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Optometry (2008) 79, 9-17
1d
agnification labels for stand magnifiers: Alwaysisleading and usually unachievable
illiam L. Brown, O.D., Ph.D., and Dennis W. Siemsen, O.D.
ayo Clinic, Department of Ophthalmology, Division of Optometry, Rochester, Minnesota.
AbstractBACKGROUND: 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 labeledmagnification can be realized.METHODS: Three catalogs were examined to obtain the type of magnification label used for each of 66different SMs. Image locations were acquired from published tables compiled by independentinvestigators when available. Otherwise, they were taken from manufacturer-provided information inthe catalogs. The image location was used to determine how many magnifiers could be used in a mannerthat 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 imageat infinity. No SMs met this condition. (F/4) � 1 magnification assumes the magnifier is close to theeye 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 markedmagnification. 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.Optometry 2008;79:9-17
KEYWORDSLow vision;Stand magnifier;Trade magnification;Nominal
magnification;Equivalent power;Enlargement ratio;Ophthalmic optics
itpmenturai
ed
A properly performed low vision examination is multi-aceted. It includes a detailed history to establish specificoals, a careful refraction, generally with a trial frame, aetermination of the equivalent power required to meet eachoal, a determination of the type of magnifying systemaving that power that best serves the patient, as well asther components not directly relevant to this report. Thexamination is time consuming, and the low vision clinicians ever alert for ways to improve efficiency. One of theuestions that prompted this study is whether the currentethod of labeling stand magnifiers (SMs) assists or hinders
linical efficiency.
Corresponding author: William L. Brown, O.D., Ph.D., Mayo Clinic,00 First Street SW, Mayo W7, Rochester, Minnesota 55905.
cE-mail: [email protected].
529-1839/08/$ -see front matter © 2008 American Optometric Association. Alloi:10.1016/j.optm.2007.03.016
When using a SM, the observer views an enlarged virtualmage through a positive-powered lens (or system of lenses)hat is supported by the stand at a fixed distance from theage. Manufacturers of SMs traditionally label them withagnification based on 1 of 2 equations. Both of these
quations stem from the desire to label the magnifier with aumber that shows the magnification that is achievable withhe magnifier compared with the magnification achieved bysing only the unaided eye. (In this article, “unaided eye”efers to the eye corrected for distance ametropia but notided by an additional magnifying lens, unless otherwisendicated.)
Because magnification can be achieved in the unaidedye by simply moving the object closer to the eye (relativeistance magnification), it has been common practice to
ompare the angular image size viewed through the mag-rights reserved.
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10 Optometry, Vol 79, No 1, January 2008
ifier with the angular size of the object when it is viewedy the unaided eye at the closest distance deemed to beomfortable. This distance was originally termed the leastistance of distinct vision (LDDV), but is now known as theeference seeing distance (RSD).1,2 To maintain image clar-ty, the eye must accommodate for the RSD. For decades,he convention has been that 4.00 diopter (D) accommoda-ion, corresponding to a RSD of 25 cm, can be maintainedomfortably for a period of time. This convention assumesrelatively young population and not a typical, elderly lowision patient. Although arguments have been made in theast in favor of alternative RSDs, 25 cm continues to be thetandard.1,2 If accommodation is represented as a plus lenst the unaided eye, then this traditional approach to magni-cation compares the magnification of the magnifier with
he magnification afforded by a �4.00 lens at the eye. Thiss the basis for the �4.00 D that occurs in both forms ofagnification commonly used to label magnifiers. (See
quations 1 and 2 below.) Each form of magnification hasnderlying assumptions that must be met for the magnifi-ation to be achieved.
One equation used to label SMs is:
M �F
4, (1)
here F is the equivalent power of the lens, and 4 representshe dioptric equivalent of the reference seeing distance, 25m. This is termed nominal magnification by recognizedtandards1,2 but is sometimes called rated magnification3 orffective magnification.4,5 The term power is sometimesonfusing during discussions of magnification and equiva-
igure 1 Illustrating the conditions for nominal magnification. Stand mf light exiting the magnifier is zero, the image is at infinity, and the accomubtends angle �’ at the entrance pupil of the eye.
ent power. In this article, power will be used to refer to a d
ioptric refracting power, as in equivalent power or backertex power. It will not be used in terms of magnifyingower; the term magnification alone will be used instead forhat application.
