Magnification labels for stand magnifiers: Always misleading and usually unachievable

Article Outline

• Abstract
• Methods
• Results
  • Nominal magnification (F/4)
  • Trade magnification ([F/4] + 1)
• Discussion
• Conclusion
• Disclaimer
• Appendix: Derivation of trade magnification, (F/4) + 1
  • Assumptions 1 and 2
  • Assumption 3
• References
• Copyright

Abstract 

Background

Stand magnifiers (SMs) are traditionally labeled with F/4 or (F/4) + 1 magnification. This study addresses whether SMs are configured so that the assumptions associated with the labeled magnification can be realized.

Methods

Three catalogs were examined to obtain the type of magnification label used for each of 66 different SMs. Image locations were acquired from published tables compiled by independent investigators when available. Otherwise, they were taken from manufacturer-provided information in the catalogs. The image location was used to determine how many magnifiers could be used in a manner that fulfills the assumptions underlying the labeled magnification.

Results

For F/4 magnification, the page is assumed to be at the focal point of the SM and the image at infinity. No SMs met this condition. (F/4) + 1 magnification assumes the magnifier is close to the eye and the image is at 25 cm. Only 18% of the SMs have a 25 cm image distance.

Conclusion

Most SMs do not have image locations that meet the conditions underlying the marked magnification. The current labeling system is inaccurate, misleading, and inefficient for clinicians. Magnification labels on SMs should be replaced with markings that include equivalent power, enlargement ratio, and image location.

Keywords: Low vision, Stand magnifier, Trade magnification, Nominal magnification, Equivalent power, Enlargement ratio, Ophthalmic optics

A properly performed low vision examination is multifaceted. It includes a detailed history to establish specific goals, a careful refraction, generally with a trial frame, a determination of the equivalent power required to meet each goal, a determination of the type of magnifying system having that power that best serves the patient, as well as other components not directly relevant to this report. The examination is time consuming, and the low vision clinician is ever alert for ways to improve efficiency. One of the questions that prompted this study is whether the current method of labeling stand magnifiers (SMs) assists or hinders clinical efficiency.

When using a SM, the observer views an enlarged virtual image through a positive-powered lens (or system of lenses) that is supported by the stand at a fixed distance from the page. Manufacturers of SMs traditionally label them with magnification based on 1 of 2 equations. Both of these equations stem from the desire to label the magnifier with a number that shows the magnification that is achievable with the magnifier compared with the magnification achieved by using only the unaided eye. (In this article, “unaided eye” refers to the eye corrected for distance ametropia but not aided by an additional magnifying lens, unless otherwise indicated.)

Because magnification can be achieved in the unaided eye by simply moving the object closer to the eye (relative distance magnification), it has been common practice to compare the angular image size viewed through the magnifier with the angular size of the object when it is viewed by the unaided eye at the closest distance deemed to be comfortable. This distance was originally termed the least distance of distinct vision (LDDV), but is now known as the reference seeing distance (RSD).¹, ² To maintain image clarity, the eye must accommodate for the RSD. For decades, the convention has been that 4.00 diopter (D) accommodation, corresponding to a RSD of 25 cm, can be maintained comfortably for a period of time. This convention assumes a relatively young population and not a typical, elderly low vision patient. Although arguments have been made in the past in favor of alternative RSDs, 25 cm continues to be the standard.¹, ² If accommodation is represented as a plus lens at the unaided eye, then this traditional approach to magnification compares the magnification of the magnifier with the magnification afforded by a +4.00 lens at the eye. This is the basis for the +4.00 D that occurs in both forms of magnification commonly used to label magnifiers. (See equations 1 and 2 below.) Each form of magnification has underlying assumptions that must be met for the magnification to be achieved.

One equation used to label SMs is:

where F is the equivalent power of the lens, and 4 represents the dioptric equivalent of the reference seeing distance, 25 cm. This is termed nominal magnification by recognized standards¹, ² but is sometimes called rated magnification³ or effective magnification.⁴, ⁵ The term power is sometimes confusing during discussions of magnification and equivalent power. In this article, power will be used to refer to a dioptric refracting power, as in equivalent power or back vertex power. It will not be used in terms of magnifying power; the term magnification alone will be used instead for that application.

