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Digitized mini optofluidic element and its application to ophthalmic lenses for presbyopia correction

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Abstract

Using the internally placed elastic membrane and multi-chamber configuration, we designed a digitized mini optofluidic element for fast switching between refractive and diffractive states of preset optical powers. Relief surface was used in the diffractive state. We applied finite element analysis to establish membrane mechanical characteristics for switching at the force level produced by the ocular elements such as ciliary muscle or lower eyelid at eye downgaze. The prototypes were made to demonstrate proof-of-concept. Membrane conformance to the diffractive grooves and imaging quality were demonstrated. The analysis supported switching under the force level exerted by the ocular elements supporting the digitized optofluidic element potential for presbyopia correction by ophthalmic lenses.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

There are several of lens-based options for presbyopia correction [1,2]. The fixed lenses of the multifocal lens-based option (MIOL) have become commonplace in contemporary cataract surgery [2] and are considered to be relatively safe; nevertheless, some patients experience more visual disturbances than patients implanted with a monofocal IOL [3]. As an alternative to the MIOL, accommodating IOLs (AIOL) have been investigated in an attempt to provide a range of foci with minimal adverse optical effects, so called focus-tuning lenses with the dominant approach being to use the optofluidic element with continually changing foci under the action of eye’s ciliary muscle [4]. An overview of the latest focus-tuning AIOL development can be found in several publications [5,6]. The performance of such a focus-tuning lens is complicated by the uncertainty of an interaction between the lens and ciliary muscle due to individual variations as it requires matching a range of pressure exerted by the ciliary muscle on the lens and the range of lens foci. Switching between preset foci at some force exerted by the ciliary muscle may provide a more predictable performance which has been considered in regard to the refractive index change of electro-active materials, the so-called material-based switchable (MBS) intro-ocular lens. One example is a switchable IOL based on liquid-crystal refractive index switching under an electric field action [7]. An effort has been also made to apply MBS to contact lenses for presbyopia correction [8]. In the case of contact lenses, the trigger mechanism of switching could be the pressure exerted by the lower eyelid with eye downgaze for near vision. Though the MBS approach may lead to fast response performance, the complexity of the corresponding ophthalmic lenses makes them challenging to implement.

This paper introduces a mini optofluidic element that combines the simplicity of the analog focus-tuning optofluidic lens operation and switching performance of the material-based switchable lenses. It discusses the corresponding surface-based switchable (SBS) technology application to the switchable intra-ocular and contact lenses.

2. Materials and methods

2.1. Principle of operation

An optofluidic concept of switching between refractive and diffractive optical states as described by Portney [9] was applied to the design and prototyping of the switchable optofluidic optical element. Each optical state manifests its own optical power and switching between the optical states allows switching between the corresponding optical power thereby avoiding a continuous change in optical power which reduces response time. Thus, the analog performance of the optofluidic element with continuous power change [5,6] was digitized by designing the lens with two optical states – refractive and diffractive optical states. If the corresponding switchable optical element is placed within a conventional lens, it converts the lens into a switchable lens. Such digitized optofluidic optical element design and its principle of operation as a section of a switchable lens is explained by Fig. 1.

 figure: Fig. 1.

Fig. 1. A section of a switchable lens demonstrates the bistate digitized optofluidic optical element of the multi-chamber design. Figure 1(a) refers to the refractive state and Fig. 1(b) refers to the diffractive state. A minimum of three elements are involved in the operation: (1) an optical substrate with a relief diffractive guiding surface, (2) an elastic membrane in close proximity to the diffractive guiding surface, and (3) a matching optical fluid that fills the space between the membrane and optical substrate, active chamber. The latter is connected to the internal chamber by multiple through-channels or through-holes for transfer of index-matching fluid. A non-matching fluid occupies the external chamber at the opposite side of the active chamber. The internal and external chambers are formed by the substrate support and membrane cover and their external surfaces become back and front surfaces of the switchable lens.

