Furthermore, in this study we limited ourselves to optical device designs of second order, i.e. spherical and cylindrical power. This technology carries the potential for more complicated designs, for example with very high magnitude optical correction (e.g. 10 D), with higher order aberration corrections, or with extended depth of focus, all of which shall be the basis of future research.
Funding
Center for Emerging and Innovative Sciences, a New York State-supported (NYSTAR) Center for Advanced Technology (award C090130); National Science Foundation (IIP: 1549700); Clerio Vision, Inc. (award 058149-002).
Acknowledgements
Portions of this work were presented at the Nonlinear Optics (NLO) Topical Meeting in 2017, in the presentation entitled “Nonlinear Optics: The Future Of Vision Correction” (paper number: NM2B.7). Furthermore, preliminary stages of some portions of this research were also presented at: (1) the Association for Research in Vision Ophthalmology (ARVO) conference of 2017 in the poster entitled “Optical bench testing of gradient-index Fresnel lenses written with femtosecond laser induced refractive index change”, (2) the OSA Fall Vision Meeting of 2016 in the poster entitled “Femtosecond-laser written gradient-index Fresnel lenses for vision correction”, and (3) at the 2016 Frontier in Optics Conference in the presentation entitled “IRIS – A New paradigm in Laser Refractive Correction” (paper number: FTh4H.4).
Two of us (WHK and LZ) have founder’s equity in Clerio Vision, but no fiduciary or management responsibility. The authors would like to extend their gratitude to Di Xu and Professor Jonathan D. Ellis for useful conversations and insightful advice.
References and links
1. L. Ding, R. Blackwell, J. F. Künzler, and W. H. Knox, “Large refractive index change in silicone-based and non-silicone-based hydrogel polymers induced by femtosecond laser micro-machining,” Opt. Express 14(24), 11901–11909 (2006). [CrossRef] [PubMed]
2. L. Ding, D. Jani, J. Linhardt, J. F. Künzler, S. Pawar, G. Labenski, T. Smith, and W. H. Knox, “Large enhancement of femtosecond laser micromachining speed in dye-doped hydrogel polymers,” Opt. Express 16(26), 21914–21921 (2008). [CrossRef] [PubMed]
3. L. Xu and W. H. Knox, “Lateral gradient index microlenses written in ophthalmic hydrogel polymers by femtosecond laser micromachining,” Opt. Mater. Express 1(8), 1416–1424 (2011). [CrossRef]
4. G. A. Gandara-Montano, A. Ivansky, D. E. Savage, J. D. Ellis, and W. H. Knox, “Femtosecond laser writing of freeform gradient index microlenses in hydrogel-based contact lenses,” Opt. Mater. Express 5(10), 2257–2271 (2015). [CrossRef]
5. J. Träger, J. Heinzer, H. C. Kim, and N. Hampp, “Polymers for in vivo tuning of refractive properties in intraocular lenses,” Macromol. Biosci. 8(2), 177–183 (2008). [CrossRef] [PubMed]
6. J. Träger, J. Heinzer, H. C. Kim, and N. Hampp, “Materials for intraocular lenses enabling photo-controlled tuning of focal length in vivo,” Proc. SPIE 6632, 66321F (2007). [CrossRef]
7. R. Sahler, J. F. Bille, S. Enright, S. Chhoeung, and K. Chan, “Creation of a refractive lens within an existing intraocular lens using a femtosecond laser,” J. Cataract Refract. Surg. 42(8), 1207–1215 (2016). [CrossRef] [PubMed]
8. G. A. Gandara-Montano, V. Stoy, M. Dudič, V. Petrák, K. Haškovcová, and W. H. Knox, “Large optical phase shifts in hydrogels written with femtosecond laser pulses: elucidating the role of localized water concentration changes,” Opt. Mater. Express 7(9), 3162–3180 (2017). [CrossRef]
9. L. Ding, D. Jani, J. Linhardt, J. F. Künzler, S. Pawar, G. Labenski, T. Smith, and W. H. Knox, “Optimization of femtosecond laser micromachining in hydrogel polymers,” J. Opt. Soc. Am. B 26(9), 1679–1687 (2009). [CrossRef]
10. L. Ding, L. G. Cancado, L. Novotny, W. H. Knox, N. Anderson, D. Jani, J. Linhardt, R. I. Blackwell, and J. F. Künzler, “Micro-Raman spectroscopy of refractive index microstructures in silicone-based hydrogel polymers created by high-repetition-rate femtosecond laser micromachining,” J. Opt. Soc. Am. B 26(4), 595–602 (2009). [CrossRef]
11. A. Vogel, J. Noack, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B 81(8), 1015–1047 (2005). [CrossRef]
12. J. F. Bille, J. Engelhardt, H. R. Volpp, A. Laghouissa, M. Motzkus, Z. Jiang, and R. Sahler, “Chemical basis for alteration of an intraocular lens using a femtosecond laser,” Biomed. Opt. Express 8(3), 1390–1404 (2017). [CrossRef] [PubMed]
13. Z. K. Wang, H. Y. Zheng, C. P. Lim, and Y. C. Lam, “Polymer hydrophilicity and hydrophobicity induced by femtosecond laser direct irradiation,” Appl. Phys. Lett. 95(11), 111110 (2009). [CrossRef]
14. L. Xu, “Femtosecond Laser Micromachining in Ophthalmic Materials (I): Material Optimization and Calibration,” in Femtosecond laser processing of ophthalmic materials and ocular tissues: a novel approach for non-invasive vision correction, L. Xu (Ph.D. Thesis, 2013), University of Rochester, pp. 68–93.
