**2. Diffractive corneal inlay (DCI)**

The starting point of the DCI design is an amplitude Fresnel zone plate, which has been devised with the optical power necessary to generate the addition. In it, instead of fully transparent zones, micro-holes are made to allow the passage of

**45**

**Figure 2.**

*Diffractive Corneal Inlays: A New Concept for Correction of Presbyopia*

light and the nutrients, forming a single structure without any substrate. The DCI [21], in addition to presenting the aforementioned micro-hole structure, has a central hole that acts as a pinhole of variable diameter; thus the DCI presents different diffractive orders. The zero order focuses the light for distant vision, while the +1 order forms the near focus. By varying the number of rings, the number and size of the micro-holes, as well as the internal diameter of the central hole, the diffraction

Here we evaluated two DCI models in comparison with a SACI with the dimensions of the KAMRA® (see **Figure 1**). Both DCIs were designed to provide a near focus corresponding to an addition of +2.50 D, and both have an external diameter of 4.15 mm. DCI 1.0 has a central hole of 1.00 mm diameter surrounded by 8 rings with a total of 6394 holes. DCI 1.6 was designed with a central hole of 1.6 mm diameter surrounded by 7 rings conformed by a total of 5989 holes. A complete opaque with the dimensions

of the SACI, as shown in **Figure 1**, was evaluated in parallel for comparison.

To evaluate the focusing properties of the DCIs, we first computed the axial irradiances provided by them in air under monochromatic illumination for a wavelength of 555 nm using the Fresnel approximation [9]. **Figure 2** shows the

*Normalized axial irradiances of the three CIs for pupil diameters of 3.0 mm (left) and 4.5 mm (right).*

*DOI: http://dx.doi.org/10.5772/intechopen.89265*

*Design of the analyzed DCIs and the SACI.*

**Figure 1.**

efficiency of the far, and near foci can be modified.

**3. Focusing properties: axial irradiance**

*Diffractive Corneal Inlays: A New Concept for Correction of Presbyopia DOI: http://dx.doi.org/10.5772/intechopen.89265*

**Figure 1.** *Design of the analyzed DCIs and the SACI.*

*Visual Impairment and Blindness - What We Know and What We Have to Know*

have been used to obtain simulated images of an optotype test chart.

The starting point of the DCI design is an amplitude Fresnel zone plate, which has been devised with the optical power necessary to generate the addition. In it, instead of fully transparent zones, micro-holes are made to allow the passage of

**2. Diffractive corneal inlay (DCI)**

Currently, all CIs are implanted monocularly in the nondominant eye producing a modified variant of the monovision system, which consists in using the dominant eye for distance vision and the nondominant one for intermediate-near vision. Commercial examples of CIs are the Flexivue Microlens® (Presbia Cooperatief, UA, Irvine, CA, USA) [1, 4, 5], the Raindrop® (ReVision Optics, Lake Forest, CA, USA) [1, 5, 6], and the small-aperture corneal inlay (SACI) whose trade name is KAMRA® inlay (Acufocus, Inc., Irvine, CA, USA) [1, 5, 7–10]. The principle of operation of each model is different. The Flexivue inlay is a bifocal device of the center-far type, since it has a central hole for the passage of nutrients that allows the vision of far and a peripheral area for the near vision that contains the power of addition. The Raindrop inlay uses a different refractive principle, which consists of introducing a lenticel of permeable material in the center of the corneal stroma to create a hyperprolate cornea. Therefore, the cornea becomes itself a center-near bifocal lens. Finally, the SACI uses the pinhole effect to extend the depth of focus of the eye in far vision. Indeed, it consists of an opaque ring of 1.6 mm internal diameter and 3.6 mm external diameter, constructed with carbon-doped polyvinylidene fluoride. It has about 8400 micro-holes with diameters between 5 and 10 μm, distributed randomly to allow the passage of nutrients through the stroma, which gives it around 5% transmittance [10]. Surgically, it is introduced at a depth of 200 μm. The SACI is the most successful commercial CI and has been widely studied both clinically and theoretically [1, 5, 7–10]. However, it has certain drawbacks. As it is an opaque ring, the amount of light that reaches the retina of each eye is different, causing a degradation of binocular distance visual acuity [11] and a potential detrimental effect on the binocular summation ratio [12]. Moreover, the SACI produces marked interocular differences in visual latency and a Pulfrich effect [13]. Other visual function that is compromised by the SACI is a deterioration in stereoacuity with respect to natural conditions, especially for near and intermediate distances [14]. In this chapter we describe a new concept of CI developed by our research group that is based on the concept of diffraction. It consists of a variation of an amplitude Fresnel zone plate [15] in which micro-holes conform the clear zones of the zone plate in a similar way as was proposed to construct the so-called photon sieves [16]. Photon sieves were conceived for its use in X-ray microscopy but were also found to have numerous applications in various scientific and technological areas [17–19]. Inspired by this concept, we conceived the first diffractive corneal inlay (DCI) in which the distribution of holes in an opaque ring has been ordered to achieve a bifocal intrastromal lens. In this way, the light diffracted by the inlay (an unwanted effect in the SACI commercial design) generates a focus, which would allow presbyopic patients to see close objects clearly. To demonstrate its properties, in the following sections theoretical and numerical results are compared with the SACI, using two different theoretical eye models implemented in the ZEMAX™ OpticStudio software (EE version 18.7, ZEMAX Development Corporation, Bellevue, Washington, USA). To evaluate the optical quality of ICs, the modulation transfer function (MTF), which defines the visibility of a given optical system for all spatial frequencies [20]; the area under the MTF curve (AMTF), computed for different object vergences; and the point spread function (PSF) [20] that describes the response of an optical system to a point source have been used. In addition, the numerically calculated PSFs