Figure 1 shows a magnifier used in a manner that fulfillshe assumptions underlying equation (1). The object isocated at the primary focal point, F, the vergence of lightxiting the magnifier is zero, the image is at infinity, and theccommodation or add required for an emmetrope to viewhe image clearly is zero. The image subtends angle �’ athe entrance pupil of the eye. The magnification, M, inquation (1) compares this angle, �’, with the angle �d
ubtended by the object when it is viewed at 25 cm withouthe magnifier (see Figure 2). Although no magnifier is usedn Figure 2, 4 D of accommodation or reading add is neededo see the image clearly.
r for which the object is located at the primary focal point, F. The vergenceion or add required for an emmetrope to view the image is zero. The image
igure 2 Object of height, y, is located at the reference seeing
agnifiemodat
istance, d, and subtends angle �d at the entrance pupil of the eye.
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11Brown and Siemsen Issue Highlight
he other commonly used magnification label uses thequation:
M �F
4� 1, (2)
nd is termed trade magnification.1,2 This is also sometimesalled conventional magnification.3-5 Figure 3 shows an SMlaced close to the eye. The distance, h, from the magnifiero the entrance pupil of the eye is assumed to approach zero,t least compared with other distances in the diagram. Theage is closer to the magnifier than the magnifier’s primaryocal point, F, so that the image is 25 cm from the magnifiernd is viewed with 4 D of add or accommodation. Themage subtends angle �’ at the eye. Once again M is theatio comparing �’ with �d, the angle subtended at the eyey the object if it is viewed at the reference seeing distance,, without the magnifier (see Figure 2). A common miscon-eption regarding trade magnification is that the SM can beeld at any distance from the eye as long as the image is 25m from the eye. To the contrary, as shown by the deriva-ion of Equation (2) in the Appendix, the SM must be heldt the eye. Another way of thinking about it is that tradeagnification assumes that an extra �4.00 D of power
from the add) is added to the magnifier power with aeparation of zero, so the resulting equivalent power of theystem is in effect (F � 4 D).
For all situations in which the image is at 25 cm, theeed for �4 D add/accommodation can be satisfied inany different ways: (1) multifocal add, (2) accommo-
ation, (3) undercorrected myopia (or overcorrected hy-eropia), and (4) tolerance to blur. The last factor, whichs responsible for depth of field/focus, allows some ver-ence from the magnifier’s image to remain uncorrectedithout a noticeable increase in blur. This tolerance
ypically is greater for patients having low vision than forhose with normal acuity. Any combination of factors 1hrough 4 can be used to provide the needed add. Forxample, an emmetrope (or ametrope wearing full dis-
igure 3 Illustrating the conditions for trade magnification. Objectheight y) is located so the image (height y’) is at an image distance, l’,qual to the reference seeing distance, d, from the SM and subtends angle’ at the entrance pupil of the eye. The SM is held as close as possible to
he eye (h � 0), and the image is viewed with �4.00 D in addition to theistance prescription.
ance correction) using combinations of accommodation p
nd/or reading add totaling 4 D fulfills this requirement.ther examples include a 4 D myope using the magnifierithout distance correction (with the 4 D uncorrectedyope being equivalent to an emmetrope using a �4 D
dd), and a 2 D uncorrected hyperope using 6 D ofccommodation. Henceforth, in this article, “add” will besed to include any of these means of achieving the plusower needed to see the image “clearly.”
