**Abstract**

A new class of corneal inlays for treatment of presbyopia is described, which uses diffraction as the working principle. The inlay consists of an opaque disk with a small central aperture surrounded by an array of micro-holes that are distributed following the order of a given Fresnel zone plate having N zones. In this way, the central hole of the disk produces an extension of the depth of focus of the eye for distance vision and contributes to the zero order of diffraction, and the light diffracted by the micro-holes in the periphery produces a real focus for near vision. In our general design, the number of zones and the diameter of the central hole are free parameters that can be used to design customized devices with different addition power and near-focus intensity. Two different designs are analyzed to show this property. In the analysis, we employed a ray tracing software to study the performance of the new inlays in the two different model eyes. The results are compared with those obtained with a model of the small-aperture inlay that is currently in the market. The different merit functions used in the comparison and the image simulations performed with the inlays in the model eyes show the excellent performance of our proposal.

**Keywords:** presbyopia, corneal inlay, diffractive optics, refractive surgery, cornea

#### **1. Introduction**

Affecting approximately 2 billion people worldwide, presbyopia is the most common refractive defect in the population, disturbing the quality of life of people over 45 years. It is expected that this situation will grow to reach 2100 million in 2020 [1]. In fact, presbyopia is a natural condition of the human being due to aging, and it is caused by the loss of ability of the crystalline lens to accommodate.

The treatment of presbyopia has historically been addressed from multiple perspectives: spectacles (reading glasses, bifocals, and progressive), multifocal contact lenses, and refractive surgery. Within this area, the most recent surgical approach is in the use of corneal inlays (CIs) [1, 2]. These implants consist of lenticels of a biocompatible synthetic material that, as the name implies, are placed into the corneal stroma. The main advantage of CI over other surgical therapies, like intraocular lenses, is that it is a minimally invasive and reversible surgery [3]; in addition, CIs are stable and do not require maintenance.

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