**44**

light and the nutrients, forming a single structure without any substrate. The DCI [21], in addition to presenting the aforementioned micro-hole structure, has a central hole that acts as a pinhole of variable diameter; thus the DCI presents different diffractive orders. The zero order focuses the light for distant vision, while the +1 order forms the near focus. By varying the number of rings, the number and size of the micro-holes, as well as the internal diameter of the central hole, the diffraction efficiency of the far, and near foci can be modified.

Here we evaluated two DCI models in comparison with a SACI with the dimensions of the KAMRA® (see **Figure 1**). Both DCIs were designed to provide a near focus corresponding to an addition of +2.50 D, and both have an external diameter of 4.15 mm. DCI 1.0 has a central hole of 1.00 mm diameter surrounded by 8 rings with a total of 6394 holes. DCI 1.6 was designed with a central hole of 1.6 mm diameter surrounded by 7 rings conformed by a total of 5989 holes. A complete opaque with the dimensions of the SACI, as shown in **Figure 1**, was evaluated in parallel for comparison.

## **3. Focusing properties: axial irradiance**

To evaluate the focusing properties of the DCIs, we first computed the axial irradiances provided by them in air under monochromatic illumination for a wavelength of 555 nm using the Fresnel approximation [9]. **Figure 2** shows the

**Figure 2.**

*Normalized axial irradiances of the three CIs for pupil diameters of 3.0 mm (left) and 4.5 mm (right).*

results, computed for CIs with external pupils of 3.0 and 4.5 mm diameter (see the red and green circles in **Figure 1**). As can be seen, the profile of the DCIs is clearly bifocal, while that of the SACI is, as expected, of a typical extended focus one. Note also that both DCIs have a more intense focus than the SACI in distant vision (zero defocus).

### **4. MTFs and AMTFs**

The MTFs and AMTFs of the inlays have been calculated using the ZEMAX™ OpticStudio software, in which two theoretical eye models have been implemented: the Liou-Brennan Model Eye (LBME) [22] and the ZEMAX Model Eye (ZME) [23].

The ZME is an eye model included in the software package. **Table 1** shows the data sheet used for the simulations with the ZME.

The LBME is one of the most popular theoretical models because it has the most realistic biometrical data obtained from 45-year-old people (young presbyopes). It takes into account the alpha angle [22] (the angle between the visual axis and the optical axis), the 0.5-mm nasal displacement of the pupil, and the gradient refractive index of the crystalline lens. Its optical parameters are shown in **Table 2**. The major difference between both models relies in the corneal asphericities (Q ) that induce different values for the spherical aberration (SA) in each eye.


#### **Table 1.**

*Parameters of ZME.*


#### **Table 2.**

*Parameters of LBME, the pupil is decentered 0.5 mm nasally, and the incidental beams have an angle of entry of 5°.*

**47**

**Figure 3.**

*ZME (dashed lines).*

*Diffractive Corneal Inlays: A New Concept for Correction of Presbyopia*

and **2**. The CIs were centered on the visual axis of each model eye.

(VA) between 0.5 logMAR and −0.2 logMAR, respectively.

