A Beginner's Guide to the Optics of Intra Ocular Lenses for Eye Care Professionals
- Subhabrata Bhattacharya
- 5 days ago
- 17 min read
Updated: 2 days ago
Understanding the basics of optics is essential for eye care professionals because it enables them to accurately diagnose and manage various visual problems. A solid foundation in optics helps professionals explain how light interacts with the eye, understand refractive errors such as myopia, hyperopia, astigmatism, and presbyopia, and determine appropriate corrective measures like glasses, contact lenses, or surgical options. Additionally, knowledge of optics allows for the proper adjustment and fitting of corrective devices, optimizing visual acuity and patient comfort. Overall, a grasp of optical principles ensures that eye care providers can deliver comprehensive, precise, and effective eye care services.
Cornea and human lens:
Assuming a basic understanding of the eye anatomy is already available to the reader, let us start by understanding that the cornea and the human lens are the two main organs in the eye that helps bend the light on the retina. This bending of light is known as refraction.
Refraction happens due to the light passing through two different mediums of different densities. As light travel through the air and reach the eye, it pass through the cornea and human lens that bends the light to reach the fovea of the retina. Fovea is a location in the retina that has the highest concentration of the cone cells. Cone cells are a type of photoreceptor cell located in the retina of the eye. They are responsible for color vision and function best in relatively bright light, unlike rod cells, which are more sensitive to low light.
The bending of light is a result of the difference of speed of light travelling in air and travelling through the cornea and human lens. The speed of light in the cornea is approximately 2.17 x 10^8 meters per second(m/s), while the speed of light in air is close to 3.0 x 10^8 m/s. This slowing
of light causes bending of light, a phenomenon that is defined by refractive index, which is a dimensionless number that describes how light propagates through a particular medium. It is defined as the ratio of the speed of light in a vacuum to the speed of light in that medium.
Refractive Index (R.I) of Intra Ocular Lens(IOL):
Higher the refractive index, more the light slows down while passing through the IOL material. That is, light passing through a material that has a higher refractive index will bend the light more. If you come across a IOL that has a refractive index of 1.50, what it means is that light is slower by 1.50 times while passing through the IOL material, than that of light passing through the air.
The cornea has a refractive index of 1.376 while the human lens has a gradient refractive index of 1.39 to 1.42 . Due to the fact that cornea has a higher refractive index than that of the human crystalline lens, that is light travelling through the cornea slows down more, the cornea accounts for two-third of refraction while the human lens accounts for one-third of refraction.
You will often hear the discussion of R.I of a particular IOL. The R.I of Tecnis Eyhance is 1.47 at 35 degree centigrade while that of the Vivinex IOL from HOYA is 1.548 at 23 degree centigrade. Notice, quoting the refractive index without quoting the exact temperature in which it is measured does not give us the full information.
What impact has temperature on refractive index of lens? The relationship between refractive index and temperature is generally such that the refractive index decreases as temperature increases. This occurs because increasing temperature causes the material's density to decrease, leading to a reduction in its optical density and thus a lower refractive index. Understanding this relationship is important for optical systems requiring high precision, as temperature variations can affect focusing, dispersion, and other optical properties.
It is not usually spelled out by IOL manufacturers if the IOL power is measured in room temperature or a temperature that is closer to our body temperature. Standard testing environments should be used that mimics closely the body temperature. If the IOL is measured in room temperature, or if the IOL optical power is measured in a temperature condition that is lower than the body temperature, then as the IOL is implanted in the body, the dioptric power of the IOL will change, though marginally. This is usually taken into account for IOL power labelling by applying IOL power change to temperature changes. On an average IOL power was seen to increase by .13 diopters between the IOLs measured at 22 deg and 35 deg centigrade(1).
What are the pros and cons of a higher refractive index for IOL platforms?
Imagine a patient requires a 21 diopter IOL that will lead to emmetropia (light refracting and falling on the fovea). For a 21 diopter IOL a lens with lower refractive index, say 1.47 (Tecnis) will be thicker compared to an IOL of 21 diopter that has a higher refractive index (Clareon/AcrySof- 1.55). This is because to bend the same light to the fovea, the IOL with lower refractive index will need a higher volume of the material compared to a higher refractive index IOL material. Thus an IOL with higher refractive index will be thinner than an IOL with lower refractive index, which helps the IOL to be implanted through a smaller incision.
