Rational Procedures for Prescribing Optical Magnifiers for Near Vision.
Ian L Bailey and Robert B Greer
School of Optometry, University of California, Berkeley.
This workshop will have series of short lectures and discussions followed by some practical hands-on exercises.
A. Determination of required Equivalent Viewing Distance (EVD)
Identifying the patent’s reading performance goals from the history.
Assessing reading performance.
Reading charts.
Determining Critical Angular Size (CAS),
Determining Preferred Angular Size (PAS)
Determining Reading Acuity (Resolution Threshold)
Determining EVD required to achieve the reading performance goals.
B. Practical determination of CAS and PAS
Working in small groups, workshop participants will practice assessment of reading performance
and the determination of the required EVD
(a) To determine Critical Angular Size
Use a Bailey Lovie Reading Chart positioned at a fixed distance from the patient’s eyes. (50cm ?)
The patient reads aloud,
At each print size, the clinician notes the reading speeds or grades the reading efficiency.
Determine the smallest print at which the patient can read with best speed or efficiency.
This is the CAS. This angle is given by the combination of letter height and viewing distance.
The smallest print at this distance gives the reading acuity
(b) To determine the Preferred Angular Size
The patient holds a Bailey-Reading chart and reads aloud from top to bottom.
The patient is allowed to change the viewing distance,
For each print size, measure the viewing distance and make note of the reading efficiency.
As the print gets smaller, each change of viewing distance indicates a preferred angular size.
Select a preferred angular size that is at significantly closer distance than the starting distance.
At the preferred angular size, the patient should still be reading with efficiency
The PAS is an angle expressed by the combination of letter height and viewing distance.
By proportions, determine the viewing distance (or the EVD) required to make 1.0M print have an angular size that is
(a) equal to the CAS
(b) equal to the PAS
(c) at the acuity limit
Ian Bailey and Robert Greer
Near Vision Magnifiers workshop
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C. Determination of the Equivalent Power of Magnifier Lens Systems
Vertex powers and equivalent powers.
Lensometers measure vertex powers that help identify the location of the focal plane relative to the lens
surface and this helps us understand the amount of convergence or divergence emerging from the lens. To
understand the angle that images subtend, we need to consider nodal rays.
An object ray directed at an angle towards the first nodal point emerges into image space at the same angle
coming from the second nodal point.
Thus, the angular subtense of object at first nodal point is equal to
the angular subtense of the image at the second nodal point.
For a distant object, the size of the object (h) and its distance (d) from the lens provides a measure of the angular
subtense of the object.
If the object distance is long, there is no need to know the exact location of the first nodal point.
On a moveable translucent screen, an in-focus image of the object may be formed,
and the size of thisimage (h’) can be measured.
Given that the object is distant, the image will be at (or very close to) the focal plane.
The distance (d’) from the image to the second nodal point is determined
from the simple ratios d’/h’ = d/h
and d’ = equivalent focal length.
The Equivalent Power is the reciprocal of the Equivalent Focal Length
Practical
(a)
A distant object will be created by using a separated pair of flashlights.
The separation of the flashlight images is the measure of object size (h).
(b)
Clear plastic rulers with frosted tape will become the screen on which the images of the flashlights will be
focused.
Move this screen to and from the magnifier until the image of the lights is seen in sharp focus.
(c)
The separation of the flashlight images is the measure of the image size (h’)
(d)
From the image size (h’), the object size (h) and the object distance (d),
the image distance d’ is determined. d’ = h’ (d/h)
And d’ = fe and Pe = 1/d’
(e)
Working in small groups, participants will measure the equivalent powers
of several magnifiers
Ian Bailey and Robert Greer
Near Vision Magnifiers workshop
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D)
Location of the image in stand magnifiers
Most stand magnifiers have a fixed focus. Typically the image is not distant. The clinician needs to know where the
image is located. The accommodation demand is determined by the distance from the patient’s eye to the image.
This is the sum of the lens-to-image distance and the eye-to-lens distance.
1)
There are several methods for determining image location, but the simplest is to use a close focusing telescope
(such as a Walters 4x12 or similar)
2)
For fixed focus stand magnifier, the image is in a fixed location
3)
First some printed material is placed in the object plane of a fixed focus magnifier
4)
The adjustable focus telescope is rested on the lens of the magnifier and the telescope length is adjusted until
the image of the print seen through the telescope is in sharp focus
5)
Without altering the telescope focus, the clinician looks through the telescope, which is pointed towards some
printed material or textured surface
6)
a)
The clinician moves back and forth to find the distance at which the object of regard comes into sharp
focus
b)
The distance from the telescope to the object of regard is equal to the image distance of the stand
magnifier
If the magnifier’s image distance is shorter than the closest focus of the telescope
a)
Then, to obtain clear focus, the clinician should adjust the telescope to the closest possible focus and the
slowly lift the telescope away from the magnifier until clear focus is achieved.
b)
The separation (s) between the telescope and the magnifier is measured
c)
Now the clinician measures the distance for the telescope is focused (as described above) and from that
distance, the separation distance (s) is subtracted
This gives the separation between the lens and the image formed by the magnifier
Practical
7)
Close focusing telescopes will be used to determine the image distance for several stand magnifiers
Ian Bailey and Robert Greer
Near Vision Magnifiers workshop
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E)
Determination of Enlargement Ratio (ER)
The enlargement ratio provided by a stand magnifier can be determined from knowing
the equivalent power and the image distance
1)
The divergence of light (V) from the image is simply the reciprocal of the lens-to-image distance. Because it
is divegence, this quantity V is negative.
2)
The object vergence (U) is simply determined from the relationship V= e+U
a)
So U = V- Pe
b)
3)
Remember both U and V have a negative sign
The Enlargement Ratio or lateral magnification is given by the ratio U/V
ER = U/V
ER = (V- Pe ) / V
Practical
4)
Enlargement Ratios will be calculated for several magnifiers using the equivalent powers and the lens-toimage distances measured in sections C and D
F)
Selecting stand magnifiers based on their optical characteristics
For the magnifiers with a known image distance (z) and Enlargement ratio (ER),
the EVD depends on the eye-to lens distance (z)
The eye-to-image distance ( eye-to-lens distance plus lens-to-image distance) gives the accommodation demand.
The optometrist can determine whether the patient has a clear image (depends on accommodation and add power)
For a given eye-to-lens distance,
EVD = Eye-to-image distance / ER
1)
Workshop participants will be provided with a copy of a list of the optical parameters and other technical
information on wide range of currently available magnifiers
2)
Technical information provided by manufacturers and distributors is not always reliable
a)
For stand magnifiers, we provide our own measurements of equivalent power, image location and
enlargement ratio
3)
We have used 10 cm and 2.5 cm as representative values of moderate and close eye-to-image distances
4)
For both of these eye-to- lens distances we have determined the eye-to-image distance (which represents the
accommodation demand), the Equivalent Viewing Distance (EVD), and the width of the field of view
a)
This information is tabulated for each of the magnifiers
5)
Scenarios will be presented in which the required EVD is identified
a)
Then, the technical data tables will be used to identify which magnifiers meet the patient’s needs
b)
Decision making strategies will be discussed, and participants will be given
a few practice exercises
Ian Bailey and Robert Greer
Near Vision Magnifiers workshop
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