15. D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE Press, 2004), Chap. 4.
16. V. Portney, “Light distribution in diffractive multifocal optics and its optimization,” J. Cataract Refract. Surg. 37(11), 2053–2059 (2011). [CrossRef] [PubMed]
17. R. L. Fork, O. E. Martinez, and J. P. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett. 9(5), 150–152 (1984). [CrossRef] [PubMed]
18. Contamac Ltd, “GM Advance,” http://www.contamac.com/product/gm-advance, 21, Aug. 2017.
19. Contamac Ltd, “Contaflex GM Adavance Technical Data”, http://www.contamac.com/sites/default/files/documents/documents/Contaflex%20GM%20Adv%20%7C%20Technical%20Data.pdf, 21, Aug. 2017.
20. National Center for Biotechnology Information, “Acofilcon A” (PubChem Coumpound Database, CID = 44154199), https://pubchem.ncbi.nlm.nih.gov/compound/44154199, 21, Aug. 2017.
21. L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members. Vision science and its applications, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18(5), S652–S660 (2002). [PubMed]
22. A. Guirao and D. R. Williams, “A method to predict refractive errors from wave aberration data,” Optom. Vis. Sci. 80(1), 36–42 (2003). [CrossRef] [PubMed]
23. G. Dai, Wavefront Optics for Vision Correction (SPIE Press, 2008), Chap. 3.
24. J. Schwiegerling and E. DeHoog, “Problems testing diffractive intraocular lenses with Shack-Hartmann sensors,” Appl. Opt. 49(16), D62–D68 (2010). [CrossRef] [PubMed]
25. F. Castignoles, T. Lepine, P. Chavel, and G. Cohen, “Shack-Hartmann multiple spots with diffractive lenses,” Opt. Lett. 36(8), 1422–1424 (2011). [CrossRef] [PubMed]
26. C. E. Campbell, “Wavefront measurements of diffractive and refractive multifocal intraocular lenses in an artificial eye,” J. Refract. Surg. 24(3), 308–311 (2008). [PubMed]
27. W. N. Charman, R. Montés-Micó, and H. Radhakrishnan, “Problems in the measurement of wavefront aberration for eyes implanted with diffractive bifocal and multifocal intraocular lenses,” J. Refract. Surg. 24(3), 280–286 (2008). [PubMed]
28. D. Gatinel, “Optical performance of monofocal versus multifocal intraocular lenses,” J. Cataract Refract. Surg. 34(11), 1817–1818 (2008). [CrossRef] [PubMed]
29. M. J. Kim, L. Zheleznyak, S. Macrae, H. Tchah, and G. Yoon, “Objective evaluation of through-focus optical performance of presbyopia-correcting intraocular lenses using an optical bench system,” J. Cataract Refract. Surg. 37(7), 1305–1312 (2011). [CrossRef] [PubMed]
30. S. W. Smith, The Scientist and Engineer’s Guide to Digital Signal Processing (California Technical Publishing, 1999), Chap. 25.
31. B. Dube, R. Cicala, A. Closz, and J. P. Rolland, “How good is your lens? Assessing performance with MTF full-field displays,” Appl. Opt. 56(20), 5661–5667 (2017). [CrossRef] [PubMed]
32. J. L. Mannos and D. J. Sakrison, “The effects of a visual fidelity criterion on the encoding of images,” IEEE Trans. Inf. Theory 20(4), 525–536 (1974). [CrossRef]
33. G. Dai, Wavefront Optics for Vision Correction (SPIE Press, 2008), Chap. 8.
34. D. R. Williams, “Aliasing in human foveal vision,” Vision Res. 25(2), 195–205 (1985). [CrossRef] [PubMed]
35. D. B. Murphy, K. R. Spring, M. Parry-Hill, and M. W. Davidson, “Comparison of Phase Contrast and DIC Microscopy” (Nikon Instruments Inc.) https://www.microscopyu.com/tutorials/comparison-of-phase-contrast-and-dic-microscopy, 16, Dec. 2017.
36. I. Cox, IGC Consulting Group, 79 Partridge Hill, Honeoye Falls, NY, 14472 (personal communication 2016).
37. A. E. Barañano, J. Wu, K. Mazhar, S. P. Azen, R. Varma, and Los Angeles Latino Eye Study Group, “Visual acuity outcomes after cataract extraction in adult latinos,” Ophthalmology 115(5), 815–821 (2008). [CrossRef] [PubMed]
38. Z. Zhou, N. G. Congdon, M. Zhang, L. Chen, Z. Zheng, L. Zhang, X. Lin, L. He, K. Choi, and D. S. Lam, “Distribution and visual impact of postoperative refractive error after cataract surgery in rural China: study of cataract outcomes and up-take of services report 4,” J. Cataract Refract. Surg. 33(12), 2083–2090 (2007). [CrossRef] [PubMed]
39. D. R. Brooks, N. S. Brown, D. E. Savage, C. Wang, W. H. Knox, and J. D. Ellis, “Precision large field scanning system for high numerical aperture lenses and application to femtosecond micromachining of ophthalmic materials,” Rev. Sci. Instrum. 85(6), 065107 (2014). [CrossRef] [PubMed]
40. D. E. Savage, D. R. Brooks, M. DeMagistris, L. Xu, S. MacRae, J. D. Ellis, W. H. Knox, and K. R. Huxlin, “First demonstration of ocular refractive change using blue-IRIS in live cats,” Invest. Ophthalmol. Vis. Sci. 55(7), 4603–4612 (2014). [CrossRef] [PubMed]
41. L. Zheleznyak, G. A. Gandara-Montano, S. MacRae, K. H. Huxlin, J. D. Ellis, G. Yoon, and W. H. Knox, “First demonstration of human visual performance through refractive-index modified ophthalmic devices written in hydrogels,” Invest. Ophthalmol. Vis. Sci. 58(8), 1274 (2017). [PubMed]