On the flip side, it is argued that IOLs with higher refractive index has a lower ABBE value, that may lead to more amount of chromatic dispersion when light travels through the IOL optic. A detailed understanding of this concept is available in the article 'Why we should stop asking about Abbe Number with Intra Ocular Lenses' ( https://www.quickguide.org/post/abbe-number-and-iols ). In short, chromatic aberration refers to the dispersion (separation) of white light when passing through a lens.
A lens which has a high refractive index, will have a lower ABBE value, that would signify a large dispersion/separation of each of the wavelength of light. Thus when white light passes through the lens, the various components of white light (VIOLET, INDIGO, BLUE, GREEN, RED) will fall at different focal distances, leading to a drop in contrast. However, this is true for lens that are exposed to air. Our eye has an ability to correct many of the higher order errors, and chromatic aberration is one of them. Therefore, the effect of chromatic aberration on the eye is debatable.
Paraxial and marginal rays of light:
IOLs are labelled per the paraxial focus. Paraxial rays of light are those that pass close to the optical axis of the IOL. The optical axis is a central line passing through the center of an optical system, such as a lens or mirror, that defines the path along which light rays ideally travel without deviation (Fig 1). Any ray of light that pass through the optical axis do not refract or bend or deviate from its light path. In optical instruments like telescopes or microscopes, the optical axis is crucial for ensuring proper focus and image clarity. Paraxial rays may be defined as rays that make small angle of incidence to the optical axis of the system and lies close to the optical axis. Paraxial rays lie close to chief ray passing through the optical axis.
IOL power is labelled according to the paraxial rays of light passing through the optic and
coming to focus at a particular distance. Marginal rays of light are ignored, as if they are inconsequential. Diopter is inversely proportional to focal length(Fig 2). That is, 1 diopter of IOL will bring to focus paraxial rays of light at a distance of 1 m or 100 cm. But a 2 diopter of IOL will bring to focus paraxial rays of light at a distance of 50 cm, or .5 or 1/2 m. Likewise, a 4 diopter of IOL will bring to focus paraxial rays of light at a distance of 25 cm. Thus higher the dioptric power of the IOL, shorter is its focal length.
In the article, Gaussian optics, Gullstrand eye, & Biometry (https://www.quickguide.org/post/all-about-gaussian-optics-gullstrand-eye-theoretical-and-ray-tracing-formula) a detailed explanation is given on the topic of lens power calculation. Lens power can be calculated according to both thin and thick lens formulas. However, for all practical purposes, IOL power has been labelled on thin lens formula, historically. A thin lens formulae does not take into account that refraction or bending of light happens in both anterior and posterior planes of the optic. Instead, it assumes, that since IOL optic is so thin, that the entire refraction or bending of light happens in one plane.
where f is the focal length of lens, n is the refractive index of lens, R1 is the anterior radius of curvature, R2 the posterior radius of curvature, and 1 represents the refractive index of air (if the power of the lens is measured with surrounding medium as air). This formula is based on thin lens and therefore does not take into consideration the thickness of the lens, since it assumes the thickness of the lens is infinitely small than the radius of curvature of the lens.
Focal length of an IOL considered according to thin lens formula:
The focal length of a thin lens is the distance from the lens's optical center or geometric center to its focal point, where parallel rays of light either converge. It is usually denoted by the symbol ( f ). However, focal length according to the thick lens formula is derived as a distance from the second principal point to the focal point, where parallel rays of light converge. The second principal point of a thick lens is the point on the optical axis that meets a line drawn perpendicular from the principal plane. In a thick lens, unlike a thin lens, the principal point may not coincide with the geometric center of the lens because the lens has a significant thickness.
An IOL is almost always a biconvex shape. A biconvex is one which has convexity on both sides. An equiconvex lens is one which has the same amount of convexity in both anterior and posterior sides. But most IOLs are not equiconvex. They may have a difference in radius of curvature between the anterior and posterior sides and this difference may vary across the dioptric range of the same IOL.