In these model eyes, both DCIs and the SACI have been inserted virtually at a distance of 200 μm from the anterior surface of the cornea, simulating the surgical procedure of the SACI [5]. In the simulation in ZEMAX, the inlays have been introduced as *.uda* (user-defined aperture) files. To simulate a thickness of 5 μm for the CIs, two CI surfaces were introduced into each eye model, as can be seen in **Tables 1**

The MTFs have been calculated for far and near foci and also for different vergences between +0.50 D and − 3.50 D in steps of 0.10 D, in order to calculate the AMTF. The AMTFs have been obtained integrating the MTF values for a frequency range from 9.49 to 59.86 cycles per degree (cpd), corresponding to visual acuities

**Figure 3** shows the MTFs at the far and near foci for 3.0-mm pupils. As can be seen, both model eyes predict a similar behavior for the three ICs in both far and near foci. It should be mentioned that for the LBME, the represented MTFs in **Figure 3** are computed as the mean values between the sagittal and the tangential MTF curves. In addition, as explained in previous sections, the higher internal diameter of the DCI 1.6 causes a higher amount of light that focuses on the far distance image with respect

*A 3.0-mm pupil: (a) MTF distance vision, (b) MTF near vision, and (c) AMTF for different defocus conditions of the three CIs: DCI 1.0 (blue), DCI 1.6 (red), and SACI (green) for LBME (continuous lines) and* 

*DOI: http://dx.doi.org/10.5772/intechopen.89265*

*Diffractive Corneal Inlays: A New Concept for Correction of Presbyopia DOI: http://dx.doi.org/10.5772/intechopen.89265*

*Visual Impairment and Blindness - What We Know and What We Have to Know*

(zero defocus).

**4. MTFs and AMTFs**

data sheet used for the simulations with the ZME.

results, computed for CIs with external pupils of 3.0 and 4.5 mm diameter (see the red and green circles in **Figure 1**). As can be seen, the profile of the DCIs is clearly bifocal, while that of the SACI is, as expected, of a typical extended focus one. Note also that both DCIs have a more intense focus than the SACI in distant vision

The MTFs and AMTFs of the inlays have been calculated using the ZEMAX™ OpticStudio software, in which two theoretical eye models have been implemented: the Liou-Brennan Model Eye (LBME) [22] and the ZEMAX Model Eye (ZME) [23]. The ZME is an eye model included in the software package. **Table 1** shows the

The LBME is one of the most popular theoretical models because it has the most realistic biometrical data obtained from 45-year-old people (young presbyopes). It takes into account the alpha angle [22] (the angle between the visual axis and the optical axis), the 0.5-mm nasal displacement of the pupil, and the gradient refractive index of the crystalline lens. Its optical parameters are shown in **Table 2**. The major difference between both models relies in the corneal asphericities (Q ) that

**Surface Radius (mm) Asphericity (Q ) Thickness (mm) Refractive index** Anterior cornea 7.80 −0.50 0.200 1.377 Anterior CI 7.80 −0.50 0.005 1.377 Posterior CI 7.80 −0.50 0.315 1.377 Posterior cornea 6.70 −0.30 3.100 1.337 Iris — — 0.100 1.337 Anterior lens 10.00 0.00 3700 1420 Posterior lens −6.00 −3.25 16.580 1.336

induce different values for the spherical aberration (SA) in each eye.

**Surface Radius (mm) Asphericity (Q ) Thickness (mm) Refractive index** Anterior cornea 7.77 −0.18 0.200 1.376 Anterior CI 7.77 −0.18 0.005 1.376 Posterior CI 7.77 −0.18 0.295 1.376

Iris — — 0.00 —

Lens Infinity — 2.43 1.407–0.006605 *z*

Posterior lens −8.10 0.96 16.26 1.336

6.40 −0.60 3.16 1.336

*z* 2

–0.001978 *r* 2

2

–0.001978 *r* 2

Anterior lens 12.4 −0.94 1.59 1.368 + 0.049057 *z* − 0.015427

*Parameters of LBME, the pupil is decentered 0.5 mm nasally, and the incidental beams have an angle of entry of 5°.*

**46**

**Table 2.**

Posterior cornea

**Table 1.**

*Parameters of ZME.*

In these model eyes, both DCIs and the SACI have been inserted virtually at a distance of 200 μm from the anterior surface of the cornea, simulating the surgical procedure of the SACI [5]. In the simulation in ZEMAX, the inlays have been introduced as *.uda* (user-defined aperture) files. To simulate a thickness of 5 μm for the CIs, two CI surfaces were introduced into each eye model, as can be seen in **Tables 1** and **2**. The CIs were centered on the visual axis of each model eye.

