Spectacle Magnification

The word aniseikonia literally means "not equal images". (a- means not, iso- means equal, -konia is image.)

There are times when this effect occurs naturally. Every time you look to one side, one of the clues that your brain processes is the fact that the image of what you are looking at with each eye is different. This is a normal aniseikonia, and one that your brain uses to help process object distance. It is a binocular distance clue, which is one of many clues that the brain uses to keep track of the objects in your immediate vicinity.

The separation between the photoreceptors in the retina and the way the images are processes in the visual cortex can possibly cause a difference in image size. This is anatomical aniseikonia. This type is not of interest to us here.

What we are interested in is optical aniseikonia. This can be either inherent [related to the dioptric system of the eye] or induced [related to the lenses used to correct the vision]. We are not really interested in which of these we may be dealing with; we are mostly interested in what the effects are on the glasses wearer.

There are magnification-induced effects that are due to the simple fact that a person wears glasses. These effects are present in any lens.

Distortion (barrel and pincushion, shown on the left above) was discussed in the lesson about lens aberrations. It is, if fact, a function of the magnification (or minification) induced by the progressive increase in prism going from the optical center of the lens to the periphery. This can be considered a form of aniseikonia. What is shown in this diagram is symmetrical, and would result from a spherical Rx.

In the middle diagram above is a meridonial aniseikonia that is induced by a spherocylindrical Rx with the axis on the 90 or 180 meridians. For example, in the upper diagram the square, shown with solid lines, might look like the shape that is the dotted lines if the Rx were pl +4.00 x180. There would be no magnification on the 180 meridian, but there would be magnification on the 90th meridian. The lower diagram would be what the result would be if the Rx were pl +4.00 x 090.

The diagram on the left is also meridonial anisekonia, but this time the axis is oblique. Again, the solid lines are the original object and the dotted lines are what the image on the retina would be. The top diagram might be the result of the Rx: pl +4.00 x045. The bottom diagram would then be pl +4.00 x135.

Astigmatism is refractive, which means that it is the result of changes in the curvature of the cornea in different meridians, or the result of a tilted crystalline lens. The result of this is that the closer the correction is to the cornea the less the image size differences on the meridians. Thus, this type of distortion or skewing of the image will be minimized by contact lenses and will be aggravated by glasses with large vertex distances.

Suppose that one eye is emmetropic and the other is hyperopic. The Rx might look like this:

OD +4.00
OS pl
This prescription is anisometropic -- literally, "not equal refractive errors". In this case the image on the right retina is likely to be bigger than the image on the left retina. There are two possible causes for the hyperopia in the right eye in this example. Either the right eye has a normal corneal curvature but is too short (axial hyperopia) or it is the normal length and has too little corneal curvature (refractive hyperopia).

Suppose that the anisometropia is axial. If we correct the right eye with a contact lens then the image on the right retina will be a different size from the image on the left retina. On the other hand, if we correct this hyperopia with a glasses lens, then the magnification that is a 'side effect' of the plus lens will increase the size of the image on the right retina and the result will be that the two images will probably be 'close' to the same size and anisekonia will not occur.

On the other hand, the hyperopia could be refractive. In this case the eyes are the same length but the right eye does not have enough plus power. Now, correcting the right eye with a contact lens will result in the images being the same size and there will be no aniseikonia. In this case the magnification inherent in the glasses lens will cause the image on the right retina to be bigger than the image on the left retina, resulting in aniseikonia.

If you would like a way to remember which type of anisometropia to correct with glasses and which to correct with contact lenses, remember that astigmatism is refractive (it would be hard to have an eye that was a different size on the 90th meridian than it is on the 180 meridian) and the magnification differences on the major meridians is minimized with contact lenses and maximized with glasses. Similarly, anisometropia that is refractive will result in aniseikonia if glasses are worn and it will 'fixed' with contact lenses. On the other hand, anisometropia that is axial will result in aniseikonia if contact lenses are worn and it will be 'fixed' with glasses.

Another way to remember the difference is to think about refractive hyperopia or refractive myopia. In each case the eye globe is the correct size, it just does not have the right curvature in the cornea. A contact lens will correct the corneal curvature, leaving the eyes the correct power and size, and no (or minimal) image size difference will occur. So, contact lenses 'fix' refractive anisometropia, and glasses 'fix' axial anisometropia.

According to the text book that I am using for the reference for this lecture, the symptoms of aniseikonia are "feeling" symptoms. Asthenopia, headaches, photophobia, giddiness, nervousness. Not a very good way to diagnose this problem, is it? If a person has a new Rx with greater anisometropia than the old pair, and is presenting with these types of symptoms, ask him or her to cover one eye for a little while and see if the feeling goes away. If it does then anisekonia would be a possible diagnosis. If it does not go away then that does not automatically mean that the problem is not aniseikonia, since covering one eye for more than a minute or so causes visual distress for many people. However, it is important to check base curve and thickness changes from the old glasses to the new ones before going the next step of trying to correct image size differences.

There are instruments that can be used to diagnose aniseikonia, but they are not readily available any more. One such instrument, introduced in 1951 by American Optical, is the Eikonometer. Another instrument that uses similar images is the Keystone Orthoscope. The diagram to the right (F&G page 330) is what would be seen in the Turville Infinity Balance Test. There are two targets, one seen by the right eye and one by the left eye. If the subject indicates that the horizontal lines are continuous then there is no aniseikonia, but if they do not line up then there is. This particular image measures vertical aniseikonia.

