Determining the Low Vision Reading Spectacle Prescription,

(the “Predicted Add”)

Ben Freed,2000

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Only after the correct distance refraction has been arrived at can attention be directed to the patient’s near vision needs.

If your patient cannot read small print because of low vision, you need to determine how many times larger the print needs to be made on the retina in order for it to be readable. We can then  enlarge the retinal image size  by that number using optical aids. In particular, high power spectacle additions allow the patient to focus on an object brought close to the eye. The new close object distance is what creates a magnified retinal image. For our clinical purposes, the estimation of the required retinal image magnification can be denoted as a number of “diopters of addition”, commonly known as the predicted add. The predicted add can of course be supplied to the patient not only in the form of a spectacle addition but in other forms, as we shall see.

To determine the predicted add we must first know the following two pieces of information:

1.    A corrected acuity. This is the smallest size print that can be read at a specified distance from an eye corrected for that distance. You are not limited to 20 feet for a valid visual acuity measurement; it can be specified at any distance, as long as the eye accommodates to, or is corrected for that distance. It is written as a fraction using the same units in the numerator and the denominator:

                                                         test distance

                                       VA=          ---------------------

                                                    smallest print read

For example, a patient who is refracted at a distance of two meters and reads down to the 16M size print on a metric chart has a corrected acuity of 2M/16. Remember that a corrected visual acuity is a fraction and therefore can be converted to an equivalent fraction using different units. For example, the same patient will likely read 20/160 if refracted at 20 feet. The ratio of corrected acuity should remain constant regardless of the test distance. This same patient, if tested with a +2.50 addition at a distance of 40 centimeters should read down to 3.2M on the near chart. You would then record the near (corrected) acuity as .4M/3.2.

2.      A goal size print. This is the print size demand that the patient needs to see. For example, most people need to read newspaper size print, others wish only to read large print books, still others may want eyeglasses only for the purpose of threading a needle. For now, let’s assume that the goal is newspaper print. If a person can resolve it, then they can probably handle most other average reading demands. Conveniently, newspaper print happens to be approximately equal in size to 1M print. Remember that 1M is that size print which, when held at 1 meter from the eye, subtends 5’ arc, the minimum angle of resolution of the normal eye for a whole letter.   

Now that we have both a corrected acuity(20/160 in the above example), and a goal size print(1M), we can determine the new required reading distance “d” that the goal size print needs to be held from the eye in order for it to be read. Then, a reading add can be prescribed which focuses at this distance. Solving for the new distance d using the ratio created by similar triangles:

                                 test distance       =    “new required reading distance”                                                                   letter size                             goal size print                                                 

                  Example:        20 ft      =      d

                                        160               1M

The right side of the equation is metric, so d is in meters. In this example, d=.125 meters, the distance at which 1M print should be held from the eye in order for it to be read by this low vision patient. The inverse of this distance is the number of diopters of add or accommodation needed to focus at this new required reading distance, in this case eight diopters. This is called the predicted add.   

Note that when the goal is 1M, the required number of diopters of add needed can be arrived at simply by inverting a corrected visual acuity. In this case, 160/20=8. This shortcut to predicting the add needed for a goal of 1M print is known as Kestenbaum’s rule. In this example, 8D is needed as an “add” over and above the distance prescription in order to focus at the new required reading distance when the goal is 1M.

Note that if there is enough accommodation or uncorrected nearsightedness present, a spectacle add is not needed.

What if the goal is different than 1M? Because of the linear relationship of similar triangles, it is easy to calculate the required add in your head: For example, if the previous patient wants to read large print books(2M), they need only four diopters of add, half as strong as predicted for 1M.

Let’s look at some examples of predicting the add(assume all acuities are best corrected):

1.    The predicted add for a person with 20/300 acuity and a goal if 1M print is 15D.

2.    The strength of the first spectacle reading lens to try with a 15D aphake with 20/400 vision and a goal of reading 1M print is 35D. 15D goes towards correcting the distance refractive error, and the remaining 20D becomes the add, which is what was predicted. The reading distance will be 1/20 meters, or 5cm.

