Calibration of Adjustable Focus Telescopesfor Near Vision
Tadaaki Tanabe 1), Hiroshi Uozato 2)
1) Welfare Center for the Blind, Nippon Lighthouse2) Graduate School of Medical Science, Kitasato University
Low vision aids used for the near point may be either simple plus lenses or telescopes focused for near. Krefman1) reported that a near vision telescope had a longer
corresponding working distance than a simple plus lens of the same equivalent viewing power (EVP). Bailey suggested that there are three different methods by which atelescope can be focused for near vision: 1) Adding positive power to the objective lens. 2) Adding positive power to the eyepiece lens. 3) Increasing the tube length2).
Method 2) is not a useful method compared to the other two because the resultant power of the system results in less than the power of the addition, which makes thetelescope a minifier.
Increasing the tube length of an adjustable focus telescopes can provide focus for many different working distances, however, it is difficult to determine the EVP. If the EVP
were known, a telescope could be manipulated just like a simple plus lens, and clinicians could select effective aids for the near task by comparing the working distances.
Reich developed a method to select the telescope with a suitable working distance and the EVP using a nomogram3).
From the point of view of convenience for clinicians, telescopes labeled with the EVP and the working distances would be more useful than a nomogram to select low
vision aids. Since present labeling on the body of a telescope by manufacturers is in units of angular magnification4) only for distance vision, it cannot easily be compared tothe magnification of a simple plus lens. This is the reason we have decided to display the calibration of the EVP and corresponding working distance on the body of the tube.
MATERIAL AND METHODS
Common telescopes are made by some manufacturers
such as Carton, Kenmax, Zeiss and so on. Some telescopes
made by Kenmax already display calibrations only in working
distances on the tubes by which users can easily focus (Fig.1).
However, the values of magnification corresponding tochanges in working distance are not easily known. Thus weFig. 1
included calibrations of the EVP and the working distance on
the telescopes.
Two equations are proposed in order to make the calibration on the tube.
One is for the working distance; the other is for the length of calibration or thechange of the tube length. The equation of the working distance(a) is describedas follows where Fe is the EVP, De is the equivalent power of the objectivelens, and m is the labeled magnification. The working distance is defined as
the distance between the objective lens and the object in this article.
m1aFe De(1)The equation of the length of calibration (⊿t) according to the changes of theEVP is described as follows.
⊿t FemDe2

dD1  D2  D1D2nDv d1  D1n

D1 d 2DV  D1 d 2Dv Dn  2ndDv  n 2Dn  ndDv Dn  n 2Dv  0

EVP (D)
02
4
68
10
12
14
1618
20
222426283032
34Length ofcalibration
(mm)
∞
0.0
306
1.3
156
2.5
106
3.8
81
5.0
66
6.3
56
7.6
49
8.8
44
10.1
39
11.3
36
12.6
33
13.9
31
15.1
29
16.4
28
17.6
26
18.92520.1
24
21.4

DISCUSSION
Adjustable focus telescopes for near vision could provide successive EVP. For
example, the EVP of the PK-6 varied from 0D to 34D by lengthening the tube as
denoted in Table 2.
Since apparent sizes of virtual images of lenses which have the same EVP
should be equal, the virtual images of near vision telescopes and the simple plus
lens magnifier of the Nikon 16D were taken as examples to ensure the validity ofcalibrations of the PK-4 and PK-6. Adjusting the calibrations of telescopes to 16D,and setting the objective lenses at the indicated corresponding working distances,the virtual images of the ruler through the telescopes and the magnifier weretaken with a digital still camera. All resulting images were cascaded in Fig.3 andrecognized as being the same size, which verified the closeness of thecalibrations. Using the calibrations on the tubes, the working distances
corresponding to the EVP of 16D were revealed as follows: 30 cm for the PK-4,
and 44 cm for the PK-6. The working distance of the magnifier of the Nikon 16D
was 6.2 cm which was derived from the reciprocal of the dioptric power of 16D.
Knowing the variation of working distances in different low vision aids
corresponding to the identical dioptric power, an appropriate low vision aid can beselected in accordance with the needed working distance for patients.