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The refractive state, as shown in Fig. 1(a), occurs with the matching optical fluid filling the space between the membrane and diffractive guiding surface of the optical substrate, i.e., the active chamber, shaping the membrane in the refractive form of a certain curvature. “Matching fluid” means that its refractive index is very close to the refractive index of the optical substrate material thus masking the diffractive guiding surface as well as the through-holes of the optical substrate to produce the optofluidic element in the refractive state of a certain optical power. As the matching fluid is removed from the active chamber into the internal chamber via through-holes placed along the thinnest portions of the optical substrate at each diffractive groove, the membrane takes a diffractive form by conforming to the diffractive guiding surface and the optofluidic optical element is taking the diffractive state of a different optical power (Fig. 1(b)). A non-matching optical fluid occupies the external chamber at the opposite side of the active chamber thus providing “fluid-membrane-fluid” structures to reduce the gravity effect [6]. The result is a digitized optofluidic element that switches between preset optical powers with membrane shape change between different optical forms which explains use of the term “Surface-Based Switchable” optical element (SBS OE) in describing the technology.

2.2. Optofluidic design

The active chamber is very shallow as the grooves are only a few microns in height and about an approximate 0.03 microliter fluid transfer is required for switching within a 3 mm active optic diameter of the Surface-Based Switchable (SBS) optical element.

PDMS (polydimethylsiloxane) material was selected for the elastic membrane. Table 1 describes the material characteristics of the membrane in PDMS [10] and the optical substrate in TPX [11] of the SBS optical element.

Tables Icon

Table 1. Materials of key optical elements.

A selection of optical fluids is critical for the SBS OE operation. Table 2 describes tetraethylene glycol as the matching fluid of the substrate and perfluorodecalin as the non-matching fluid summarizing their characteristics [1217].

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Table 2. Optical fluids of the Surface-Based Switchable optical element.

Key characteristics of the fluids are: (1) PDMS is impermeable to matching and non-matching fluids; (2) the matching fluid refractive index matches the refractive index of the optical substrate material; and (3) matching and non-matching fluids manifest a significant difference in refractive indices to allow reducing a guiding surface groove height and, therefore, transfer of only a tiny amount of optical fluid in and out of the active chamber for fast switching between the optical states.

2.3. Membrane mechanical characteristics analysis

Final Element Analysis (FEA) was applied to analyze PDMS membrane conformance to the guiding diffractive surface [18] (Innova, Irvine CA USA). The primary goal of FEA was to establish membrane elastic characteristics for conformance to the diffractive guiding surface of the relief shape with different groove heights. The conformance of the membrane to the groove of 6 µm height is shown in Fig. 2(a). Figure 2(b) demonstrates a Conformance Curve (CC) with a zone where the curve transitions from fast to slow pace.

 figure: Fig. 2.

Fig. 2. Membrane conformance to a diffractive surface groove and Conformance Curve. Figure 2(a) shows deformation of 10 µm thick PDMS membrane over the diffractive surface groove of width L = 219 µm, height H = 6 µm and the locations of the largest strain in red color. The membrane conformance to the groove is within width L’ of the groove width L with membrane smoothing $S = L - L^{\prime}$. Figure 2(b) demonstrates the membrane Conformance Curves where conformance defined as C = L’/L is a function of load (pressure difference between external and internal chambers). Conformance Curve A is for groove width L = 88 µm and height H = 6 µm. Conformance Curve B is the modification of Conformance Curve A by including switching pressure, pressure up to which the membrane is kept in the refractive form. The switching pressure is set at 0.20 PSI load resulting in switching to the diffractive state of C=0.67. Conformance Curve C of the membrane of Fig. 2(a) at the diffractive groove height H = 3.41 µm is C = 0.83 at 0.20 PSI load. The corresponding groove height was used in the prototyping and switchable optical element design.

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At certain conditions, the Conformance Curves rapidly increases with load to continue at a slower pace. Good fitting of such curves is

$$y = \frac{x}{{a + bx + c{x^2} + d\sqrt x }}$$
where y = Conformance and x = Load (PSI) magnitudes are used as unitless parameters. The example of the parameters of Conformance Curve B (Fig. 2(b)) is: a = −0.09; b = 0.6; c = 0.04; d = 0.6 (above 0.2 PSI load)

FEA has also revealed that as long as the ratio (groove width, L)/(groove height, H) > 10 (Rule of 10), a transition from fast to slow pace is pronounced. A load at this transition zone shall be used for switching between refractive and diffractive states. The corresponding conformance selected at the transition zone is called Transition Point (TP). The transition from fast to slow pace starts nearly the conformance with the membrane smoothness S equals twice the groove height H (S=2H) and the corresponding conformance value is selected as the Transition Point. Another recommendation by FEA was the benefit derived from truncating and rounding the diffractive peaks to avoid membrane damage and minimize the strain.

