THE OPTICAL SYSTEM OF THE HUMAN EYE
The optical system of the human eye is composed of:
- Four main noncoaxial optical elements: The anterior and posterior corneal and lens surfaces.
- The pupil.
- The retina. It is aplanatic to compensate for the native spherical aberration (SA) and coma through its nonplanar geometry.
The optical surfaces are aligned almost coaxially, but the deviations from a perfect optical alignment result in a range of axes and their inter-relationships (Fig. 1). That guides us to the following definitions:
- The visual axis (VA): It is the line connecting the fixation point with the foveola, passing through the two nodal points of the eye, but not necessarily through the pupil center.
- The optical axis (OA): It is the axis connecting the center of curvatures of the optical surfaces of the eye. It can be recognized by the Purkinje images I, II, III, and IV, namely of the outer corneal surface (I), inner corneal surface (II), anterior surface of the lens (III), and the posterior surface of the lens (IV). If the ocular optical surfaces were perfectly coaxial, these four images would be coaxial, but seldom observed.
- The principle line of sight (LOS): It is the ray from the fixation point reaching the foveola via the center of the entrance pupil (EP).
- The pupillary axis (PA): It is the normal line to the corneal surface that passes through the center of the EP and the center of curvature of the anterior corneal surface.
- The achromatic axis: It is defined as the axis connecting the EP center with the nodal points.
- The vertex keratoscope (VK) normal: It is the axis that is perpendicular to the plane of the capturing machine (original the keratoscope) and intersecting with the anterior corneal surface at the corneal apex (corneal vertex). Therefore, corneal apex is not necessarily the highest point of anterior corneal slope and not necessarily the anatomical center of the cornea.
- Angle kappa (measured in degrees): It is the angle between PA and VA. Angle kappa may be a source of false findings and should be differentiated from misalignment (Chapter 17).It also affects the decision and the plan for laser-based and lens-based refractive surgery. In laser-based refractive surgery, angle kappa should be compensated for by recentration of the laser profile and the flap cut, particularly in hyperopic treatment (hyperopia, hyperopic astigmatism, and mixed astigmatism), and in myopic astigmatic treatment when the myopic astigmatic magnitude is ≥1.5 diopters (D). In lens-based refractive surgery, premium IOL implantation is contraindicated when angle kappa is >400 µm to avoid the risk of postoperative intractable dysphotopsia.Normal distribution of angle kappa was studied by using Orbscan II (Placido-based) and the Synoptophore. It was found that values of angle kappa measured by the Orbscan II were almost as twice as when measured by the Synoptophore. Based on Orbscan II, Hashemi and associates determined an average value of angle kappa of 5.46 ± 1.33° in Iranian adults with an insignificant intergender difference. In another study, Gharaee H and associates determined average value of 4.96 ± 1.38° in total, average horizontal angle kappa of −0.02 ± 0.49 mm, and average vertical angle kappa of −0.09 ± 0.32 mm.In addition, studies reporting normative angle kappa values in different conditions found that angle kappa was significantly higher in exotropes than in esotropes or controls, and tended to be larger in the left eye than in the right eye. Moreover, there was a positive correlation between angle kappa and positive refractive errors, which can be explained by the negative correlation with the axial length of the globe.Unlike Placido-based topographers, Scheimpflug-based tomographers cannot measure angle kappa directly. Therefore, the Pentacam cannot measure angle kappa directly. There are two methods to estimate the angle by the Pentacam, chord μ in the Holladay report (Fig. 2), and considering half the values of X and Y coordinates of pupil center if Holladay report is not available. Chord μ is the chord distance from vertex normal (assumed to be the visual axis) and the EP. On the Pentacam, the normal value is 0.20 ± 0.11 mm, so values above 0.42 mm (highlighted in yellow) would be highly unusual. Figure 3 shows the X and Y coordinates of the pupil center. In this example, angle kappa is estimated to be (−0.10, +0.02) in OD and (−0.02, −0.05) in OS.
- Angle alpha (measured in degrees): The angle formed at the first nodal point by OA and VA.
- Angle lambda (measured in degrees): The angle between PA and LOS.
- Chord μ (measured in mm): As mentioned above, it is the chord distance from vertex normal (assumed to be the visual axis) and the EP.
The refractive power of the human eye comes mainly from the cornea and the crystal lens. In emmetropia, corneal power ranges from 39 to 48 D (average 43.05 D), while the power of the crystalline lens ranges from 15 to 24 D (average 19.11 D). The refractive media in the human eye is: tear film (n = 1.336), cornea (n = 1.376), aqueous humor (n = 1.336), crystalline lens (n = 1.406), and vitreous humor (1.336); where “n” is the refractive index (RI) of the media measured relatively to air (n = 1.000). The dioptric power of the media is determined by the radius of curvature, the RI, and the distance amongst various interfaces.
CORNEAL GEOMETRY
The cornea has two surfaces separated by corneal substance. The anterior surface is coated with the tear film, and they form one refractive surface separating air from the corneal substance. The posterior surface separates corneal substance from aqueous humor. The cornea is not a part of a perfect sphere. The shape of both surfaces is defined as an aspheric prolate, toric, asymmetric conoidal shape (Figs. 4 and 5). Each of the previous expressions is explained in detail in the following paragraphs.