(5)This expression has the form of a quadratic equation , the solution of which isgiven by:2 b  b  4acx
2aThus the solution for the quadratic equation (5) are:
D1 Workingdistance
（cm）

( 4)

Substituting (3) into (4),2Table 2. EVP, working distanceand length of calibration for PK-6(2)2

Derivation of the equations (1)(2) are described by Reich3).
Therefore, when the power of the objective lens and the labeled
magnification are constant, the working distance and the length of calibration
can be calculated relative to the EVP. Hereby, how to determine the power ofthe objective lens is the problem. Even if Reich and Bailey proposed someconvenient methods without disassembling the telescope, they contain an error
caused by accommodation or an empirical measurement. Thus we decided toseparate the object lens from the barrel and measured the anterior andposterior vertex focal power using a lensometer and we measured the thicknessof the lens with calipers. Fortunately, the objective lenses of PK-4 and PK-6
made by Kenmax Ltd. were easily disassembled, so we used those twotelescopes for the examples to make our calibrations. The equation to get theequivalent power of the objective lens with those factors is derived as follows:
where Dn=anterior vertex focal power, Dv=posterior vertex focal power,
d=thickness of the lens, D1=anterior surface power, D2=posterior surface power,
n=refractive index of the material, and De=equivalent power.
dD1  D2  D1D2n D1  Dn nDn  D2 (3)dd D1  Dn   n
1 Dn

shown in Table 2. The values of the shortest
working distances were investigated by thefollowing method. By gradually reducing thedistance between the telescope and the object at
the longest length of the tube, the shortest working
distance can be measured when the virtual image
can be clearly recognized with a relaxed
emmetropic eye at the least accommodation.
The calibrations should
be marked on the tubes
accordingtothecalculations. The marking
for the shortest working
distance of calibrations
should be flush with theedge of the objective lens
grip at the greatest
Fig. 2extension of the tube(Fig.2).

d 2Dv Dn  2ndDv  d 2Dv Dn d 2Dv Dn  4n 222d Dv

(6)Once the anterior surface power(D1) and the posterior surface power(D2) arecalculated with the substitution of the anterior vertex focal power(Dn), theposterior vertex focal power(Dv) and the thickness(d), the equivalentpower(De) of the objective lens is given by:dDe  D1  D2  D1D2n(7)RESULTS
Since the anterior vertex focal power(Dn), the posterior vertex focalpower(Dv) and the thickness(d) of the objective lens of PK-4 and PK-6 weremeasured, the equivalent power(De) can be calculated using the equation(6)(3)(7). The values are indicated in Table 1.
Table 1. Anterior and posterior vertex focal power, thickness, equivalent power
Anterior vertex
Posterior vertex
Equivalent power
Thickness (mm)focal power (D) focal power (D)
(D)
PK-4
21.25
22.25
3.5
21.21
PK-6
16.30
17.00
4.2
16.27

Using the equations (1)(2), the relation between the EVP, the working
distance and the length of calibration was calculated. The example for PK-6 is10th International Conference on Low Vision, Vision 2011 in Kuala Lumpur, Malaysia.
Kuala Lumpur Convention Centre, 20-24 February 2011.

Fig. 3To select a proper low vision aid for near vision, the equivalent viewing distance(EVD) should be calculated by using a reading chart5). The EVP is obtained by thereciprocal of the EVD. The calibration on the tubes of telescopes should be
adjusted to the obtained EVP so as to check the corresponding working distances.
By comparing the indicated working distances on the tubes, clinicians can easily
determine which working distance is closest to the needed working distance forthe task and choose the best telescope to use. Take an example of a low visionpatient who wants to read newspaper from a distance of about 30 cm. If he/she
can read 6M unit of a near vision reading chart at 20 cm working distance, EVD iscalculated as 20/6=3.3(cm). Since EVP is given by the reciprocal of 0.033(m),EVP is 30D. In this case the PK-6 is a proper aid because it has 26 cm of working
distance which is closest to 30 cm of any of the aids at an EVP of 30D.
CONCLUSION
Calibrations marked on the tube of the telescope for near vision is much moreconvenient for clinicians than using the nomogram described on the paper when
they select low vision aids in the office referring to the needed EVP.
They can easily adjust the tube length according to the EVP and find theappropriate working distance immediately.
ACKNOWLEDGEMENT
The method to calibrate the EVP and the working distances on the tube of anadjustable focus telescope for near vision has a patent pending in Japan.
REFERENCES
1)

Krefman RA. Working distance comparison of plus lenses and reading telescopes. Amer J of Optom & Physiol Optics 1980; 57:835-838.

2)

Bailey IL. Principle of near vision telescope. Optom Monthly 1981; 32-34.

3)

Reich LN. Adjustable focus telescopes for near vision. Optom Vis Sci 1991; 68:183-188.

4)

George CW, Andrew ML. The term magnification. Clin Exp Optom 2001; 84:113-119.

5)

Lovie-Kichin JE, Whittaker SG. Prescribing near magnification for low vision patients. Clin Exp Optom 1999; 82: 214-224.