Because patients rarely use magnifiers in the mannermplied by the marked magnification, choosing a magni-er on that basis might be considered pointless. However,
f the patient could be trained to use the magnifier underhe conditions required by the magnification, then theabels might be useful. This presupposes that the opticalesign of the SM permits the conditions to be fulfilled.ecause the majority of SMs are fixed focus, there is
imited flexibility to change the conditions of use toatch the label’s assumptions. A reasonable expectationight be that an SM labeled with nominal magnification
s designed so that the page rests at the primary focaloint of the lens. It might further be expected that a SMabeled with trade magnification might be designed so theergence of light emerging from the lens is �4.00 D, sohe image is 25 cm from the eye with the eye against theagnifier. The purpose of this report is to investigate
ow many SMs are designed to allow the conditionsequired by the labeled magnification to be met.
ethods
atalogs of magnifiers for which the magnifier descriptionncluded (1) nominal or trade magnification and (2) themage location were surveyed.6-8 When possible, the imageocations used in this study were taken from measurementsade independent of the manufacturers,6 but when inde-
endent measurements were not available, data provided byhe manufacturers were used.
For the SMs labeled with nominal magnification, themage must be at infinity to satisfy the assumptions for F/4.his corresponds to zero vergence for light emerging from
he magnifier. Because many low vision patients tolerateome blur, a variation of up to 0.50 D for the emergingergence was considered to be within tolerance. An emerg-ng divergence of 0.50 D corresponds to an image locationf 200 cm, so image distances from 200 cm to infinity wereonsidered acceptable for nominal magnification.
For SMs labeled with trade magnification, the �0.50 Dolerance was applied to the required emerging vergence of
4.00 D. A range of acceptable image distances wasetermined to be 22.2 cm to 28.6 cm, corresponding toergences of �4.50 D and �3.50, respectively.
If the image location for a particular SM failed to fall inhe range required for the labeled magnification, it was alsoompared with the range required for the other magnifica-ion to see if the label could be changed to reflect the
erformance of the magnifier.
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12 Optometry, Vol 79, No 1, January 2008
esults
he parameters for 66 magnifiers were examined, of which8 were labeled with trade magnification, and 18 wereabeled with nominal magnification. Hemispheric magnifi-rs (a.k.a., “dome” or “bright field” magnifiers) were ex-luded because by design the image is very close to theage, not at infinity (ruling out nominal magnification), andhe magnifier is usually held at arm’s length, not at the eyeruling out trade magnification). The brands of magnifiersonsidered, together with the number labeled with tradeagnification (TM) and nominal magnification (NM), were:schenbach (TM � 10, NM � 12), COIL (TM � 20, NM
0), Schweizer (TM � 11, NM � 0), Lighthouse (TM �, NM � 0), Peak (TM � 0, NM � 4), Agfa (TM � 0, NM1), and Selsi (TM � 0, NM � 1).The SMs were sorted into 1 of 4 categories based on the
mage distance l’: (1) less than 22.2 cm, (2) 22.2 cm to 28.6m, (3) 28.6 cm to 200 cm, and (4) greater than 200 cm.hose in category 1 have image distances too short toatisfy the requirements for either nominal or for tradeagnifications. Those in category 2 have image locations
hat meet the requirements for trade magnification but notor nominal magnification. Category 3 magnifiers havemage distances that are too long to satisfy trade magnifi-ation but too short to satisfy nominal magnification. Themage distances in category 4 magnifiers are close enougho infinity to satisfy nominal magnification (but not tradeagnification).
ominal magnification (F/4)
ighteen of the 66 SMs were labeled with nominal magni-cation. As shown in Table 1, second column from theight, no fixed-focus SMs were identified that met theequirement that the image be at infinity. The page is closero the magnifier than the magnifier’s primary focal point forll SMs studied. Therefore, the only way that the image cane placed at infinity is to lift the stand off the page until theage and primary focal point are coincident as shown inigure 1. However, lifting the stand off the page defeats ahief reason for using an SM—to rest the magnifier at axed, stable distance from the page.
The use of nominal magnification varies among manu-acturers. Approximately half of the 22 Eschenbach SMs inhis study were labeled with nominal magnification,hereas none of the COIL, Lighthouse, or Schweizer SMssed nominal magnification.
rade magnification ([F/4] � 1)
orty-eight of the 66 SMs in this study were labeled withrade magnification. The object must be located so themage is 25 cm from the lens, and the vergence emergingrom the upper surface of the magnifying lens is �4.00 D.
able 1 shows that only 9 of the 48 SMs labeled with trade magnification have image distances within the range of 22.2o 28.6 cm, satisfying the �0.50 D tolerance for an imageistance of 25 cm. Interestingly, an additional 3 SMs la-eled with nominal magnification had image distances thatay within the range for trade magnification. Only these 12Ms can be used in the way that satisfies the assumptionsequired to provide magnification of (F/4) �1. Recall,owever, that this will only happen if (1) the SM lens is heldgainst the glasses and (2) a �4.00 D add is used to view themage.
