Lens Design and the Eye's Center of Rotation

Deborah Kotob, ABOM

Course Objectives:

Upon completion of this course participants will be able to:

  1. Describe the function and location of the eyes center of rotation
  2. Relate the effect of precise center of rotation distance measurement as a lens design optimization parameter
  3. Explain how ZEISS can accurately estimate the ocular center of rotation for 99% of wearers

Faculty/Editorial Board

Deborah KotobDeborah Kotob, ABOM, is the Director of Education and Training for Jobson Medical Information. Her experience spans more than thirty years in the optical industry. During this time, her roles included optical boutiques owner, optician, optical frame sales, and over ten years in lens manufacturing as a Lens Consultant, Trainer, and LMS content developer. She lectures, trains, conducts webinars on a variety of optical and practice development topics.

Credit Statement

This course is approved for one hour of ABO CE credit, Ophthalmic Level 2, Course # STWJHI068-2


This is a product spotlight CE supported by an educational grant from ZEISS.

In the March 2023 issue, the CE titled “A Revolution in Single Vision Lenses”briefly touched on the eye’s center of rotation (CoR). To view off-axis objects through a spectacle lens, the eyes rotate behind a spectacle lens around a fixed point near the middle of the eyeball called the center of rotation. The chief ray of the oblique pencil passes through the eye’s center of rotation as it travels from the back vertex of the lens to the fovea, located in the center of the macula region of the retina (Fig. 1). The fovea is responsible for the sharp central vision we humans use to see fine detail and color vision.

The eyes’ center of rotation is a special point in the eye that plays a key role at ZEISS in the optimization of precision spectacle lenses including their new ClearView stock SV and SFSV lenses. ZEISS determined that a more accurate CoR distance measurement can be of decisive importance in determining the visual comfort offered to the wearer with his or her new lenses. Therefore, we are dedicating this course to the eye’s center of rotation and the key role it plays in lens design optimization.

Many individual parameters or measuring points are important when fitting lenses into a spectacle frame.They determine how natural the wearer’s vision will be and how fast he or she can adapt to their new lenses. These parameters include, for example, the back vertex distance (BVD), the distance between the pupils and the center of the patient’s bridge,monocular pupillary distance (MPD), the viewing or fitting height and the tilt of the lenses in the frame, both pantoscopic tilt and wrap angle tilt of the frame. However, there is one point in the eye that is not directly measured by the optician, the eye’s center of rotation. Yet the eye’s center of rotation is a further parameter that is considered in the production of ZEISS precision lenses. Historically it was Donders who first described center of rotation and Moritz von Rohr in 1908 who used an average CoR for the Punktal lenses, and Fry and Hill have researched the importance of CoR. Currently at ZEISS, the CoR value is calculated using a complex algorithm incorporated in the production of spectacle lenses in 1970 and has been constantly enhanced and optimized in ZEISS lens designs ever since. This is only possible by collecting a large volume of datasets from wearers—more than 500,000 in all! The CoR measurement is a relatively fixed point in the eyeball around which the eye rotates in its orbit (socket) during the visual process.

Why is the eye's center of rotation important for the ophthalmic lens wearer? Monocularly each of our eyes provides an approximate 130-degree field of vision. With two eyes, we can see nearly 180 degrees. Calculating the optimal lens surface using a more accurate center of rotation provides the lens design calculator with more accurate power requirements in the lens periphery, where different gaze positions intersect points on the back of the lens that fall outside the central paraxial zone. Using their large CORE Technology data set, ZEISS can accurately estimate the ocular center of rotation for 99 percent of wearers. With this important parameter incorporated in the design of ophthalmic lenses, aberrations (geometric and power) are reduced, increasing the field of vision.

The location of the center of the eye as it rotates is important in lens design calculations to maximize the fields of clear vision. The actual location of the center of rotation can differ significantly from person to person, which means that many eyeglass wearers will not enjoy the best possible lens design performance.

All ophthalmic lenses benefit from accurate center of rotation data. The higher the power, the greater the benefit. The incorporation of the eye's center of rotation in the lens design is of special significance for wearers who need high prescription lenses since off axis aberrations and Minkwitz aberrations in PALs are worse for high powers, astigmatism and high add powers.

Now ClearView stock and semi-finished single vision lens blanks are optimized with the same ZEISS CORE Technology used to maximize the fields of clear vision in all ZEISS freeform lenses. Utilizing their proprietary Center of Rotation Evaluation (CORE) technology provides a more accurate calculation of the lens design, maximizing the fields of clear vision. Based on extensive vision research and anatomical measurements of actual eyeglass wearers, the CORE algorithm estimates the center of rotation to within 1 mm for 99 percent of wearers. The result is superior visual clarity over more of the lens, without any requirement for additional measurements. CORE technology is now built into all ZEISS customized lenses and ClearView SV and SFSV lens blanks.

The CoR measurement is different for myopes versus hyperopes, and when it is a parameter used in the lens optimization of the surface, the wearer experiences more natural and comfortable vision.