FEA also pointed the benefit of including in the SBS OE design a controlled pressure element to set a pressure at which a switching between the optical states occurs, so called switching pressure PS. It is desirable to set a switching pressure PS ≈ PPT where PTP is a load at the Transition Point of the Conformance Curve of the membrane at the narrowest groove of the diffractive guiding surface. This ensures that the membrane refractive form is maintained up to a switching pressure PS and switched to the diffraction state manifests high refraction efficiency.

The membrane smoothing value S (Fig. 2(a)) is maintained for all grooves at the same load leading to the conformance $C = \frac{{L - S}}{L} = 1 - \frac{S}{L}$ increase with the groove width L increase. This is the reason we analyzed membrane mechanical characteristics for conformance at the smallest diffractive groove width of the diffractive guiding surface of the digitized optofluidic element. All other grooves will have higher conformance and, therefore, diffraction efficiency.

2.4. Diffractive state optical quality evaluation

Conformance analysis in the prior section demonstrated the presence of membrane non-conformance in the diffractive state. For instance, Fig. 2(a) shows that the membrane at the membrane smoothness area is shaped by a small radius. The membrane smoothing reduces diffraction efficiency at each groove, and small radius shape at the membrane smoothing spreads out background light at the image in the diffractive state potentially resulting in ocular straylight that reduces image contrast.

The task is to assess the effect of different levels of light background on the image contrast. Modeling was conducted to determine the effect of out-of-focus blur simulating ocular straylight on the Modulation Transfer Function of the in-focus image representing a measure of image contrast. Zemax Optical Design Software (Zemax, LLC, Kirkland, WA USA) was used to collect corresponding data for the eye model [19] using a multi-configuration optical file with one configuration set for zero-order image and another for 1st-order image. In such modeling the “switchable” element consisting of fluids and optical substrate of the materials used in prototyping and switchable lens design, was placed within the intraocular lens. An equivalent outcome is expected if placed within a contact lens because of the equivalency of optical substrate material, fluids and diffractive guiding surface.

Contrast evaluation involves the use of a 0-order configuration to emulate optical straylight and 1st-order configuration for forming the image in the diffractive state. The combined configurations produce the overlap of the ocular straylight over the image and the resulting spot diagram is used for Huygens Modulation Transfer Function (MTF) calculation by the Zemax program, Fig. 3.

 figure: Fig. 3.

Fig. 3. Modeling the optical performance of the switchable lens in the diffractive state. Figure 3(a) demonstrates blur formed by the Eye Model in 0-order configuration as emulation of ocular straylight. Figure 3(b) demonstrates focusing by the Eye Model in 1st order configuration. Figure 3(c) shows Huygens MTFs at different light split between 0-order and 1st-order configurations. It is equivalent to the definition of diffraction efficiencies at 1st-order diffraction state. MTFs at DE = 100%, 85% and 50% represent conditions where 0%, 15% and 50% fraction of light are spread out by membrane smoothing of the smallest width groove.

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Modeling involved taking MTF of the eye model with both 0-order (object at infinity) and 1st-order (object at near) as best foci at the retina serving as the image plane thereby creating an optical condition analogous to switchable element operation. The MTF of 1st-order image was taken with 100% of rays allocated to this configuration which became the Reference MTF. Then the shape of the back surface of the intraocular lens was changed to create a blur by 0-order rays. The back surface shape change was limited by the ability to optimize 1st-order image MTF to the Reference MTF. The optimization was conducted for r2, r4, r6 phase terms by the same merit function as for the Reference MTF to reach equivalent 1st-order image quality at the same best focus. The setting now allows application to different diffraction efficiencies at 1st-order by splitting rays between two configurations and calculating the corresponding Huygens MTFs; Fig. 3(c) demonstrates the MTFs at 100%, 85% and 50% diffraction efficiencies of the smallest width groove in Table 3.

Tables Icon

Table 3. Diffractive Guiding Surface and through-holes

Next, the diffraction efficiency of the switchable lens in the diffractive state was determined. The process involved setting up the same membrane smoothing magnitude at all grooves because the membrane was under the same load at all grooves. The switching of the design was defined at the membrane smoothing S = 2H at each groove; it was the Transition Point (TP). The load at the TP was 0.2 PSI as shown by the Conformance Curve C in Fig. 2(b).