While most IOLs are biconvex some are meniscus lens which is designed for extremely low power IOL for high myopia (example Alcon MA60MA meniscus IOL). A meniscus lens is one which has convexity (outward surface) on one side and concavity( inward surface) on the other side(fig 4).
Types of meniscus lenses:
Positive meniscus lens: Convex side is thicker; used to converge light rays (MA60MA, ALCON, diopter range +5.0D to +1.0D)
Negative meniscus lens: Concave side is thicker; used to diverge light rays.
(MA60MA, ALCON, -1.0D to -5.0D)
Lens shape and relationship with higher order aberration:
It is important to understand at this stage that lens shape induces different forms of higher order aberrations, like spherical aberration. From the thin lens formula, of 1/f= (n-1)(1/R1 -1/R2) we can see that the anterior and posterior curvatures of an IOL can be changed, and yet power can be the same. For example, you can derive a +20 diopter IOL by a biconvex lens with the power coming from the anterior or posterior curvatures equally, or can also make the same IOL of 20.0 diopter from a plano-convex lens. In both cases, the power remains the same, but the aberration as light pass through the two lenses will be different. The below image proves the point:
Thus IOLs of same power may contribute to different amounts of spherical aberration depending on their anterior posterior geometry.
Spherical and Aspheric IOLs
A spherical shape is a three-dimensional object where every point on its surface is equidistant from its center. This uniform distance is called the radius. Examples include spheres like a basketball or a perfectly round ball. Spheres have no edges or vertices, and their surface is smooth and curved uniformly in all directions. Two decades back, all IOLs were spherical. A spherical shape means that the radius is same across all the meridians. While IOL power of these spherical IOLs were calculated according to paraxial thin lens formula, the effect of spherical aberration was largely ignored.
Spherical aberration, as the word suggests is an higher order aberration that cannot be corrected with glasses, unlike myopia, hyperopia or astigmatism. An aberration is a deviation or distortion in an optical system that causes imperfect images. Spherical aberration happens when the marginal rays passing through the lens margin are over refracted than the paraxial rays or the rays that pass close to the optical axis of the lens.
Why does the marginal rays over refract? To understand this, the concept of Snell's Law is important. Snell's Law describes how light
bends, or refracts, when it passes from one transparent medium to another with a different refractive index. Snell's law states that the ratio of the sine of angle of incidence and the sine of angle of refraction is constant for a given pair of medium and color of light. Therefore, as angle of incidence of light on the IOL optic increase, the angle of refraction also increase, so that the ratio is constant.
As light pass through the margin of the spherical IOL optic, it is over refracted and therefore light falls at a focal distance that is shorter than the paraxial rays focal point. In the below picture, only paraxial rays of light are passing through the lens optic (left). The rays of light are coming to a focal point that defines the power of the lens. On the right is the same lens showing both paraxial and marginal rays of light passing through the lens optic. You can see, that marginal rays of light are over refracted, leading to stretching of the focal point potentially causing a degradation in image quality. For a more detailed understanding of the concept of spherical aberration you may refer to the article Spherical Aberration, Q factor & choice of IOL (https://www.quickguide.org/post/spherical-aberration-asphericity)
Spherical aberration degrades image quality, but increases depth of focus. Depth of field can be defined as the nearest and furthest image in a picture that are acceptably clear. In the below picture some objects are sharp and clear while others not. The ones that can be clearly seen falls within depth of field of the camera. Depth of focus is often loosely interchanged with the word depth of field. Depth of focus however is on the image side of the retina, while the depth of field on the object side. Both are intertwined. Visually you will have no depth of field if the lens does not offer depth of focus on the retinal side.
Spherical aberration happens when the pupil dilates. When does the pupil dilate? In mesopic conditions or low light conditions. Example, when the street lights are the only source of light during the night time as you drive. This leads the pupil to dilate, that is, increase in size to allow more light to pass into the eye and reach the retina. As the pupil dilates, the marginal rays of light that pass through the cornea and the lens now enter the retina, falling at a different place than the paraxial rays, thereby causing a degradation of image quality. Therefore aspheric IOLs were introduced (like AcrySof IQ SN60WF) to negate the positive spherical aberration of the cornea and help provide a better image quality.