Sixteen of the SMs, half of which are labeled with (F/4)1 magnification, have image distances greater than 28.6
m. It is not possible to focus the image clearly with a 4.00add no matter what the distance is between the SM and
he eye because the image distance exceeds the focal lengthf the add.
For 38 SMs the image distance is less than 25 cm. TheseMs can be used with a �4.00 D add if the magnifier isoved away from the eye so the image seen through the SM
s 25 cm from the spectacle plane, but the conditions forrade magnification are not met.
All of the Schweizer, Lighthouse, and COIL SMs used inhis study were labeled with trade magnification, whereaspproximately half of the 22 Eschenbach SMs used trade
Table 1 Numbers of stand magnifiers with image distanceswithin 1 of 4 ranges, listed by manufacturer and accordingto whether the magnifier is labeled with nominal or trademagnification
Number of SMs with imagedistances l’ (cm)
�22.2 22.2-28.6 28.6-200 �200Totals
COILNominal 0 0 0 0 0Trade 7 6 7 0 20
EschenbachNominal 2 2 8 0 12Trade 10 0 0 0 10
LHNominal 0 0 0 0 0Trade 5 1 1 0 7
AgfaNominal 1 0 0 0 1Trade 0 0 0 0 0
PeakNominal 3 1 0 0 4Trade 0 0 0 0 0
SchweizerNominal 0 0 0 0 0Trade 9 2 0 0 11
SelsiNominal 1 0 0 0 1Trade 0 0 0 0 0
TotalsNominal 7 3 8 0 18Trade 31 9 8 0 48
agnification.
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13Brown and Siemsen Issue Highlight
iscussion
one of the SMs listed in the catalogs used in this studyave an image distance of infinity as required for nominalagnification to be appreciated. Consequently, the F/4 no-
ation for SMs is reduced to merely an indirect means toalculate the equivalent power of the magnifier. For exam-le, if the magnification is labeled 3X, then F � (4) (M) �4) (3) � �12 D, which is in theory the equivalent power ofhe magnifier alone. Unfortunately, this power is oftenignificantly inaccurate.9-11 Sometimes the manufacturerarks the magnifiers with back vertex power rather than theore appropriate equivalent power.11 Because the image is
ot at infinity for any of the SMs, it is not possible to viewhe image clearly through any of these SMs using theistance correction alone. If a presbyopic patient tries toiew through the magnifier using the distance correction,he may comment, “It’s clearer if I hold the magnifier offhe page.” Elevating the magnifier off the page moves theocal point of the SM to the plane of the page; the imageoves to infinity where it can be viewed with the distance
orrection. This illustrates the principle that if the image islearer when the magnifier is off the page, then more plusower is needed in the spectacle plane to see the imagelearly when the magnifier rests on the page. It has beenuggested that fixed-focus SMs are designed with the pagelane inside the focal point so that distortion at the edge ofhe lens is reduced.12 Another consideration is that if the SMs designed with the page at the focal point, a manufacturingrror that places the page slightly outside the focal pointauses the emerging rays to be convergent. A clear imageould not be seen through either the distance or nearortion of a multifocal lens.
For trade ([F/4] �1) magnification to be experienced byhe observer, 3 conditions must be fulfilled: (1) the imageistance must be 25 cm, (2) the SM must be held against thelasses, and (3) a �4.00 D add must be used. Only about0% of the SMs labeled with trade magnification (9 of 48)ulfill condition 1. The remaining 80% of SMs labeled withrade magnification cannot be used in the manner requiredo satisfy the assumptions for trade magnification.