Figure 1 shows a magnifier used in a manner that fulfills the assumptions underlying equation (1). The object is located at the primary focal point, F, the vergence of light exiting the magnifier is zero, the image is at infinity, and the accommodation or add required for an emmetrope to view the image clearly is zero. The image subtends angle ω’ at the entrance pupil of the eye. The magnification, M, in equation (1) compares this angle, ω’, with the angle ω_d subtended by the object when it is viewed at 25 cm without the magnifier (see Figure 2). Although no magnifier is used in Figure 2, 4 D of accommodation or reading add is needed to see the image clearly.

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• Figure 1. 

  Illustrating the conditions for nominal magnification. Stand magnifier for which the object is located at the primary focal point, F. The vergence of light exiting the magnifier is zero, the image is at infinity, and the accommodation or add required for an emmetrope to view the image is zero. The image subtends angle ω’ at the entrance pupil of the eye.

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• Figure 2. 

  Object of height, y, is located at the reference seeing distance, d, and subtends angle ω_d at the entrance pupil of the eye.

The other commonly used magnification label uses the equation:

and is termed trade magnification.¹, ² This is also sometimes called conventional magnification.³, ⁴, ⁵ Figure 3 shows an SM placed close to the eye. The distance, h, from the magnifier to the entrance pupil of the eye is assumed to approach zero, at least compared with other distances in the diagram. The page is closer to the magnifier than the magnifier’s primary focal point, F, so that the image is 25 cm from the magnifier and is viewed with 4 D of add or accommodation. The image subtends angle ω’ at the eye. Once again M is the ratio comparing ω’ with ω_d, the angle subtended at the eye by the object if it is viewed at the reference seeing distance, d, without the magnifier (see Figure 2). A common misconception regarding trade magnification is that the SM can be held at any distance from the eye as long as the image is 25 cm from the eye. To the contrary, as shown by the derivation of Equation (2) in the Appendix, the SM must be held at the eye. Another way of thinking about it is that trade magnification assumes that an extra +4.00 D of power (from the add) is added to the magnifier power with a separation of zero, so the resulting equivalent power of the system is in effect (F + 4 D).

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• Figure 3. 

  Illustrating the conditions for trade magnification. Object (height y) is located so the image (height y’) is at an image distance, l’, equal to the reference seeing distance, d, from the SM and subtends angle ω’ at the entrance pupil of the eye. The SM is held as close as possible to the eye (h ≅ 0), and the image is viewed with +4.00 D in addition to the distance prescription.

For all situations in which the image is at 25 cm, the need for +4 D add/accommodation can be satisfied in many different ways: (1) multifocal add, (2) accommodation, (3) undercorrected myopia (or overcorrected hyperopia), and (4) tolerance to blur. The last factor, which is responsible for depth of field/focus, allows some vergence from the magnifier’s image to remain uncorrected without a noticeable increase in blur. This tolerance typically is greater for patients having low vision than for those with normal acuity. Any combination of factors 1 through 4 can be used to provide the needed add. For example, an emmetrope (or ametrope wearing full distance correction) using combinations of accommodation and/or reading add totaling 4 D fulfills this requirement. Other examples include a 4 D myope using the magnifier without distance correction (with the 4 D uncorrected myope being equivalent to an emmetrope using a +4 D add), and a 2 D uncorrected hyperope using 6 D of accommodation. Henceforth, in this article, “add” will be used to include any of these means of achieving the plus power needed to see the image “clearly.”