A diffraction efficiency (DE) of the diffractive state for a diffractive guiding surface of (n) grooves can be determined per Eq. (2):

$$DE = \sum\limits_{i = 1}^n {[\frac{{{{({r_i} - 2H)}^2} - r_{i - 1}^2}}{{r_n^2}}} ]$$
The DE ≈ 0.94 was calculated for the switchable element design in the diffractive state per the diffractive groove radii listed in Table 3 and groove height H = 0.00341 mm at the Transition Point referenced in the Conformance Curve C in Fig. 2(b). According to the MTFs in Fig. 3(c), the effect of blur on the MTF simulating membrane smoothing on contrast becomes noticeable at DE below ≈0.85 (5% of MTF reduction) and, therefore, switchable element with DE = 0.94 maintains the highest possible image quality in the diffractive state.

2.5. Prototyping

Surface-based switchable (SBS) optical element prototypes (Fig. 4) were made for “proof-of-concept” (with some parts made by Omnica Corporation, Irvine, CA USA).

 figure: Fig. 4.

Fig. 4. Prototype of Surface-Based Switchable optical element. Figure 4(a) demonstrates the prototype parts that include substrate support (PMMA material) with 4 side channels, the “chamber plug” (PMMA material) to create an internal chamber and support the thin optical substrate (TPX material) by the central post. Substrate support’s 2 side channels were used to fill the active chamber between the substrate and PDMS membrane and another 2 side channels were used to fill the internal chamber with the matching fluid. Membrane cover (PMMA material) had 2 side channels used to fill the external chamber between the membrane and membrane cover with non-matching fluid. Figure 4(b) shows diffractive grooves and distribution of through-holes at the optical substrate.

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Optical substrates of 100 microns thickness were made from TPX (polymethylpentene) with a diffraction zone diameter of 3.162 mm suitable to intraocular and contact lens applications. The groove height ($H$) and radii of grooves (${r_j}$, j=1, 2, … is the groove number) are defined by Eqs. (3a) and (3b) [20] where the design wavelength ${\lambda _d}$ = 0.55 µm corresponds to the peak of eye photopic color sensitivity and refractive indices of the optical substrate (n) and non-matching fluid (n’) are listed in Tables 1 and 2.

$$H = \frac{{{\lambda _d}}}{{n({\lambda _d}) - n^{\prime}({\lambda _d})}}$$
$$r_j^2 = 2j{\lambda _d}{F_d}$$

A height of the grooves for the TPX (Table 1) against non-matching fluid (Table 2) was H = 3.78 µm and peaks of the diffractive groove were truncated by 0.375 micron and rounded during lathe cut to avoid membrane damage and minimize the strain; the final groove height was 3.41 µm. The groove height in the prototypes was smaller than one used in the Finite Element Analysis due to the eventually selected of the substrate material and non-matching fluid. The effect is the increase in membrane conformance for the same load with all FEA conclusions maintained.

Through-holes number of 158, each 0.050 mm diameter, were laser drilled through the optical substrate thinnest portions next to the groove’s transitions and distributed over each groove with equal spacing (Potomac Photonic, Baltimore, MD USA). Table 3 lists the dimensions of the grooves for the focal length Fd = 252 mm and through-holes distribution. Fd = 252 mm was selected to correspond to a near focus of an intraocular lens and contact lens. Theoretical groove radii were determined by Eq. (3b). Diffractive guiding surface was also measured by the optical profilometry with Nanovea HS2000 Profilometer which was 3D Non-Contact Profilometer utilizing Chromatic Confocal optical technology (Nanovia Inc., Irvine CA USA). Table 3 lists theoretical and measured radii together with groove width determined from the measured radii as well as the through-holes distribution per the groove of the optical substrate.

PDMS membrane sheets of 20 microns thick were purchased under the tradename SilpuranR (Wacker Chemie AG, Munich Germany) and sized for the prototyping. The rest of the prototype parts were made of PMMA (polymethyl methacrylate).

Three processes were applied during prototype assembly to investigate their capabilities: (a) TPX-PMMA solvent with primer bonding, (b) PDMS to PMMA by surface functionalization and oxygen plasma bonding, [2123] and (c) PMMA-PMMA simple solvent-based bonding [24].

Complete optofluidic prototypes were assembled to analyze the fabrication processes and imaging characteristics. For imaging, the prototypes were filled with the optical fluids per Table 2 and one channel at the internal chamber was left connected to a 100-microliter syringe to serve as the Actuator and all other channels were blocked. To evaluate membrane conformance, the incomplete optofluidic prototypes were used – samples without membrane cover attached to expose the membranes. The side channels were used to fill in the active and internal chambers with blue dye matching fluid (tetraethylene glycol). One channel connected to the internal chamber was left connected to 100-microliter syringe to serve as the Actuator and the other 3 channels were blocked.

