**5. PSF and image simulation**

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

influence of the LBME asymmetry and the SA is both minimal.

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

**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

*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* 

**48**

**Figure 4.**

*ZME (dashed lines).*

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.

#### **Figure 5.**

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

**Figure 6.** *PSFs normalized to the maximum of each triplet of CIs for pupil of 4.5 mm in distance vision (top) and near vision (bottom).*

**Figure 5** shows that, for both the LBME and the ZME in distance vision, DCI 1.6 has a more intense focus than the other two CIs, but it has a slightly wider peak than DCI 1.0. In near vision the same trend is shown, the maximum of the DCI 1.6 is higher than that of the other two CIs, but its surrounding halo is also more extended. Note that the SACI has an even greater halo. For 3.0-mm pupil at near vision, the first impression is that the PSF for DCI 1.6 is better than the one for DCI 1.0 PSF # 1; however, it should be borne in mind that, while the maximum value of the first one is the unity, the energy is very dispersed (the halo). In DCI 1.0, although the maximum is less than 0.802, the energy is more concentrated, and therefore the PSF is better. The explanation of why the PSF of DCI 1.6 is globally better is simple: the diffraction efficiency of DCI 1.6 is better, focusing more light on the near-vision focus. On the other hand, as expected, for 3.0-mm pupil diameter, the CIs' performance is similar in both eye models.

**51**

**Figure 7.**

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

to the influence of the SA and also, to the asymmetry of the LBME.

**Figure 6** shows the same composition as **Figure 5** but with the 4.5-mm pupil. As we explained before, by increasing the pupil diameter, the influence of SA is higher on each eye model. On the one hand, a focal shift is produced, as already shown in **Figure 3c**, and on the other hand, the shape and height of the PSF are also affected. The comparison of the performance of both eye models for 4.5-mm pupil diameter shows more noticeable differences than those observed with the small pupil. In all cases, the LBME has more extended and asymmetrical halos than ZME. This is due

Finally, after the quantitative comparison of the merit functions for the three

The simulated images for 4.5-mm pupil are shown in **Figure 8**. It can be seen that the differences between the eye models are most noticeable, mainly in the halos in near vision. The halos of the ZME are symmetrical, while those of the LBME are not. Despite these differences, the behavior of the three CIs maintains the same trend. The images at the foci for both DCIs are comparable in contrast

*Image simulation for 3.0 mm of pupil in distance vision (top) and near vision (bottom) for the three Cis in the two model eyes. The intensity of the image simulation of SACI in near vision has been multiplied 4×.*

CIs, images of an optotype chart have been simulated. To this end, the PSFs obtained from ZEMAX were normalized to their respective maximum values and then weighed by the axial irradiances of each IC calculated in Section 3. These normalized and weighted PSFs were convolved with Landolt C optotypes corresponding to three different values of VA: 0.4 logMAR, 0.2 logMAR, and 0.0 logMAR. **Figures 7** and **8** show simulated images for 3.0 and 4.5-mm pupil diameters, respectively. For 3.0-mm pupil, it can be seen that, while the DCIs have a greater contrast than the SACI, the resolution of the three ICs is similar because the extension of the corresponding PSFs are almost the same (see **Figure 5**). At the near focus, it is observed that there is no focus on SACI, but in DCI 1.0 although the contrast is lower, the resolution is higher, and the halo is smaller than for DCI 1.6. When comparing the performance of the eye models, as already mentioned, there are no significant differences because when using a small pupil, the influence of

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

high-order aberrations is minimal.

#### *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*

*PSFs normalized to the maximum of each triplet of CIs for pupil of 4.5 mm in distance vision (top) and near* 

**Figure 5** shows that, for both the LBME and the ZME in distance vision, DCI 1.6 has a more intense focus than the other two CIs, but it has a slightly wider peak than DCI 1.0. In near vision the same trend is shown, the maximum of the DCI 1.6 is higher than that of the other two CIs, but its surrounding halo is also more extended. Note that the SACI has an even greater halo. For 3.0-mm pupil at near vision, the first impression is that the PSF for DCI 1.6 is better than the one for DCI 1.0 PSF # 1; however, it should be borne in mind that, while the maximum value of the first one is the unity, the energy is very dispersed (the halo). In DCI 1.0, although the maximum is less than 0.802, the energy is more concentrated, and therefore the PSF is better. The explanation of why the PSF of DCI 1.6 is globally better is simple: the diffraction efficiency of DCI 1.6 is better, focusing more light on the near-vision focus. On the other hand, as expected, for 3.0-mm pupil diam-

eter, the CIs' performance is similar in both eye models.

**50**

**Figure 6.**

*vision (bottom).*

**Figure 6** shows the same composition as **Figure 5** but with the 4.5-mm pupil. As we explained before, by increasing the pupil diameter, the influence of SA is higher on each eye model. On the one hand, a focal shift is produced, as already shown in **Figure 3c**, and on the other hand, the shape and height of the PSF are also affected. The comparison of the performance of both eye models for 4.5-mm pupil diameter shows more noticeable differences than those observed with the small pupil. In all cases, the LBME has more extended and asymmetrical halos than ZME. This is due to the influence of the SA and also, to the asymmetry of the LBME.