To understand how IOLs are designed to provide negative spherical aberration to negate the positive spherical aberration of the cornea, we mush understand the concept of prolate and oblate shape.
From the above picture you can understand that a prolate shape is one which is steep in the middle and flat in the periphery. Therefore, marginal light rays that pass through the periphery of the IOL will fall at a point that is beyond the paraxial focal point (remember paraxial focal point means light that pass through the center or close to optical axis of the IOL falling at one point defining the lens focal length). This will contribute to negative spherical aberration, like in the below image. So a prolate shape contributes to negative spherical aberration. On the other hand, a lens with a oblate shape will lead to positive spherical aberration as such a lens will be steep in the periphery and flat in the middle. As marginal rays of light pass through the periphery of the oblate lens, the angle of incidence will me more, and per the Snell's law, therefore the angle of refraction will be higher. Both, follow a constant ratio.
Between a prolate and a oblate shape are the spherical IOLs. Due to spherical shape of such IOLs ( Alcon SP SA60AT), such IOLs also contribute to positive spherical aberration, thereby adding to the positive corneal spherical aberration.
Spherical shape: The lens has the same curvature across its entire surface. While this is advantageous for manufacturing and allows for a decent overall focus, it also causes peripheral rays of light passing through the lens to focus closer to the lens than the central rays.
Peripheral rays focus anteriorly: Due to the spherical curvature, light rays hitting the outer (peripheral) parts of the lens are bent more than central rays, leading to an earlier or more anterior focus for these rays. This results in a positive spherical aberration, where peripheral rays focus in front of the retina, causing a blur or decreased image quality.
Impact on vision: This aberration can reduce optical quality, especially in low-light or large pupil conditions where peripheral rays contribute more significantly to image formation.
Conic sections
The shape of any lens, whether prolate, oblate or spherical can be defined by conic sections, as they can be derived from the surface of a cone. Like the spherical , there are other shapes like elipse, parabola, hyperbola, etc. You may refer to the article 'Spheric, Aspheric and Freeform lenses' (https://www.quickguide.org/post/spherical-aspheric-and-freeform-lenses) for a complete overview on many different shapes a lens can be derived by cutting a section from the cone.
The shape of the conic section, that is ellipse/circle/parabola, etc. can be described by its conic constant or kappa, denoted by 'K'. The radius of curvature is varying, and therefore is described by the K. When K is equal to zero, the shape derived from the cone is that of a circle/sphere.
Aspheric IOL - an IOL that does not have a conic constant as zero, that is an IOL whose shape deviates from a spherical shape. These IOLs often correct the positive spherical aberration of the cornea.
The AcrySoft IQ, an aspheric IOL, has a 9% reduction (2) in the thickness of the IOL compared to its older version AcrySof SN60AT (yellow non aspheric IOL) to provide for the negative spherical aberration that would negate the positive spherical aberration of the cornea. This central reduction of the IOL optic in the posterior part as well as the distribution of power across the IOL optic through variation of the radius of curvature, leads to a prolate optic, that provide negative spherical aberration(2) negating the positive spherical aberration of the cornea.
Utilizing spherical aberration to provide improved depth of focus - EDOF and enhanced monofocal IOL
So, by now we have realized that during day time, when the pupil is constricted, the rays of light for a person without any refractive error will fall on the fovea leading to no or very little blur circle. This will cause a sharp image, but the depth of focus may be reduced. As the pupil dilates the best focus of the patient shifts towards anterior or posterior direction from the paraxial focal point, leading to night myopia.
Night myopia, also known as "nighttime nearsightedness," is a condition where a person's vision becomes temporarily more nearsighted in low-light or nighttime conditions. This phenomenon is often linked to the effects of positive spherical aberration.
How spherical aberration relates to night myopia:
Increased Spherical Aberration in Low Light: At night or in dim lighting, the pupil dilates to allow more light in. A larger pupil size increases the impact of spherical aberration because peripheral rays are more involved, and these rays are not focused as sharply. This leads to blurred or distorted vision, particularly for distant objects, making the eye appear temporarily more myopic.