The target above, taken from the Grolman Vectographic Nearpoint Card, is similar to what was used by the Eikonometer or Orthoscope. This set of targets would show aniseikonia in any meridian. Each eye sees the small lines on a different side of the spokes, so that when the eyes are used together if the little lines line up as shown in the middle then no image size difference is present.

According to the textbook, these methods rarely diagnosed an image size of less than 4%, where clinical symptoms may show up with differences of 1-2%. The textbook also indicates that an image size difference greater than 5% will probably result in a loss of binocular vision anyway, making special lens designs inappropriate. (page 330)

Aniseikonia only requires correction if there is good correctable vision in both eyes. The general rule of thumb is that if one eye is not correctable to 20/60 or better then fusion of the images will not take place anyway, so a special lens design to correct for image magnification differences is not appropriate. A second concept to note is that the lens design is not intended to either remove magnification or to exactly match the magnification from each lens. It is only necessary to decrease the magnification differences to the point where binocular vision is restored.

The mathematical method of determining the amount of spectacle magnification and correcting the differences is discussed in Optical Formulas Tutorial, pages 163-168 (top). I am not going to repeat them here. I recommend that you at least read this material through for basic understanding. I am not going to cover in this lesson what the magnification numbers mean, since it is in the text book. Ask your instructor if you will be responsible for actually being able to use these formulas.

There are a variety of tables and charts that can be used instead of the formulas, all of which are based on the spectacle magnification formula. Fannin & Grosvenor provide these two: for changes in vertex distance and for changes in base curve. If you are interested in being able to use the tables instead of the formulas, I suggest that you go to each of those links and print them out. Try using them with the exercises in the Formulas textbook and see how close they come to the answers that the formulas give.

First, the powers inside the boxes are back surface powers, which I have taught you should be written with minus signs. The person who created this chart did not learn optics from me. (Smile. That was a joke.) So, all the base curves are + power curves, and the back curves, which are what you find in the table, are - power back curves.

Second, the chart assumes that the index of the material for the lens is 1.530. This is 'good enough'. We are not going to make a different set of these for every material. If you ever actually do this you will probably use CR39 or crown glass. So the index assumption is 'good enough'.

Third, the point here is that the lenses all have plano power. They LOOK like they have minus power because of the back curves, but if you go back and use the back vertex power (which is what the lensmeter shows and what the wearer sees) in the thick lens formula from first semester you will see that all that unusual thickness adds plus power making the lenses plano power. This spectacle magnification lesson tells you that the thickness also gives magnification, allowing you to test if the wearer's visual problem is due to aniseikonia.

Once you have determined that a person is having a potential problem with aniseikonia and you have determined what you might be able to do about it, there is a way to decide if your lens design might work before ordering a specially ground Iseikonic design lens. You can make a plano lens that matches the front base curve of the wearer's least magnified lens and with a center thickness that will give the magnification difference that you are able to produce with your lens design. You attach the lens (called an afocal fit-over lens or a size lens) to the wearer's glasses for a few days to see if the problem goes away. These charts will give you some of the possibilities for magnifying afocal lenses for plus Rx's and magnifying afocal lens for minus Rx's. If you are interested in trying to do anything of this nature, print out those charts.

For example, suppose a wearer has a magnification of -10% in the right lens and -7% in the left lens. You design iseikonic lenses that will decrease the 3% difference to a 1.0% difference, and you want to know if that will work before you have the new lenses specially ground. Assume that the front base curve of the current glasses is +4.00. Looking at the second of those two charts, a plano lens with a +4.00 front curve will need a back curve of -4.08 and a center thickness of 5.76 mm to give a 2% magnification. You tape this lens over the lens that originally had a magnification of -10%, bringing the difference between the lenses to 1.0%. After wearing this combination for a few days, if the person finds that the problem is solved, then you go to the expense of making the new lenses. [This assumes, of course, that: (1) you can make a lens like that; and (2) the person is willing to wear something that heavy and unsightly for a few days.]

Fannin & Grosvenor recommend that the frame be as small as possible, have a relatively thick eyewire (plastic or metal) and be symmetrical (B measurement relatively close to A measurement). The reasons for these recommendations are that the iseikonic design lens tends to be thick, heavy, and/or have unusual base curves.

Also note that, if making the lens of glass, iseikonic designs are exempt from drop ball testing according to ANSI Z80-1999. They are not, however, exempt from being impact resistant according to FDA regulations, regardless of the material used.

And one final note: aspheric lenses are designed to minimize magnification. They were not as readily available when the textbook was written, and minus aspheric designs were not as well know as they are now. Aspheric designs should probably be the first consideration when trying to correct for refractive aniseikonia.

Whether or not you ever get involved in doing this type of lens design, it is important for you to understand what will increase or decrease spectacle magnification. So:

Steepen Base Curve	Increase magnification / Decrease minification
Flatten Base Curve	Decrease magnification / Increase minification
Increase in thickness	Increase magnification / Decrease minification
Decrease in thickness	Decrease magnification / Increase minification
Increase in vertex distance	plus lens increases magnification / minus lens increases minification
Decrease in vertex distance	plus lens decreases magnification / minus lens decreases minification