Finally, after the quantitative comparison of the merit functions for the three CIs, images of an optotype chart have been simulated. To this end, the PSFs obtained from ZEMAX were normalized to their respective maximum values and then weighed by the axial irradiances of each IC calculated in Section 3. These normalized and weighted PSFs were convolved with Landolt C optotypes corresponding to three different values of VA: 0.4 logMAR, 0.2 logMAR, and 0.0 logMAR.

**Figures 7** and **8** show simulated images for 3.0 and 4.5-mm pupil diameters, respectively. For 3.0-mm pupil, it can be seen that, while the DCIs have a greater contrast than the SACI, the resolution of the three ICs is similar because the extension of the corresponding PSFs are almost the same (see **Figure 5**). At the near focus, it is observed that there is no focus on SACI, but in DCI 1.0 although the contrast is lower, the resolution is higher, and the halo is smaller than for DCI 1.6. When comparing the performance of the eye models, as already mentioned, there are no significant differences because when using a small pupil, the influence of high-order aberrations is minimal.

The simulated images for 4.5-mm pupil are shown in **Figure 8**. It can be seen that the differences between the eye models are most noticeable, mainly in the halos in near vision. The halos of the ZME are symmetrical, while those of the LBME are not. Despite these differences, the behavior of the three CIs maintains the same trend. The images at the foci for both DCIs are comparable in contrast

#### **Figure 7.**

*Image simulation for 3.0 mm of pupil in distance vision (top) and near vision (bottom) for the three Cis in the two model eyes. The intensity of the image simulation of SACI in near vision has been multiplied 4×.*

#### **Figure 8.**

*Image simulation for 4.5 mm of pupil in distance vision (top) and near vision (bottom) for the three Cis in the two model eyes. The intensity of the image simulation of SACI in near vision has been multiplied 4×.*

and definition. The reason that they resemble for distance vision is because with a large pupil, a part of the light that passes outside the inlays (external diameter of 4.15 mm) goes to the far focus. Therefore, the intensity ratio between the far and near foci increases and is similar for both DCIs.

By comparing both pupils, the best foci in the distance are for the DCIs with 4.5-mm pupil. The best focus for near vision is the DCI 1.0 since it presents more diffractive rings contributing to the near focus.

#### **6. Conclusions**

We have demonstrated that both DCI designs have a clearly bifocal profile due to their diffractive nature. Moreover, they also have better MTFs and AMTFs than the SACI (see **Figures 3** and **4**). The results presented in this chapter confirm the versatility of the DCI design because, opposite at what happens for the SACI which only presents a fixed depth focus, the distribution of the holes in the DCI can be modified (customized) to alter the relationship between the far- and near-vision foci. It is also verified that while for the 3.0-mm pupil, the three CIs have a similar behavior in both eye models, for 4.5 mm the differences are more due to the highorder aberrations of each model.

The PSFs show the differences between each CI for each situation; on the one hand, the DCIs generally show higher peaks and a high energy concentration and less extension of the PSF, but higher than SACI. These results can be clearly appreciated in the simulated images shown in **Figures 7** and **8**.

In summary, the DCI is a diffractive CI that combines the principle of operation of the small-aperture inlay, for the central hole, with the diffraction generated by the micro-holes in the ring to generate a focus in near vision. The micro-holes allow the construction of a single-piece inlay able to be inserted into the corneal stroma allowing nutrients to pass through it. The results show that the light throughput of

**53**

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

customize the CI for each patient based on their visual needs.

structure of the DCIs, should be carried out in the future.

Generalitat Valenciana (PROMETEO/2019/048).

Politècnica de València, Spain (fellowship FPI-2016).

The authors declare no conflict of interest.

the DCI is higher than the SACI, in addition to better PSFs and simulated images. In addition, we have demonstrated the differences that can be obtained in the results (light distribution between the foci) depending on the design of a DCI allowing to

However, since it is a numerical simulation work with a ray tracing program, studies in an optical bench and clinical trials with contact lenses, which include the

*Funding*: Ministerio de Economía y Competitividad (DPI2015-71256-R);

\*, Vicente Ferrando1

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

and Walter D. Furlan3

2 Hospital Universitari i Politècn ic La Fe, Valencia, Spain

\*Address all correspondence to: diemonma@upvnet.upv.es

1 Universitat Politècnica de València, Valencia, Spain

3 Universitat de València, Valencia, Spain

provided the original work is properly cited.

, Salvador Garcia-Delpech<sup>2</sup>

,

D. Montagud-Martínez and V. Ferrando acknowledge the financial support from the Universitat Politècnica de València, Spain (fellowships FPI-2016 and PAID-10-

D. Montagud-Martínez acknowledges the financial support from the Universitat

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

**Acknowledgements**

18, respectively).

**Conflict of interest**

**Author details**

Juan A. Monsoriu1

Diego Montagud-Martínez1

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

the DCI is higher than the SACI, in addition to better PSFs and simulated images. In addition, we have demonstrated the differences that can be obtained in the results (light distribution between the foci) depending on the design of a DCI allowing to customize the CI for each patient based on their visual needs.

However, since it is a numerical simulation work with a ray tracing program, studies in an optical bench and clinical trials with contact lenses, which include the structure of the DCIs, should be carried out in the future.