Because patients rarely use magnifiers in the manner implied by the marked magnification, choosing a magnifier on that basis might be considered pointless. However, if the patient could be trained to use the magnifier under the conditions required by the magnification, then the labels might be useful. This presupposes that the optical design of the SM permits the conditions to be fulfilled. Because the majority of SMs are fixed focus, there is limited flexibility to change the conditions of use to match the label’s assumptions. A reasonable expectation might be that an SM labeled with nominal magnification is designed so that the page rests at the primary focal point of the lens. It might further be expected that a SM labeled with trade magnification might be designed so the vergence of light emerging from the lens is −4.00 D, so the image is 25 cm from the eye with the eye against the magnifier. The purpose of this report is to investigate how many SMs are designed to allow the conditions required by the labeled magnification to be met.

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Methods 

Catalogs of magnifiers for which the magnifier description included (1) nominal or trade magnification and (2) the image location were surveyed.⁶, ⁷, ⁸ When possible, the image locations used in this study were taken from measurements made independent of the manufacturers,⁶ but when independent measurements were not available, data provided by the manufacturers were used.

For the SMs labeled with nominal magnification, the image must be at infinity to satisfy the assumptions for F/4. This corresponds to zero vergence for light emerging from the magnifier. Because many low vision patients tolerate some blur, a variation of up to 0.50 D for the emerging vergence was considered to be within tolerance. An emerging divergence of 0.50 D corresponds to an image location of 200 cm, so image distances from 200 cm to infinity were considered acceptable for nominal magnification.

For SMs labeled with trade magnification, the ±0.50 D tolerance was applied to the required emerging vergence of −4.00 D. A range of acceptable image distances was determined to be 22.2 cm to 28.6 cm, corresponding to vergences of −4.50 D and −3.50, respectively.

If the image location for a particular SM failed to fall in the range required for the labeled magnification, it was also compared with the range required for the other magnification to see if the label could be changed to reflect the performance of the magnifier.

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Results 

The parameters for 66 magnifiers were examined, of which 48 were labeled with trade magnification, and 18 were labeled with nominal magnification. Hemispheric magnifiers (a.k.a., “dome” or “bright field” magnifiers) were excluded because by design the image is very close to the page, not at infinity (ruling out nominal magnification), and the magnifier is usually held at arm’s length, not at the eye (ruling out trade magnification). The brands of magnifiers considered, together with the number labeled with trade magnification (TM) and nominal magnification (NM), were: Eschenbach (TM = 10, NM = 12), COIL (TM = 20, NM = 0), Schweizer (TM = 11, NM = 0), Lighthouse (TM = 7, NM = 0), Peak (TM = 0, NM = 4), Agfa (TM = 0, NM =1), and Selsi (TM = 0, NM = 1).

The SMs were sorted into 1 of 4 categories based on the image distance l’: (1) less than 22.2 cm, (2) 22.2 cm to 28.6 cm, (3) 28.6 cm to 200 cm, and (4) greater than 200 cm. Those in category 1 have image distances too short to satisfy the requirements for either nominal or for trade magnifications. Those in category 2 have image locations that meet the requirements for trade magnification but not for nominal magnification. Category 3 magnifiers have image distances that are too long to satisfy trade magnification but too short to satisfy nominal magnification. The image distances in category 4 magnifiers are close enough to infinity to satisfy nominal magnification (but not trade magnification).

Nominal magnification (F/4) 

Eighteen of the 66 SMs were labeled with nominal magnification. As shown in Table 1, second column from the right, no fixed-focus SMs were identified that met the requirement that the image be at infinity. The page is closer to the magnifier than the magnifier’s primary focal point for all SMs studied. Therefore, the only way that the image can be placed at infinity is to lift the stand off the page until the page and primary focal point are coincident as shown in Figure 1. However, lifting the stand off the page defeats a chief reason for using an SM—to rest the magnifier at a fixed, stable distance from the page.

Table 1. Numbers of stand magnifiers with image distances within 1 of 4 ranges, listed by manufacturer and according to whether the magnifier is labeled with nominal or trade magnification

The use of nominal magnification varies among manufacturers. Approximately half of the 22 Eschenbach SMs in this study were labeled with nominal magnification, whereas none of the COIL, Lighthouse, or Schweizer SMs used nominal magnification.