2.6. Switching Response Time

How fast the switching between the optical states occurs depends on a fluid flowrate at the through-holes of the multi-chamber configuration. The question can be addressed with the help of the Bernoulli Eq. (4a) [25].

$$P + \frac{1}{2}\rho \cdot {V^2} + \rho \cdot g\cdot h = constant$$
where P = pressure, ρ = density, V = volume, h = elevation, g = gravitational acceleration.

The Bernoulli equation is the approximation in analyzing fluid flow along a streamline between two locations with several assumptions - the incompressibility, steady flow requirement (flowrate does not change in time) and no viscosity. The matching fluid (tetraethylene glycol) is incompressible, but it is unsteady. i.e., flowrate is time dependent. This involves additional pressure to accelerate and, therefore, the Bernoulli equation is an approximation in this application. The matching fluid also manifests viscosity, but the effect is expected to be minimal if travel distance is small as in this case.

In the present application, the elevation was not considered, and Eq. (4a) was reduced to Eq. (4b) showing a flowrate dependance on a difference in pressure.

$${P_1} - {P_2} = \frac{1}{2}\cdot \rho \cdot (V_2^2 - V_1^2)$$

For the matching fluid mass density of 1.009 g/mL, through-hole diameter of 0.050 mm and difference in pressure set by the switchable pressure of 0.2 PSI (load at the switching pressure of the Conformance Curve B of Fig. 2(b)), the Bernoulli equation provided flowrate capacity QC = 3.4 µL/sec. Total fluid volume is approximately 0.03 µL. The fluid volume at each groove is the same except the first one where part of the volume is occupied by the central pole supporting thin optical substrate. The total number of grooves is 9. Thus, the highest flowrate requirement is at the second groove because of the smallest number of through-holes, total 11 per Table 3. Therefore, the transporting fluid volume per through-hole at the “small” sample was VH = 0.03/ 9/ 11 = 0.000303 µL. The minimum flow time FT to transfer the volume VH at the through-hole was FT = VH / QC ≈ 0.0001 second. Even for the unsteady fluid transfer with extra time required for acceleration the flow time would be very short, practically instantaneous. Thus, one can conclude that fluid transfer between active and internal chambers does not affect a Response Time of switching between different optical powers in the designed optofluidic configuration. It helps to quickly restore a corresponding optical state upon eye blinking in case of a switchable contact lens; either refractive state for far viewing or diffractive state for near viewing with eye downgaze.

3. Results

Figure 5 demonstrates an elastic membrane shape change with matching fluid transfer at one of the incomplete samples (the samples without membrane cover attached).

 figure: Fig. 5.

Fig. 5. Demonstration of membrane conformance to diffractive guiding surface in incomplete prototype sample. Figure 5(a) is a photo of an incomplete sample with the membrane in diffractive form. Figures 5(b)–5(e) are photos of membrane closeup in different stages of the blue dye matching fluid in the active chamber. Figure 5(f) demonstrates data taken by Nanovea HS2000 Profilometer comparing groove shapes of the optical substrates (solid red) and membrane surface in the diffractive form of Fig. 5(b).

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Figure 5(a) is the incomplete sample with the membrane conforming to the guiding surface as the blue dye matching fluid was removed from the active chamber. Membrane conformance to the diffractive grooves is difficult to observe over the whole sample because of very small groove height and magnification was required. The following figures were snapshots from a video clip of the fluid transfer process taken at closeup to magnify the images. Figure 5(b) shows the membrane in diffractive form conforming to a diffractive guiding surface where the through-holes are visible due to the removal of the matching fluid but the presence of blue dye. Figure 5(c) shows an intermediate step where some matching fluid partially occupies the active chamber; the through-holes are partially visible with the matching fluid flow. Figure 5(d) is the membrane in the refractive form with the active chamber filled with the matching fluid masking the grooves and through-holes. Figure 5(e) is another interim step where the matching fluid was partially removed; the disturbances of the fluid flow are visible around the areas of through-holes. Figure 5(f) confirms a close line-up of diffraction profiles of optical substrate and membrane in the diffractive form in terms of radii and the slopes of the grooves. The groove heights difference in only a small fraction of micron.

Figure 6 demonstrates images formed by a complete sample filled with clear optical fluids and its testing at the optical bench.

 figure: Fig. 6.