Adding to the confusion surrounding SM labels is theact that even the same manufacturer may use nominalagnification to label some of its magnifiers and tradeagnification to label others. Eschenbach, for example,
abels most of its SMs with (F/4) �1 magnification butome with F/4. Interestingly, most of the Eschenbach SMsave been designed so the peripheral optics of the asphericenses are optimized at an eye-to-image distance of 400 mm,he focal length of a �2.50 D add.7 The information on theschenbach SMs includes not only the manufacturer’s as-ertions for magnification and equivalent power, but alsohe eye-to-lens distance that will place the eye 400 mm fromhe image. Ironically then, these SMs have been optimizedor a working distance that contradicts the assumptionsnderlying the labeled magnification. This practice makes
he use of trade magnification very misleading for a clini- iian who uses the labeled magnification as a guide to find aagnifier that is expected to be useful for a patient.A more helpful means of labeling a magnifier is to
rovide critical parameters that allow the clinician to antic-pate how the patient will perform when the magnifier issed with an add. The equivalent power (or equivalentiewing distance) of a combined magnifying systemwhether this is an SM/add system, a closed circuit televi-ion/add system, a telemicroscope, or some other system) ishe important number that allows the retinal image sizesrovided by different magnifiers to be compared.3-5,9,10
The equivalent dioptric power, Feq, for a SM/add systems easily calculated if the add power and the ER of the SMre known:
Feq � Add � ER. (3)
The enlargement ratio, also known as the lateral orransverse magnification, is simply the ratio of the height, y’, ofhe image seen through the magnifier to the object height, y,see Figure 3): ER � y’/y. Because the page is located at axed object distance from the lens of the SM, the image
ocation is fixed, and therefore the ER is fixed. Selecting anppropriate SM is straight forward when the ERs are known.or example, assume a patient reads a newspaper satisfacto-ily with a �10 D add using any combination of add,ccommodation, and blur tolerance. The equivalent powerf this system is �10 D because there is no lens in theagnifying system other than the add. If the patient is to
ead newsprint with an SM, the SM-add system must haven equivalent power of �10 D. If the patient is to use theM with glasses that have a �3.00 D add, then the SM mustave an ER of at least 3.3 (ER � Feq/Add � 10/3 � 3.3).ny SMs with ERs less than 3.3 can be eliminated from
esting.The enlargement ratio is 1 of 2 important numbers that
hould be included on the label of an SM. The other is themage location. Knowing the image location is critical tosing an SM successfully with a multifocal add. For exam-le, if it is known that the image is located 30 cm from theM lens, then a patient using a �2.50 add with a 40-cmiewing distance can be properly positioned 10 cm from theagnifier lens before being asked to read. The 10 cm from
he eye to the magnifier plus the 30 cm from the magnifiero the image equals the 40-cm viewing distance through the
2.50 D add. Without proper guidance, the patient is likelyo hold the magnifier at a more comfortable 30 cm from theye, resulting in a blurred image. Unless this distance ishanged (and the patient may not think to do it), discour-gement may ensue, and the patient may be unsuccessfulnd become convinced that there is no help. A patient using�5.00 D add cannot use this magnifier because the image
s too far from the magnifier to focus with the 20-cmorking distance of the add, even if the magnifier is held up
o the eye. This magnifier should not even be tested with the5.00 D add. This is one of the efficiency issues that can be
mproved when image location is known.
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14 Optometry, Vol 79, No 1, January 2008
Although the equivalent power of the SM alone is help-ul information, the enlargement ratio and the image loca-ion are more important. These have been published forany SMs.6,9 The Lighthouse PowerMag series of SMserits mention because they are the only series of magni-ers that are currently marked with enlargement ratio and
mage location.For example, parameters from a few representative SMs
rom 3 different manufacturers are shown in Table 2.olumn 1 shows the description of the magnifier given by
he manufacturer. Columns 2, 3, and 4 show the equivalentioptric power of the magnifier, the image distance from theagnifier, and the enlargement ratios respectively as mea-
ured by Bailey et al. and listed in a Lighthouse catalog.13
onsider the following example using the Lighthouse Pow-rMag 9528 (labeled with trade magnification 7.42X, power5.66 D) to illustrate. Suppose a �1.50 D add (focal length7 cm) is used to view the image located 53 cm from theagnifier (see Table 2). The separation between the add andagnifier needed to focus the image clearly is 14 cm
67-53). Table 2 shows the ER � 14.6, so for the system thequivalent power is:
Feq � (Add) (Enlargement ratio) � (�1.5D) (14.6) � � 21.9 D.