Trade magnification ([F/4] + 1) 

Forty-eight of the 66 SMs in this study were labeled with trade magnification. The object must be located so the image is 25 cm from the lens, and the vergence emerging from the upper surface of the magnifying lens is −4.00 D. Table 1 shows that only 9 of the 48 SMs labeled with trade magnification have image distances within the range of 22.2 to 28.6 cm, satisfying the ±0.50 D tolerance for an image distance of 25 cm. Interestingly, an additional 3 SMs labeled with nominal magnification had image distances that lay within the range for trade magnification. Only these 12 SMs can be used in the way that satisfies the assumptions required to provide magnification of (F/4) +1. Recall, however, that this will only happen if (1) the SM lens is held against the glasses and (2) a +4.00 D add is used to view the image.

Sixteen of the SMs, half of which are labeled with (F/4) +1 magnification, have image distances greater than 28.6 cm. It is not possible to focus the image clearly with a 4.00 D add no matter what the distance is between the SM and the eye because the image distance exceeds the focal length of the add.

For 38 SMs the image distance is less than 25 cm. These SMs can be used with a +4.00 D add if the magnifier is moved away from the eye so the image seen through the SM is 25 cm from the spectacle plane, but the conditions for trade magnification are not met.

All of the Schweizer, Lighthouse, and COIL SMs used in this study were labeled with trade magnification, whereas approximately half of the 22 Eschenbach SMs used trade magnification.

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Discussion 

None of the SMs listed in the catalogs used in this study have an image distance of infinity as required for nominal magnification to be appreciated. Consequently, the F/4 notation for SMs is reduced to merely an indirect means to calculate the equivalent power of the magnifier. For example, if the magnification is labeled 3X, then F = (4) (M) = (4) (3) = +12 D, which is in theory the equivalent power of the magnifier alone. Unfortunately, this power is often significantly inaccurate.⁹, ¹⁰, ¹¹ Sometimes the manufacturer marks the magnifiers with back vertex power rather than the more appropriate equivalent power.¹¹ Because the image is not at infinity for any of the SMs, it is not possible to view the image clearly through any of these SMs using the distance correction alone. If a presbyopic patient tries to view through the magnifier using the distance correction, she may comment, “It’s clearer if I hold the magnifier off the page.” Elevating the magnifier off the page moves the focal point of the SM to the plane of the page; the image moves to infinity where it can be viewed with the distance correction. This illustrates the principle that if the image is clearer when the magnifier is off the page, then more plus power is needed in the spectacle plane to see the image clearly when the magnifier rests on the page. It has been suggested that fixed-focus SMs are designed with the page plane inside the focal point so that distortion at the edge of the lens is reduced.¹² Another consideration is that if the SM is designed with the page at the focal point, a manufacturing error that places the page slightly outside the focal point causes the emerging rays to be convergent. A clear image would not be seen through either the distance or near portion of a multifocal lens.

For trade ([F/4] +1) magnification to be experienced by the observer, 3 conditions must be fulfilled: (1) the image distance must be 25 cm, (2) the SM must be held against the glasses, and (3) a +4.00 D add must be used. Only about 20% of the SMs labeled with trade magnification (9 of 48) fulfill condition 1. The remaining 80% of SMs labeled with trade magnification cannot be used in the manner required to satisfy the assumptions for trade magnification.

Adding to the confusion surrounding SM labels is the fact that even the same manufacturer may use nominal magnification to label some of its magnifiers and trade magnification to label others. Eschenbach, for example, labels most of its SMs with (F/4) +1 magnification but some with F/4. Interestingly, most of the Eschenbach SMs have been designed so the peripheral optics of the aspheric lenses are optimized at an eye-to-image distance of 400 mm, the focal length of a +2.50 D add.⁷ The information on the Eschenbach SMs includes not only the manufacturer’s assertions for magnification and equivalent power, but also the eye-to-lens distance that will place the eye 400 mm from the image. Ironically then, these SMs have been optimized for a working distance that contradicts the assumptions underlying the labeled magnification. This practice makes the use of trade magnification very misleading for a clinician who uses the labeled magnification as a guide to find a magnifier that is expected to be useful for a patient.