This center of rotation point is additionally important for the production of progressive lenses. And it is an absolute must for the production of progressive lenses using freeform technology at ZEISS. It is one of the pieces of the jigsaw that determines how comfortably the wearer's eyes can glide between the various viewing ranges for near, intermediate and far vision.

ZEISS constantly rechecks the calculation of the algorithm with the aid of a large data set from a large number of eye examinations. This is all supported by the medical expertise and experience of colleagues from Carl Zeiss Meditec AG. It varies within a small range of millimeter dimensions and is calculated for each individual wearer's prescription.

Center of rotation (Z'): As its name suggests, the eye's center of rotation is in the middle of the eye (Fig . 2). According to the National Institute of Health, all movements or rotations of the eyeball are performed around a center of rotation (CoR) that is located inside the globe, behind the posterior pole of the lens and close to the posterior nodal distance. (NIH)

Change in the position of the eye's center of rotation in shortsighted eyes: Short-sightedness, or myopia, usually results if the eyeball is too "long."" A deviation of as little as 1 millimeter can result in myopia of around 3 diopters. This means the eye turns differently around its center of rotation and therefore also views differently through the lens.

Change in the position of the eye's center of rotation in farsighted eyes: In farsightedness, or hyperopia, the eyeball is too "short" and produces images of a distant object focused behind the retina. A blurred image is the result. Once again, this means the eye turns differently around its center of rotation and therefore views differently through the lens.

The eye's center of rotation also plays an important role in astigmatism. The astigmatic eye images the world in two focal lines which are located at different distances either both in front of or both behind the retina, or one in front of and one behind the retina in each case. At the center between the two focal lines, the image is blurred and does not have any preferred direction: the term "mean sphere" is used to describe this. This mean value is used to calculate the eye's center of rotation that is then incorporated in the calculation of toric lenses (lenses with different optical power and focal length in two orientations perpendicular to each other).

The center of rotation therefore depends on the type of visual defect present and applies to each individual eye (Fig. 3). Thus, it will not change, for the individual eye in the presence of associated phoria—an image positional error attributable to a deviation of the two visual axes from each other that requires considerable effort from the person affected in order to avoid double images. Prismatic lenses can correct associated phoria and therefore enhance visual comfort.


The geometry of eyeballs differs from individual to individual. For example, a high myope typically has a 4 mm longer eyeball than someone with perfect vision. Importantly, this means that the location of a special point in the eye—its center of rotation (CoR)—also varies by prescription (Fig. 3). Using an accurate position of the CoR for lens design optimization plays a vital role in the visual comfort of the wearer — in particular, allowing them to see more clearly in the lens periphery. ZEISS uses its medical and optical expertise to understand how the CoR changes by prescription. It is calculated by prescription using a patented algorithm generated from more than 300 precise patient measurements. The difference in CoR location from high plus through to high minus lenses is considered in the lens design with CORE technology.

The CoR distance is generally assumed to be at 13.5 mm center of rotation regardless of the prescription. However:

  • Actual CoR varies by up to 2 mm each direction based on ametropia (myopia, hyperopia or astigmatism).
  • As a result, some wearers will experience a loss of clarity away from the optical center.
  • CORE technology calculates CoR within 1 mm for 99 percent of patients: Improves off-axis and binocular optical performance especially for higher Rxs. - No measurement required.

A spectacle lens is stationary in the visual field. Its position is described by the back vertex distance (the distance between the spectacle lens and the corneal apex) and its centration, relative to the line of fixation when the subjects look through the optical center of the lens. The CoR determines where the line of sight (fixation) intersects the spectacle lens for peripheral visual field of view and therefore, has effects important for peripheral lens design. Thanks to freeform lens design technology and ZEISS CORE. technology, the position of the CoR is more precisely accounted for which is important considering that CoR determines the clarity of the retinal image formed for the off-axis points on the lens. The action of the extrinsic ocular muscles controls the rotation of the eyes in their orbit.

With digital freeform design and surfacing, the design software calculates the optimal surface to produce the desired design outcome for every individual Rx, lens material index of refraction, lens thickness, base curve, frame dimensions and individual fit parameters. With ZEISS CORE Technology, the input software also has the CoR value associated with the individual wearer's ametropia and prescription incorporated into the design steps.

The goal of a spectacle lens design is to minimize blur from off-axis gaze effects due to oblique aberrations. This requires a known value for the position of the eye's center of rotation distance with respect to the lens. When the eye rotates behind the lens, away from the optical axis, the distance from the corneal apex to the back surface of the lens increases. To measure and compare the off-axis effects of different lens forms, a reference surface is needed. The vertex sphere (Fig . 4) is an imaginary spherical surface centered at the eye's center of rotation. The radius of the CoR is called the center of rotation distance (CRD) and is where the off-axis powers of the lens are measured at the vertex sphere. These oblique vertex sphere powers are measured along the oblique ray path from the vertex sphere.

When we place an ophthalmic lens between the fixation point or object viewed and the center of rotation of the eye, then the CoR value must be part of the lens optimization calculations. The more precise the CoR value, the wider the field of view and oblique aberrations are more effectively minimized improving peripheral lens optics. This is a win for the patient and the optician!