If the patient reads newsprint with this system having Feq
�21.9 D, then any other magnifying system having theame equivalent power should also allow the patient to readewsprint, at least on the basis of image size. Two examplesf other systems with the same equivalent power are (1) a22.0 D hand magnifier with no add, and (2) a closed
ircuit TV with the electronic magnification set at 11Xiewed at 50 cm with a �2.00 add (Feq � Electronic magAdd � 11 x 2 � 22 D).Note that because the image is located 53 cm from the
M, the maximum add that can be used with the magnifiers �1.9 D (�1/0.53 m), with zero separation between theagnifier and the bifocal. A �4.00 D add cannot be used
ecause the 25-cm required viewing distance is too short forhe 53-cm image location. This is an example for which therade magnification labeled on the magnifier is unobtain-
Table 2 Optical parameter information (equivalent powerFe, image distance, and enlargement ratio) for 4 selectedstand magnifiers
Magnifier description Fe (D)Imagedistance (cm)
Enlargementratio
LH PowerMag 95287.42X (25.66D)
25.7 53.0 14.6
COIL#6289 7.1X(24.2D)
24.1 24.4 6.9
COIL#6279 5.4X(17.7D)
18.2 33.3 7.1
Eschenbach #15254.2X (17D)
16.7 13.3 3.2
ble. a
It has been widely recognized that the amount of mag-ification experienced by a patient depends on how theagnifier is used.3-5,9-11,14 While viewing the image
hrough the magnifier, if the patient uses more plus power inhe spectacle plane than the distance prescription (e.g.,ccommodation, multifocal add, uncorrected myopia), theesultant magnification is a function of not only the magni-er power but also the amount of accommodation and theeparation between the magnifier and the eye. The labeledagnification is experienced only under very specific con-
itions. In the example above, it has already been noted thathe conditions assumed for the labeled trade magnificationannot be met. However, it is instructive to emphasize theifference that a different add makes. Consider in ourxample if the patient uses a �1.00 D add (focal length 100m) instead of a �1.50 D add. The eye must move to 47 cmrom the magnifier (100-53) to see the image clearly, andhe equivalent power of the system is:
eq � (Add) (Enlargement ratio) � (�1.00 D) (14.6) �
� 14.6 D.
Amazingly, a modest 0.50-D change in the add results indevastating reduction in equivalent power, from 21.9 D to4.6 D. If the patient were using a progressive addition lensnd decided to move away to a more comfortable 47 cmrom the SM, instead of reading the expected 1.0 M news-rint, the readable print would have to be 21.9/14.6 � 1.5 Xarger or 1.5 M print. For this magnifier, the enlargementatio is very large, corresponding to a rather large 53-cmistance from magnifier to image. A rather small change indd power will cause a much greater change in equivalentower in this situation than if the enlargement ratio were-3, as for the fourth magnifier in Table 2, for example. Thisllustrates how the equivalent power experienced by theatient is highly dependent on the manner in which theagnifier is used. This is very likely the reason that many
atients are unable to use SMs successfully. The clinicianust know the appropriate parameters of the SM to pre-
cribe the magnifier appropriately and to instruct the patient.f the patient experiences difficulty using an SM, follow-upust be provided to determine if the instructions are being
ollowed correctly.
onclusion
ost SMs labeled with F/4 or (F/4) �1 do not have imageocations that allow the conditions underlying the magnifi-ation to be fulfilled. The magnification implied by the labelears no relationship to the magnification experienced byhe patient when using the magnifier.
It is time to remove magnification labels from SMs.nstead, SMs should include the equivalent power of the SMlone, the enlargement ratio, and the image distance so thequivalent power of the optical system consisting of the SM
nd the add can be calculated simply.