Fig. 6. Prototype imaging characteristics. Figure 6(a) shows an optical bench used for intraocular lens testing. Figure 6(b) shows complete sample filled with clear optical fluids. Figures 6(c)–6(e) are the images formed by the sample in different stages of membrane shape: Fig. 6(c) is resolution target imaging in refractive state. Figure 6(d) is in an interim state at the same focus position as Fig. 6(c) with the matching fluid partially removed. Figure 6(e) is the image in diffractive state with matching fluid removed by the syringe, where the image was at a shorter focal length than the image on Fig. 6(c) thus requiring refocusing the bench microscope.

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A sample was filled with the clear fluids listed in Table 2. For imaging testing the Edmond Optic plano-convex lens #P000001236768-19312 (15 mm diameter and 15 mm effective focal length (diffraction-limited performance at 3 mm diameter aperture) was stacked over the prototype sample and both were placed at the Optical Bench (Fig. 6(a)). The images of the resolution target were recorded at 3 mm diameter aperture to compare with typical images formed by a conventional intraocular lens. The complete sample on Fig. 6(b) shows 6 side channels - 2 opposite channels connected to the external chamber for filling with clear non-matching fluid, 2 opposite channels connected to the active chamber and 2 opposite channels connected to the internal chamber both filled with clear matching fluid. All channels were blocked except one connecting the internal chamber to a 100-microliter syringe shown in Fig. 6(a).

Figure 6(c) is the image of 1951 USAF resolution target by the mini optofluidic prototype in the refractive state. As the matching fluid was partially transferred from the active chamber via the internal chamber, the image started to disappear (Fig. 6(d)) until the image became invisible. The bench microscope was then refocused by lifting it up to another image formed by the optofluidic prototype, Fig. 6(e). The second image position of a reduced focal length indicated the diffractive state of the sample.

4. Discussion

This paper has described the design of a surface based switchable optical element and demonstrated the principle of operation by prototyping. It included multi-chamber construction, membrane and diffractive guiding surface dimensions and recommended optical fluids and material for the optical substrate for a fast transfer of the matching fluid between connected active and internal chambers via multiple through-holes of 0.050 mm diameter placed at the thinnest parts of each diffractive groove. Fluidic dynamic analysis of the fluid transfer supported the fast-switching capability of the multi-chamber digitized optofluidic element due to a tiny amount of fluid involved.

The imaging quality at the refractive state was comparable with that observed with a common monofocal intra-ocular lens at the optical bench testing. Mechanical and optical analysis and experimental demonstration supported high membrane conformance to the diffractive guiding surface and resulted in high diffraction efficiency reaching DE=0.94 by the switchable optical element in the diffractive state with 9-groove design of the diffractive guiding surface and 0.83 conformance at the narrowest peripheral groove.

We can extend the diffractive guiding surface to 4 mm diameter with 15 grooves according to Eq. (4b); the peripheral groove width becomes 70 µm which is still followed Rule of 10 for the groove height H = 3.41 µm. The resulting diffraction efficiency DE = 0.93 per Eq. (2) still ensures high optical performance in the diffractive state.

The digitized optofluidic prototype was designed with applications to ophthalmic lenses in mind where the switching actuation is the interaction with the ocular elements of the eye; that is ciliary muscle contraction pressure in the case of an intraocular lens or lower eyelid pressure with eye downgaze in the case of a contact lens, as follows:

  • (1) The design of the diffractive guiding surface was for focal distance Fd = 252 mm with the active area of 3 mm diameter ($2 \cdot {r_9}$ per Table 3) which is an average daytime pupil diameter of the eye of an >40 year old person (typical age when presbyopia correction becomes necessary) [26,27].
  • (2) Finite Element Analysis the membrane conformance to the diffractive guiding surface referred to 0.2 PSI of switching pressure. The value falls within the range of the pressure exerted by the ciliary muscle contracting forces [2830]. The same load of 0.2 PSI is suitable for contact lens application as a pressure exerted by the lower eyelid is 0.31 ± 0.14 PSI [31] and is sufficient to activate the switching.
Figure 7 demonstrates modeling of switchable ophthalmic lenses with digitized optofluidic elements of the multi-chamber design for intraocular lens and contact lens applications; both are equivalent designs of the optofluidic prototype reported in this paper and with addition of switching pressure control and actuation chamber. The goal of the design is to target 0.35 mm a switchable lens central thickness. Such thickness is in the realm of conventional RGP type contact lenses [32]. Mini-scleral lens configuration is targeted for the switchable contact lens design to minimize over the eye lens movement. The switchable intraocular lens maintains a similar to contact lens meniscus shape. Its activation takes a cue from the Lumina IOL by Akkolens International that relies on Alvarez principle to produce power change by a lateral displacement of two complementary sub-elements of identical cubic surface profiles under the action of ciliary muscle [6]. In the case of switchable intraocular lens, a lateral displacement of the haptic caused by the ciliary muscle is to produce the optical state switching. The switchable intraocular lens is for presbyopia correction and considered for piggyback placement over a conventional aphakia correcting IOL and its small thickness is the benefit..