Impact on Focus: The combined effect of spherical aberration and dilation can cause the eye's focus point to shift anteriorly (in front of the retina), which results in worse distant vision — giving the illusion of increased nearsightedness.
Night myopia is typically linked to positive spherical aberration because the dilation allows peripheral rays to focus closer to or in front of the retina, causing a temporary increase in nearsightedness during low-light conditions.
Note, myopia is liked to an improved near or intermediate vision, though at the cost of distance. Therefore, IOL scientists have very cleverly utilized this concept thereby building in the IOL optic a certain amount of positive spherical aberration ( example Rayner EMV) to help improve the intermediate vision, but stopping short of adding positive spherical aberration at a point where it starts degrading the distance image quality. A detailed review of how this may be done is available in my article 'Guide to Extended Depth of Focus (EDOF) IOLs optics' https://www.quickguide.org/post/edof-optics.
It is important to understand the concept of 'best focus' or circle of least confusion in the context of spherical aberration. When the pupil is small, for example in day time, the marginal rays of light do not reach the retina. As a result the image is sharp with a significantly lower blur circle. As we enter into a mesopic condition, the pupil is large, as a result of which marginal rays of light that now pass the pupil fall in front of the paraxial focal point, creating a longitudinal positive spherical aberration.
The place where the patient best focus shift, that is the place where the image is a circle of least confusion is shown in below image.
To find the best focus of the patient in a dilated pupil in presence of positive spherical aberration (SA), follow the steps:
Spherical aberration correction
A) Identify the point where the marginal ray is meeting the paraxial ray (marked by green arrow)
B) Join this point to the paraxial focal point (green line).
C) Now identify the point where the inferior marginal ray (red line) is meeting the caustic (green line)
D) The point where the two lines meet is the 'best focus' for the patient.
The best focus is the place where an object at infinity will have the least blur circle, and the image would therefore be acceptable to the patient.
The concept of best focus is applied in EDOF or enhanced monofocal IOL, to provide depth of focus to patient. The Rayner EMV adds positive spherical aberration, to bring the 'best focus' anterior to the paraxial focal point, to increase the depth of focus, thereby improving the intermediate vision of the patient. Add to this, an approach of mini monovision, a tactic there the dominant eye is targeted for the distance (emmetropia) and the non dominant eye is targeted for some amount of myopia to help in near, leads to an even more increase of depth of focus. Recent experience of doctors show that such concept of mini monovision with enhanced or monofocal plus lens is providing improved depth of focus to the patient and may are reading N10 without without the need for glasses.
Juan Tabernero and co-authors(3), used adaptive optics to determine what amount of spherical aberration would help in near and intermediate without significantly affecting the distance. Starting from 0.07 to 0.3 mm of spherical aberration, the increase in depth of focus followed a linear trend, with a rate of change of 0.4 D of depth of focus per 0.1 mm of spherical aberration. The authors showed that on average, when ocular spherical aberration increases more than 0.15 mm (all spherical aberration data in this section refer to a pupil diameter of 4.5 mm), the far distance visual acuity is worse than 0.15 logMAR units, which is hardly clinically acceptable. To be able to achieve a far visual acuity better than this value, the most effective EDOF IOL (on average) to extend the DoF would correspond to values of spherical aberration that range between 0.07 mm and 0.15 mm
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References:
Testing the dioptric power accuracy of exact-power-labeled intraocular lenses November 2009Journal of Cataract and Refractive Surgery 35(11):1995-9
Aspheric IOL Guide, https://crstodayeurope.com/articles/2007-oct/1007_20-php/
Juan Tabernero, PhD, Carles Otero, PhD, John Kidd, BSc, Laura Zahiño, OD, Ana Nolla, OD, Jose Luis Güell, MD, Pablo Artal, PhD, Shahina Pardhan, PhD, Depth of focus as a function of spherical aberration using adaptive optics in pseudophakic participants, J Cataract Refract Surg 2025; 51:307–313
Spherical Aberration, the next frontier by Jack T Holladay, NOVEMBER/DECEMBER 2006 I CATARACT & REFRACTIVE SURGERY TODAY