Corneal Dimensions
Corneal dimensions include diameters, meridians, radii of curvature, corneal zones, corneal thickness, corneal shape, and corneal power.
Diameters
The sclerocorneal junction (base of the cornea) is an ellipse. The vertical corneal diameter is 10.6 mm on average, whereas the average horizontal corneal diameter is 11.7 mm.
Meridians
The normal cornea in the adults has two meridians that are 90° apart. Due to the elliptical base of the cornea at the sclerocorneal junction, the vertical diameter is generally shorter than the horizontal one, meaning that the vertical meridian is steeper (smaller radius of curvature) than the horizontal one (greater radius of curvature). Due to this difference, corneal shape is considered as toric. This toricity is responsible for corneal astigmatism. In younger eyes, this toricity is represented as with-the-rule (WTR) astigmatism, where the vertical meridian is steeper than the horizontal one. This steepness reverses with age, leading to against-the-rule (ATR) astigmatism.
Radius of Curvature
The cornea has two surfaces, anterior with an approximate radius of 7.8 mm and posterior with an approximate radius of 6.5 mm. These two radii are for the central (axial) zone of the cornea. The radii increase while moving to the periphery, indicating a flatter corneal periphery. The normal cornea flattens progressively from center to periphery by 2–4 D, with the nasal area flattening more than the temporal area; this is shown on the curvature map as the nasal side becoming blue (flat)6 more quickly (Fig. 6). The normal average anterior/posterior radii ratio is 1.21 in virgin nonoperated corneas. This ratio is altered by keratorefractive surgeries, which is a leading source of wrong IOL measurements.
Corneal Thickness
Due to the difference in radius between the two corneal surfaces, the cornea is thinner in its central zone than at its periphery. There are two important values in corneal thickness, the central corneal thickness (CCT) and thinnest corneal thickness (TCT). Both are discussed later in this chapter.
Corneal Zones
Clinically, the cornea is divided into zones that surround fixation (corneal vertex or apex) and blend into one another:
- The central zone (central 3 mm): It overlies the pupil and is responsible for high definition vision. The central part is almost spherical and is also called the apical or axial zone.
- The paracentral zone (3–6 mm): It has a doughnut shape with an outer diameter of 6 mm. It represents an area of progressive flattening toward the third zone.
- The peripheral zone (6–9 mm): It is also known as the transitional zone. This zone is asymmetrically flatter than the central zone. The nasal and superior segments are flatter than the temporal and inferior ones.
- The limbal zone (>9 mm): It is adjacent to the sclera and is the area where the cornea steepens before merging with the sclera at the limbal sulcus.The central and paracentral zones are responsible for the refractive power of the cornea, and they are in charge of contact lens fitting. Being steeper in the center and flatter at the periphery gives the cornea what is known as a “prolate” aspheric shape.
Corneal Shape
The corneal shape is “Conoidal” (Fig. 5). It is a composition of toricity, asphericity, and asymmetry. From a meridional viewpoint, the cornea is “Toric,” which is the source of corneal astigmatism. From the zonal viewpoint, the cornea is “aspheric” because the radius of curvature differs from the center toward the periphery. From a sectorial viewpoint, the cornea is asymmetric because the nasal sector is usually flatter than the temporal sector as shown in Figure 6.
Corneal asphericity is represented by some of values, such as Q-value, p-value, E-value, and eccentricity. The most popular one is the Q-value, which represents the ratio between the central and the peripheral radii of curvature. The relationship between corneal shape, Q-value, corneal SA, depth of focus, and contrast sensitivity is discussed in detail in Chapter 16.
Corneal Power
The anterior corneal surface with its associated tear film layer plays a role of a convex refractive surface. Due to both its convexity and separation between two different media: air (smaller RI; n = 1.000) and corneal substance (larger RI; n = 1.376), it is the most powerful refractive surface in the optical system of the eye. The refractive power of the central (apical or axial) zone of the anterior corneal surface is approximately 49 D.
On the other hand, although the posterior surface of the cornea is convex, it acts as a negative concave surface because it separates corneal substance (larger RI; n = 1.376) from aqueous humor (smaller RI; n = 1.336). The refractive power of the posterior corneal surface is approximately −6 D.
Moreover, corneal epithelium has an impact on corneal power. The shape of the epithelial layer is responsible for about 0.40 D of astigmatism. The mean Q-value is −0.20 ± 0.13 (0.06 to −0.60) with the epithelium and −0.26 ± 0.23 (0.07 to −1.51) without the epithelium. In other words, the cornea is more prolate without the epithelium, which means that the epithelial layer forms a negative lens (thinner in the center) as shown in Figure 7.
Fig. 7: The effect of corneal epithelium on the corneal shape. The cornea is more prolate without the epithelium.
This fact has a clinical impact on laser-based procedures, especially in surface ablation techniques. This fact is more important in the case of irregular corneal surface because the epithelium has a remodeling (filling) feature, which masks the real corneal power and a significant portion of the underlying corneal irregularities as shown in Figure 8. Moreover, the remodeling feature of the epithelium affects the outcomes of laser-based procedures, characterized by a partial loss of effect after both myopic and hyperopic corrections. The epithelium forms a positive convex lens after myopic ablation and a negative concave lens after hyperopic correction (Fig. 9).
Corneal power methods of measurements and their clinical applications are discussed in Chapter 5.