The MTFs have been calculated for far and near foci and also for different vergences between +0.50 D and − 3.50 D in steps of 0.10 D, in order to calculate the AMTF. The AMTFs have been obtained integrating the MTF values for a frequency range from 9.49 to 59.86 cycles per degree (cpd), corresponding to visual acuities (VA) between 0.5 logMAR and −0.2 logMAR, respectively.

**Figure 3** shows the MTFs at the far and near foci for 3.0-mm pupils. As can be seen, both model eyes predict a similar behavior for the three ICs in both far and near foci. It should be mentioned that for the LBME, the represented MTFs in **Figure 3** are computed as the mean values between the sagittal and the tangential MTF curves. In addition, as explained in previous sections, the higher internal diameter of the DCI 1.6 causes a higher amount of light that focuses on the far distance image with respect

#### **Figure 3.**

*A 3.0-mm pupil: (a) MTF distance vision, (b) MTF near vision, and (c) AMTF for different defocus conditions of the three CIs: DCI 1.0 (blue), DCI 1.6 (red), and SACI (green) for LBME (continuous lines) and ZME (dashed lines).*

to the DCI 1.0. For this reason, the MTF at the far focus of the DCI 1.6 is the better one. The opposite is true for the near focus, while SACI theoretically presents an extended focus, as can be seen in the AMTF; it does not have a defined focus for near vision. In contrast, the diffractive profile of the DCIs generates the near focus that can be seen in **Figure 3c**. The MTF for the near-vision focus of DCI 1.0 is better than for DCI 1.6 because the total area of the inlay is higher. On the other hand, differences between both eye models are hardly observed, because for a 3.0-mm pupil, the influence of the LBME asymmetry and the SA is both minimal.

**Figure 4** shows the same merit functions as in **Figure 3** but is calculated for 4.5-mm pupils. The influence of the SA on the eye models can be seen in **Figure 4c**. While the AMTFs of the three CIs in the ZME maintain their focus of vision at distance (zero defocus), in the LBME, the AMTF peaks of the far focus are shifted 0.1 D due to the influence of the SA; however, in the near focus, this effect is not so obvious. It is important to note the effect of the pupil size on the depth of focus of the inlays. As can be seen in the comparison between **Figure 3c** and **4c**, the AMTF

#### **Figure 4.**

*A 4.5-mm pupil: (a) MTF distance vision, (b) MTF near vision, and (c) AMTF for different defocus conditions of the three CIs: DCI 1.0 (blue), DCI 1.6 (red), and SACI (green) for LBME (continuous lines) and ZME (dashed lines).*

**49**

**Figure 5.**

*vision (bottom).*

*Diffractive Corneal Inlays: A New Concept for Correction of Presbyopia*

of both ICDs is less affected than the AMTF of the SACI, since for the latter the

As stated above, the PSF describes the ability of an optical system (in our case an eye model with a CI) to form a good image of a point source. An ideal PSF corresponds to a diffraction-limited system and is known as the airy disk, with a highintensity central peak, which is more or less concentrated depending on the pupil size. For real systems the PSF spreads out; as more extended is the PSF, the system is worse.

**Figures 5** and **6** show the PSFs obtained for the 3.0 and 4.5-mm pupils, respectively, of the three ICs in both eye models. PSFs calculated with ZEMAX were weighted according to the axial irradiances calculated in Section 3 for each CI. Considering that the foci in distance and in near vision have different range intensities, different normalizations were performed in order to compare them. In this way, the PSFs at the far and near foci are normalized to the maximum value of the DCI 1.6 PSF in the ZME, and the PSFs of the near-vision focus are normalized to the maximum of the PSF of the near-focus DCI 1.6 of the ZME in each focus, respectively. This means that in **Figures 5** and **6**, the eye models of the three CIs in each focus can

be only compared, but far and near PSFs have different normalizations.

*PSFs normalized to the maximum of each triplet of CIs for pupil of 3.0 mm in distance vision (top) and near* 

*DOI: http://dx.doi.org/10.5772/intechopen.89265*

depth of focus is severely reduced.

**5. PSF and image simulation**

of both ICDs is less affected than the AMTF of the SACI, since for the latter the depth of focus is severely reduced.
