Astigmatic Refractive Error

This article is intended for educational purposes only.

Key words:

  • Cornea: The clear dome of tissue protruding from the white conjunctiva on the front surface of eye that covers the iris and pupil (see anatomy).
  • Refract: The bending of light (for our use). Refractive error (Pertaining to the eye): Meaning the rays of light entering an eye does not focus on the retina, causing blur.
  • Correction: Used in terms of eyeglasses or contact lens: To correct a refractive error. The correction is the amount of power, in diopters, needed to bring the rays of light back to focus on the retina.
  • Meridian: "A plane section of a surface of revolution containing the axis of revolution" (The American Heritage Dictionary). Or for our purposes - a small cross section of a basketball or football shape that travels through the dead center.

Spherical Refractive Error:

Spherical refractive error: A non-astigmatic eye has a perfectly round, or spherical cornea. All meridians have an equal curvature, resulting in uniform power in all directions. The correcting lens only needs to be ground to one power in order to make this eye see well. We usually tell patients that this cornea is shaped like a basketball whereas an astigmatic cornea is shaped like the profile (long side) of a football, as in diagram 1.

The term "spherical" is used because the cornea could represent a small section of a bigger "ball" shaped object. As you can see from diagram 2, (and anatomy of the eye) that the cornea only represents a small cross section, or cap of a sphere superimposed on a larger oblong eyeball.

Diagram 1
compare spherical vs. astigmatic eye

Diagram 2
spherical cornea

Where the rays of light entering the eye focus is contingent on several factors including the degree of curvature on the cornea, the crystalline lens inside the eye and the length of the eye. In the astigmatic cornea in diagram 1 it is a certainty that the rays of light passing through the cornea at 90 degrees WILL focus in front of the rays of light passing through the cornea at 180 degrees. This is because the sharper curvature at 90 degrees gives the optical system of cornea more power to converge light (as in diagram 4 below).

Astigmatic Refractive Error:

Astigmatism is a type of refractive error that usually refers to the need of two separate corrections in one eye. This happens because the astigmatic cornea has different curvatures in two meridians 90 degrees apart. As seen below, both curves are regular but represent different radii.

There is such a thing as irregular astigmatism where the curves are not regular or there are more than two different curves, but this is usually due to pathology and cannot be corrected by glasses (hard or rigid contact lenses are used to simulate a smooth front surface).

Light passing through the cornea (diagram 3) will focus in different places at the 90/180 meridian depending in the overall power of the eye.

Diagram 3
plus and minus power and eye curvature


It actually takes about 60 diopters (on the average) of converging power to focus rays of light entering the eye onto the retina (see myopia/hyperopia). If the optics system of the eye, for example, converges light at 62 diopters rather than the needed 60 diopters the person will have a "refractive error" of 2 diopters. This person has an overpowered or nearsighted eye. Her eye will converge light 2 diopters too much (+2), so the focal point will land in front of the retina. A lens in front of the eye is needed to weaken her eye's optical system (a -2.00 lens) to make the rays of light focus on the retina.

Diagram 4
plus and minus power and eye curvature

In the following example (diagram 4), this person has TWO refractive errors in ONE eye, or astigmatism. The cornea in this diagram at 90 degrees is 2.50 diopters too powerful, converging light well in front of the retina. While at 180 the refractive error is only 1.00D. To write a prescription to correct this in a glasses format we would write: -1.00 - 1.50 X 180 ( "minus one minus one fifty axis one eighty).

Diagram 5
plus and minus power and eye curvature

Refractive error (glasses prescription):

-1.00-1.50 X 180

The first number in this prescription, -1.00, is called the "sphere", which corrects for the FLATTER meridian. A spherical lens corrects in ALL directions equally (-1.00D). As seen in diagram 5, the spherical lens corrects for all the flatter meridian (180) refractive error and 1.00 diopter of the 2.50 diopter in the 90 degree meridian. This leaves -1.50 uncorrected refractive error at 90.

With only the sphere correction (-1.00) so far, focal points A and B BOTH move towards the retina. Focal point A is now focused on the retina (no refractive error or "corrected") and focal point B is closer, but still in front of the retina, leaving a smaller refractive error. Now we add a cylindrical lens to correct the remaining 1.50 diopters of refractive error on the cornea at 90. This will move ONLY point B, which now focuses on the retina. The reason this lens only corrects at 90 is that a cylndrical lens has power in only one direction, as seen below (diagram 6).

Diagram 6
plus and minus power and eye curvature

In diagram 6 we see that in a cylindrical lens the actual POWER is 90 degrees from the axis of this lens, so we specify AXIS 180 in order to correct the excess corneal error at 90 degrees of -1.50D. Note, again, that there is NO power (curvature) in the meridian of the axis (180) so it will not affect point A and only move point B in diagram 4. This is a minus (power) cylindrical lens and therefore the notation is called "minus cylinder format". There is such a thing as "plus cylinder" format, which is not used very much anymore.

Diagram 7
plus and minus power and eye curvature

In diagram 7, we see a representation of how the cylinder axis actually applies to a pair of glasses. Remember, just to confuse you, the actual power of the cylindrical lens is 90 degrees away from the axis. So at axis 90, the "weakening" minus power is actually at 180. The cornea of a prescription with cylinder at 90 has the "football" shape standing on end, with the longest side pointing up and down.

Astigmatism, second try:

If you did not understand the above. This is the EXACT SAME eye as above, but presented in a mathematical manner.

Ok, if a person has a refractive error it needs to be "neutralized" to zero so the rays of light can to focus on the retina and therefore making the individual in question see clearly. The REFRACTIVE ERROR is the amount the cornea and crystalline lens system is too weak or too strong. The CORRECTION is the lens put in front of the eye to neutralize the refractive error. The CORRECTION must make the REFRACTIVE ERROR zero if the person is to see clearly.

eyeglass prescription and calculation of refractive correction

In the example above, the first thing we did was add a spherical correction. This corrected equally in all directions and took away all the refractive error except the astigmatic error, as shown to the left.

Now the rays of light focus on the retina in both the 180 and 90 degree meridians (left).

Walking through the spectacle prescription of: -1.00 - 150 X 180, we see the first or "sphere" number as stage 1. Adding -1.00 in all meridians of the eye, neutralizing part of the refractive error. The second two numbers, the cylinder power (-1.50) and the orientation of where to apply the cyl power (axis, or X, 180), is shown above at stage 2. Again, "axis 180" actually implies the power being applied at the 90 degree meridian (left).


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