 figure: Fig. 7.

Fig. 7. Modeling digitized mini optofluidic element as the unit imbedded into the corresponding ophthalmic lens. Figure 7(a) refers to the application to an intraocular lens where ciliary muscle serves as the Actuator that interacts with the external chamber of the optofluidic element via the switching pusher and actuation chamber for switching between foci. Ciliary muscle contraction action is reported to be maintained with age [3335]. Figure 7(b) refers to the application to a contact lens where the lower eyelid serves as the Actuator with eye downgaze that interacts with the external chamber of the optofluidic element via the actuation chamber for switching between foci.

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It is highly desirable to maintain the optical fluids used with the digitized optofluidic prototype due to their unique characteristics (Table 2) and replace other parts by more suitable materials. For instance, in the case of the switchable intraocular lens (SIOL) where lens foldability is important for a small incision implantation, the rigid material (TPX) of the optical substrate shall be replaced by the foldable hydrophobic acrylic of the same refractive index 1.46 [36] and the PMMA material used for all other parts by a foldable material where choice is not limited by a refractive index. In the case of a switchable contact lens (SCL) where gas permeability is important, the PMMA material shall be replaced by a rigid gas permeable (RGP) material and the switchable optofluidic element itself is to be incapsulated by very thin layers of a soft material to (a) form a soft skirt of the scleral lens to maintain lens orientation on the eye with actuation chamber at the lower segment of the lens and (b) provide smooth nonabrasive surfaces in contacts with the cornea and eyelids [37]. The centrally placed switchable optical element is not of a gas permeable material but being 4 mm or less in diameter, it blocks only about 10% of the area of the corneal surface for gas permeability [38].

5. Conclusion

The present manuscript has introduced digitized optofluidic element of multi-chamber configuration in terms of its design and prototyping for proof-of concept evaluation. Such a surface-based switchable element combines a simplicity of focus adjustable optofluidic elements and fast switching performance of material-based electronic elements. Its analysis supported switching operation under a force level exerted on the ophthalmic lenses by the corresponding ocular elements; it would be ciliary muscle in the case of a switchable intraocular lens and lower eyelid at eye downgaze in the case of a switchable contact lens. This manuscript demonstrated the potential of the surface-based switchable technology for presbyopia correction by ophthalmic lenses.

Acknowledgment

The authors acknowledge and appreciate the support of Nicholas J. Casella for assisting with prototypes testing and conducting silicone-acrylic plasma bonding with surface functionalization.

Disclosures

V. Portney is the owner of Vision Advancement LLC and has financial and proprietary interest in surface-based switchable technology. F.R. Christ and M.D. Christ are owners of InVision Biomedical, Inc. and have financial interest in surface-based switchable technology.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (7)