A more helpful means of labeling a magnifier is to provide critical parameters that allow the clinician to anticipate how the patient will perform when the magnifier is used with an add. The equivalent power (or equivalent viewing distance) of a combined magnifying system (whether this is an SM/add system, a closed circuit television/add system, a telemicroscope, or some other system) is the important number that allows the retinal image sizes provided by different magnifiers to be compared.³, ⁴, ⁵, ⁹, ¹⁰

The equivalent dioptric power, F_eq, for a SM/add system is easily calculated if the add power and the ER of the SM are known:

The enlargement ratio, also known as the lateral or transverse magnification, is simply the ratio of the height, y’, of the image seen through the magnifier to the object height, y, (see Figure 3): ER = y’/y. Because the page is located at a fixed object distance from the lens of the SM, the image location is fixed, and therefore the ER is fixed. Selecting an appropriate SM is straight forward when the ERs are known. For example, assume a patient reads a newspaper satisfactorily with a +10 D add using any combination of add, accommodation, and blur tolerance. The equivalent power of this system is +10 D because there is no lens in the magnifying system other than the add. If the patient is to read newsprint with an SM, the SM-add system must have an equivalent power of +10 D. If the patient is to use the SM with glasses that have a +3.00 D add, then the SM must have an ER of at least 3.3 (ER = F_eq/Add = 10/3 = 3.3). Any SMs with ERs less than 3.3 can be eliminated from testing.

The enlargement ratio is 1 of 2 important numbers that should be included on the label of an SM. The other is the image location. Knowing the image location is critical to using an SM successfully with a multifocal add. For example, if it is known that the image is located 30 cm from the SM lens, then a patient using a +2.50 add with a 40-cm viewing distance can be properly positioned 10 cm from the magnifier lens before being asked to read. The 10 cm from the eye to the magnifier plus the 30 cm from the magnifier to the image equals the 40-cm viewing distance through the +2.50 D add. Without proper guidance, the patient is likely to hold the magnifier at a more comfortable 30 cm from the eye, resulting in a blurred image. Unless this distance is changed (and the patient may not think to do it), discouragement may ensue, and the patient may be unsuccessful and become convinced that there is no help. A patient using a +5.00 D add cannot use this magnifier because the image is too far from the magnifier to focus with the 20-cm working distance of the add, even if the magnifier is held up to the eye. This magnifier should not even be tested with the +5.00 D add. This is one of the efficiency issues that can be improved when image location is known.

Although the equivalent power of the SM alone is helpful information, the enlargement ratio and the image location are more important. These have been published for many SMs.⁶, ⁹ The Lighthouse PowerMag series of SMs merits mention because they are the only series of magnifiers that are currently marked with enlargement ratio and image location.

For example, parameters from a few representative SMs from 3 different manufacturers are shown in Table 2. Column 1 shows the description of the magnifier given by the manufacturer. Columns 2, 3, and 4 show the equivalent dioptric power of the magnifier, the image distance from the magnifier, and the enlargement ratios respectively as measured by Bailey et al. and listed in a Lighthouse catalog.¹³ Consider the following example using the Lighthouse PowerMag 9528 (labeled with trade magnification 7.42X, power 25.66 D) to illustrate. Suppose a +1.50 D add (focal length 67 cm) is used to view the image located 53 cm from the magnifier (see Table 2). The separation between the add and magnifier needed to focus the image clearly is 14 cm (67-53). Table 2 shows the ER = 14.6, so for the system the equivalent power is:

Table 2. Optical parameter information (equivalent power F_e, image distance, and enlargement ratio) for 4 selected stand magnifiers

If the patient reads newsprint with this system having F_eq = +21.9 D, then any other magnifying system having the same equivalent power should also allow the patient to read newsprint, at least on the basis of image size. Two examples of other systems with the same equivalent power are (1) a +22.0 D hand magnifier with no add, and (2) a closed circuit TV with the electronic magnification set at 11X viewed at 50 cm with a +2.00 add (F_eq = Electronic mag x Add = 11 x 2 = 22 D).