3.    A 20D myope with 20/200 vision should be able to read .5M at 5cm. with their glasses off. This is because they have twice as much “built-in” add as what is predicted for a goal of 1M and therefore can read print twice as small as 1M when they take their glasses off. If they wear an old pair of distance glasses which measure -10.00, they will be able to read 1M at a distance of 10 cm.

4.    An emmetropic six year old with 20/200 vision and normal accommodation can read 2M print(the size of his first reader) by holding the print at 20 centimeters and accommodating five diopters.

We can prescribe an equivalent number of diopters to the predicted add not only in the form of a spectacle addition, but in the form of other optical aids for reading. The predicted add is an amount of diopters which in effect creates a required retinal image size. Any optical system which creates the same retinal image size has the same “equivalent power”.

Optical aids can supply equivalent power in one of four forms for reading:

1.    spectacle additions

2.    hand magnifiers

3.    stand magnifiers

4.      reading telescopes

In the next section, we will examine the remaining three forms to see how they provide the equivalent power needed to create the desired retinal image size.

Finally, it is important to realize that the predicted add is just a starting point for testing near low vision lenses. Some patients may need more magnification to read comfortably.

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The Equivalent Power of Near Vision Optical Aids

This section is intended as a brief introduction to the basic optics of near low vision aids.

The equivalent dioptric power of the predicted add and thus the required retinal image size can be supplied not only in spectacle form as described previously, but in the form of the following other optical aids:

1.    hand held magnifiers

2.    stand magnifiers

3.    reading telescopes

      To determining the equivalent power of hand and stand magnifiers as they are used by low vision patients(the equivalent power of reading telescopes will be treated separately), it is necessary to consider two optical situations(assume emmetropia, or an eye wearing a distance correction):

1) Parallel light leaves the magnifier’s lens and enters the eye. This happens when the object’s distance from the magnifier lens is equal to the focal length of the lens. No add or accommodation is needed to see the image clearly, and the equivalent power of the system equals the dioptric power of the magnifier.

Since the light entering the eye is parallel, the image is at infinity. The implication is that although the observer may change his distance to the lens, the retinal image size remains constant, and the equivalent power of this system is unchanged. What does change, however, is the field of view. The further away the eye is from the lens, the smaller the field of view, and vice verse. As the observer comes close enough to the lens such that the magnifier lens is in the spectacle plane, the field of view is maximized, and the lens acts as a spectacle add. 

2) The light emerging from the magnifier is diverging. This happens when the object is closer to the magnifier than the focal length of the magnifier lens.

The resulting diverging light requires that the observer use an add or accommodation to clear the image. To determine the equivalent power in this situation,  consider that the magnifier lens and the add(or accommodation) needed are two lenses comprising a two-lens system.

     The following general lens formula is required to determine the equivalent power of  such a two-lens system(again, assume an emmetropic eye):

    Feq = F1 + F2 - cF1F2

where:   

Feq is the total equivalent power of the two lens system

F1 is the dioptric power of lens #1 (the magnifier lens)

F2 is the power of lens#2(the add or accommodation needed to focus the image)

c is the separation in meters between lens 1 and 2 

The equivalent power of this system(F=F1+F2-cF1F2) is dependent not only on the powers of the two lenses, but the distance between them. When the magnifier is held at the eye, c=0 and the power is equal to the sum F1 and F2.

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Equivalent power of reading telescopes:

A reading telescope(such as your operating loupe) is a distance telescope with a plus lens reading “cap” attatched to or incorporated in the objective. The Feq is determined by multiplying the dioptric power of the cap by the magnification of the afocal distance telescope. The cap acts as a simple add and the telescope acts to “pump up” its power. As an example, consider a 3X telescope with a +5.00 reading cap. The equvalent power of the system is 15 diopters. It produces the same retinal image size as a spectacle add of 15 diopters.