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15Brown and Siemsen Issue Highlight
isclaimer
either author has any financial interest in, or relationshipith, any of the manufacturers or suppliers mentioned in
his article.
eferences1. American National Standard for Ophthalmics: devices for low vision,
ANSI Z80.9 - 2004. Merrifield, Virginia: Optical Laboratories Asso-ciation, 2005.
2. International Standards Organization. ISO 15253:2000, Ophthalmicoptics and instruments—optical devices for enhancing low vision.Geneva, Switzerland; 2001.
3. Cole RG. A functional approach to the optics of low vision devices. In:Cole RG, Rosenthal BP, editors. Remediation and management of lowvision. St. Louis: Mosby; 1996:139-77.
4. Byer A. Magnification associated with low vision systems. In: BrilliantRL, editor. Essentials of low vision practice. Boston: Butterworth-
Heinemann; 1999:111-30.5. Chung STL, Johnston AW. Practical options in magnification and fieldof view of stand magnifiers. Clin Exp Optom 1989;72(5):140-7.
6. Optelec US, Inc. Lighthouse products by Optolec. New York: January,2006.
7. Eschenbach Optik GmbH & Co. 2004/2005 catalog. Ridgefield, CT:2004.
8. Carclo Tech. Plastics (Slough) Ltd. COIL eye care products catalogue.Berkshire, England: Slough; 2005.
9. Bailey IL, Bullimore MA, Greer RB. Low vision magnifiers—theiroptical parameters and methods for prescribing. Optom Vis Sci 1994;71(11):689-98.
0. Bullimore MA, Bailey IL. Stand magnifiers: An evaluation of newoptical aids from COIL. Optom Vis Sci 1989;66(11):766-73.
1. Chung STL, Johnston AW. New stand magnifiers do not meet ratedlevels of performance. Clin Exp Optom 1990;73(6):194-9.
2. Jose RT. Treatment Options. In: Jose RT, editor. Understanding lowvision. New York: American Foundation for the Blind; 1983:230.
3. Lighthouse International. The lighthouse professional products pricelist. New York: 2003-2004.
4. Johnston AW. Understanding how simple magnifiers provide image
enlargement. Clin Exp Optom 2003;86(6):403-8.
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16 Optometry, Vol 79, No 1, January 200816 Optometry, Vol 79, No 1, January 2008
1529doi:
ppendix: Derivation ofrade magnification, (F/4) �
By definition of relative magnification, of whichrade magnification is a special case:
M �tan �’
tan �d
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y Gaussian optics,y’
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y�
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L’. (3)
ubstituting equation (3) into (2) and rearranging: a
-1839/08/$ -see front matter © 2008 American Optometric Association10.1016/j.optm.2007.03.016
M �d(L ’ �F)
L ’ (l ’ �h). (4)
ssumptions 1 and 2:
Assume (1) the reference distance d � �0.25 mnd (2) that the object is located so the image is 25 cmrom the magnifier (l’ � �0.25 m). Then L’ �/(�0.25 m) � �4 D and:
M ��0.25m(�4D � F)
�4D(�0.25m � h)�
.25F � 1
1 � 4h(5)
ssumption 3:
Finally, assume (3) that the magnifier is held closeo the eye so h � 0. Then:
M �.25F � 1
1 � 0r
M �F
4� 1 (6)
rade magnification (8) It is therefore seen that tradeagnification, (F/4) � 1 (Equation 6), is derived byoving the magnifier to the eye (h � 0) and locating
he object so the image is 25 cm from the magnifier
nd from the eye.. All rights reserved.
Feu
17Brown and Siemsen Issue Highlight 17Brown and Siemsen Issue Highlight
1529doi:
igure 4 Illustrating the general conditions for relative magnification. The SM, located at distance, h, from the entrance pupil of theye, is placed on the page (object). A virtual image is formed at image distance l’. The observer uses an add (or accommodation or
ncorrected myopia) to view the image, which subtends angle �’ at the entrance pupil of the eye.-1839/08/$ -see front matter © 2008 American Optometric Association. All rights reserved.10.1016/j.optm.2007.03.016