Note that because the image is located 53 cm from the SM, the maximum add that can be used with the magnifier is +1.9 D (=1/0.53 m), with zero separation between the magnifier and the bifocal. A +4.00 D add cannot be used because the 25-cm required viewing distance is too short for the 53-cm image location. This is an example for which the trade magnification labeled on the magnifier is unobtainable.

It has been widely recognized that the amount of magnification experienced by a patient depends on how the magnifier is used.³, ⁴, ⁵, ⁹, ¹⁰, ¹¹, ¹⁴ While viewing the image through the magnifier, if the patient uses more plus power in the spectacle plane than the distance prescription (e.g., accommodation, multifocal add, uncorrected myopia), the resultant magnification is a function of not only the magnifier power but also the amount of accommodation and the separation between the magnifier and the eye. The labeled magnification is experienced only under very specific conditions. In the example above, it has already been noted that the conditions assumed for the labeled trade magnification cannot be met. However, it is instructive to emphasize the difference that a different add makes. Consider in our example if the patient uses a +1.00 D add (focal length 100 cm) instead of a +1.50 D add. The eye must move to 47 cm from the magnifier (100-53) to see the image clearly, and the equivalent power of the system is:

Amazingly, a modest 0.50-D change in the add results in a devastating reduction in equivalent power, from 21.9 D to 14.6 D. If the patient were using a progressive addition lens and decided to move away to a more comfortable 47 cm from the SM, instead of reading the expected 1.0 M newsprint, the readable print would have to be 21.9/14.6 = 1.5 X larger or 1.5 M print. For this magnifier, the enlargement ratio is very large, corresponding to a rather large 53-cm distance from magnifier to image. A rather small change in add power will cause a much greater change in equivalent power in this situation than if the enlargement ratio were 2-3, as for the fourth magnifier in Table 2, for example. This illustrates how the equivalent power experienced by the patient is highly dependent on the manner in which the magnifier is used. This is very likely the reason that many patients are unable to use SMs successfully. The clinician must know the appropriate parameters of the SM to prescribe the magnifier appropriately and to instruct the patient. If the patient experiences difficulty using an SM, follow-up must be provided to determine if the instructions are being followed correctly.

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Conclusion 

Most SMs labeled with F/4 or (F/4) +1 do not have image locations that allow the conditions underlying the magnification to be fulfilled. The magnification implied by the label bears no relationship to the magnification experienced by the patient when using the magnifier.

It is time to remove magnification labels from SMs. Instead, SMs should include the equivalent power of the SM alone, the enlargement ratio, and the image distance so the equivalent power of the optical system consisting of the SM and the add can be calculated simply.

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Disclaimer 

Neither author has any financial interest in, or relationship with, any of the manufacturers or suppliers mentioned in this article.

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Appendix: Derivation of trade magnification, (F/4) + 1 

By definition of relative magnification, of which trade magnification is a special case:

But from Figure 2, and from Figure 4, so

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• Figure 4. 

  Illustrating the general conditions for relative magnification. The SM, located at distance, h, from the entrance pupil of the eye, is placed on the page (object). A virtual image is formed at image distance l’. The observer uses an add (or accommodation or uncorrected myopia) to view the image, which subtends angle ω’ at the entrance pupil of the eye.

Distances d and l’ are negative, while h is positive. By Gaussian optics, and , so

Substituting equation (3) into (2) and rearranging:

Assumptions 1 and 2 

Assume (1) the reference distance d = −0.25 m and (2) that the object is located so the image is 25 cm from the magnifier (l’ = −0.25 m). Then L’ = 1/(−0.25 m) = −4 D and:

Assumption 3 

Finally, assume (3) that the magnifier is held close to the eye so h ≅ 0. Then:

or Trade magnification (8) It is therefore seen that trade magnification, (F/4) + 1 (Equation 6), is derived by moving the magnifier to the eye (h ≅ 0) and locating the object so the image is 25 cm from the magnifier and from the eye.

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