The Spherical Equivalent

Excerpt

In optics, incident rays are either refracted or reflected off a surface at an angle constant to the degree of refractivity or reflectivity of the given medium. The eye is essentially an optical focusing system for the refraction of light stimuli onto a complex network of neurons and specialized photoreceptors. This complex system delivers sensory information to the visual cortex for interpretation. These neural impulses are translated from the retina via cone photoreceptors populating the fovea centralis, which depolarize upon exposure to photopic stimuli.

The cones also account for central 10° of peak visual field sensitivity and color sensitivity. The optical function of the eye is directly proportional to its gross focusing power.

The human eye chiefly possesses two convex refractive components, including:

1. The cornea

2. The crystalline lens

The total refractive power of the human eye is estimated to be about +60 diopters (D). Based on the Gullstrand schematic eye, the dioptric power of the cornea ranges from +43D to +48D. Both the cornea's anterior and posterior surfaces possess refractive properties. The precorneal tear film or air-tear film interface accounts for the refractivity of the anterior cornea.

The corneal dioptric powers vary between individuals depending upon the difference between the radii of curvature of anterior corneal and back vertex surfaces. Under normal circumstances, corneal curvature is steepest around its apex, about 3 millimeters centrally. Incident paraxial rays of light travel via the corneal apex onto refractive components along the visual axis, including both the anterior and posterior surfaces of the crystalline lens. The power of the crystalline lens varies with density, transparency, and the effect of accommodation.

All visual stimuli consist of photons of light. Visible light exists between wavelengths ranging from 400 nanometers (nm) to about 700 nm of the electromagnetic spectrum. When we view objects, our eyes are exposed to these particles of light (photons), which travel through the visual system as paraxial/parallel 'strings' or rays. The cornea and crystalline lens are essentially two powerful convex (converging) lenses that function to bring incident rays of light to a focal point at the fovea centralis. Due to variations in the power of convergence between central and paracentral corneal and lenticular surfaces, paraxial rays of light may yield differences in the depth of focus. This phenomenon is called spherical aberration and occurs mostly under dim illumination.

Several defects in clarity and regularity of the cornea and lens also result in light scattering phenomena and other forms of induced aberrations. Other examples include chromatic aberrations and higher-order aberrations.

An interaction of axial length (AL), corneal power (K), and power of the anatomic crystalline lens account for the ocular refractive state. The vitreous humor possesses a lower refractive index than the crystalline lens. The role of the vitreous in refraction tends to be minimal under normal conditions. Optimal vitreous clarity and optical transparency propagate light transmission to the sensory retina. Physiological changes in the homogeneity of the posterior media do not impact the eye's refracting power. These alterations, however, can alter the refractivity of vitreous media and bring about a light-scattering phenomenon.

Morphologically, the eye's total convergent power varies from person to person. This depends upon the interaction of the abovementioned factors (AL, K, and lens power). Optical defocus can result when light rays are not focused at the fovea. Such variations in the focal point of images are termed 'errors of refraction' or ametropias. Besides innate conditions, refractive errors also develop due to degenerative or transient anatomical and physiological changes secondary to disease states. Uncomplicated refractive errors can be corrected optimally via spectacle lenses, prescription contact lenses, or refractive surgery. Uncorrected refractive errors rank among the leading causes of avoidable visual impairment.

Refractive errors are classified as:

1. Hyperopia

2. Myopia

3. Astigmatism

In the absence of refractive errors, the eye's refractive state is classified as emmetropic. The developmental process via which the human eye tends towards emmetropia is termed emmetropization. Emmetropization takes place between early childhood and teenage years. Endogenous factors which influence emmetropization include alterations in lens thickness and axial length extension. Multiple hypothesized innate or environmental stimuli which interfere with the process of emmetropization bring about ametropia.

Hyperopia

A hyperopic eye under-converges incident rays of light while being devoid of the effect of accommodation. The point of focus thus falls beyond the retinal plane. The resultant blur is termed hyperopic defocus. The hyperopic or far-sighted optical system possesses either lesser gross dioptric power or a shorter axial length. The dioptric equivalent of a convex lens is expressed as a plus (+) numerical factor.

Myopia

A myopic eye over-converges incident rays, thus causing the focal point to fall in front of the fovea. This mainly occurs due to greater crystalline lens thickness (correlating to higher lens dioptric power) and longer than average axial length with normal optics. The dioptric equivalent of a concave lens is expressed in a minus (-) unit.

Hyperopia and myopia make up spherical ametropias. They are corrected using spherical lenses. A spherical lens possesses even thickness circumferentially and has the same power at different angles when positioned in the trial frames. Concave (minus) lenses are thinner at the center and thicker near their edges, which provides greater image divergence. Convex (or plus) lenses are thickest around the optical center and thinner peripherally. This enables greater image convergence for hyperopic correction.

Astigmatism

For an astigmatic eye, incident light rays do not converge onto a focal point. Instead, they are refracted to several foci. Astigmatic errors can be either simple, compound, or mixed in nature. If one focal point is incident at the fovea while the other point converges anteriorly to the foveal plane, it is termed simple myopic astigmatism (See image). With simple hyperopic astigmatism, one point is focused on the fovea, and the other lies behind the retina (see image).

When both focal points are incident anterior to the fovea, it is termed compound myopic astigmatism. In instances where the principal foci of both meridians are incident beyond the retinal plane, this condition is termed a compound hyperopic astigmatism. For the scenario of mixed astigmatism, one focus point is incident in front of the retina, while the other focuses beyond the retinal plane (See image).

A schematic representation of astigmatism can be best described by the 'conoid of Sturm' (See image). In this model, incident rays on a curved surface refract along two orthogonal meridians (with different curvatures) until they converge on separate focal points. The refractive surface forms a cone base while the focal point becomes the apex, yielding a conoid plane diagram.

Manifest astigmatic errors are mostly representative of corneal astigmatism. In with-the-rule astigmatism, the meridian of highest corneal power (the power meridian) lies along 90 degrees, which places the axis of correction along 180°. While with against-the-rule astigmatism (See image), the power meridian lies along 180 degrees, thus placing the axis of cylindrical correction along 90 degrees.

Astigmatic errors are corrected with the use of sphero-cylindrical spectacle lenses or toric contact lenses. The term 'toric' indicates varying degrees of curvature along the meridians of a curved surface. Before spectacle dispensing, the power and axis of a cylinder are refined during subjective refraction. The cylindrical axis must be localized with 15 degrees for moderate errors and within 3 degrees to 5 degrees for high errors.

For conditions that can cause variability or unspecificity of cylindrical (chiefly axis) refinement or in patients that do not tolerate toric corrections, spherical equivalent prescriptions can provide an adequate alternative when dispensing corrective lenses. The spherical equivalent typifies the optical (spherical) prescription, which places the astigmatic eye in a refractive state of meridional balance within the circle of least confusion (See image).