Fig. 1.
Fig. 1. A section of a switchable lens demonstrates the bistate digitized optofluidic optical element of the multi-chamber design. Figure 1(a) refers to the refractive state and Fig. 1(b) refers to the diffractive state. A minimum of three elements are involved in the operation: (1) an optical substrate with a relief diffractive guiding surface, (2) an elastic membrane in close proximity to the diffractive guiding surface, and (3) a matching optical fluid that fills the space between the membrane and optical substrate, active chamber. The latter is connected to the internal chamber by multiple through-channels or through-holes for transfer of index-matching fluid. A non-matching fluid occupies the external chamber at the opposite side of the active chamber. The internal and external chambers are formed by the substrate support and membrane cover and their external surfaces become back and front surfaces of the switchable lens.
Fig. 2.
Fig. 2. Membrane conformance to a diffractive surface groove and Conformance Curve. Figure 2(a) shows deformation of 10 µm thick PDMS membrane over the diffractive surface groove of width L = 219 µm, height H = 6 µm and the locations of the largest strain in red color. The membrane conformance to the groove is within width L’ of the groove width L with membrane smoothing $S = L - L^{\prime}$ . Figure 2(b) demonstrates the membrane Conformance Curves where conformance defined as C = L’/L is a function of load (pressure difference between external and internal chambers). Conformance Curve A is for groove width L = 88 µm and height H = 6 µm. Conformance Curve B is the modification of Conformance Curve A by including switching pressure, pressure up to which the membrane is kept in the refractive form. The switching pressure is set at 0.20 PSI load resulting in switching to the diffractive state of C=0.67. Conformance Curve C of the membrane of Fig. 2(a) at the diffractive groove height H = 3.41 µm is C = 0.83 at 0.20 PSI load. The corresponding groove height was used in the prototyping and switchable optical element design.
Fig. 3.
Fig. 3. Modeling the optical performance of the switchable lens in the diffractive state. Figure 3(a) demonstrates blur formed by the Eye Model in 0-order configuration as emulation of ocular straylight. Figure 3(b) demonstrates focusing by the Eye Model in 1st order configuration. Figure 3(c) shows Huygens MTFs at different light split between 0-order and 1st-order configurations. It is equivalent to the definition of diffraction efficiencies at 1st-order diffraction state. MTFs at DE = 100%, 85% and 50% represent conditions where 0%, 15% and 50% fraction of light are spread out by membrane smoothing of the smallest width groove.
Fig. 4.
Fig. 4. Prototype of Surface-Based Switchable optical element. Figure 4(a) demonstrates the prototype parts that include substrate support (PMMA material) with 4 side channels, the “chamber plug” (PMMA material) to create an internal chamber and support the thin optical substrate (TPX material) by the central post. Substrate support’s 2 side channels were used to fill the active chamber between the substrate and PDMS membrane and another 2 side channels were used to fill the internal chamber with the matching fluid. Membrane cover (PMMA material) had 2 side channels used to fill the external chamber between the membrane and membrane cover with non-matching fluid. Figure 4(b) shows diffractive grooves and distribution of through-holes at the optical substrate.
Fig. 5.
Fig. 5. Demonstration of membrane conformance to diffractive guiding surface in incomplete prototype sample. Figure 5(a) is a photo of an incomplete sample with the membrane in diffractive form. Figures 5(b)–5(e) are photos of membrane closeup in different stages of the blue dye matching fluid in the active chamber. Figure 5(f) demonstrates data taken by Nanovea HS2000 Profilometer comparing groove shapes of the optical substrates (solid red) and membrane surface in the diffractive form of Fig. 5(b).
Fig. 6.
Fig. 6. Prototype imaging characteristics. Figure 6(a) shows an optical bench used for intraocular lens testing. Figure 6(b) shows complete sample filled with clear optical fluids. Figures 6(c)–6(e) are the images formed by the sample in different stages of membrane shape: Fig. 6(c) is resolution target imaging in refractive state. Figure 6(d) is in an interim state at the same focus position as Fig. 6(c) with the matching fluid partially removed. Figure 6(e) is the image in diffractive state with matching fluid removed by the syringe, where the image was at a shorter focal length than the image on Fig. 6(c) thus requiring refocusing the bench microscope.
Fig. 7.
Fig. 7. Modeling digitized mini optofluidic element as the unit imbedded into the corresponding ophthalmic lens. Figure 7(a) refers to the application to an intraocular lens where ciliary muscle serves as the Actuator that interacts with the external chamber of the optofluidic element via the switching pusher and actuation chamber for switching between foci. Ciliary muscle contraction action is reported to be maintained with age [3335]. Figure 7(b) refers to the application to a contact lens where the lower eyelid serves as the Actuator with eye downgaze that interacts with the external chamber of the optofluidic element via the actuation chamber for switching between foci.

Tables (3)

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Table 1. Materials of key optical elements.

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Table 2. Optical fluids of the Surface-Based Switchable optical element.

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Table 3. Diffractive Guiding Surface and through-holes

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

y = x a + b x + c x 2 + d x
D E = i = 1 n [ ( r i 2 H ) 2 r i 1 2 r n 2 ]
H = λ d n ( λ d ) n ( λ d )
r j 2 = 2 j λ d F d
P + 1 2 ρ V 2 + ρ g h = c o n s t a n t
P 1 P 2 = 1 2 ρ ( V 2 2 V 1 2 )
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