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Ophthalmic lenses and dispensing
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Action of a prism
The transverse test
Action of a cylinder
Use of the focimeter
The correction of ametropia
Effective power in DV
Effective power in NV
Vergence impressed in NV
Centration of spectacle lenses
Effects of centration errors
Lens thickness and weight
Lens design and performance
Iso-V-Prism zones
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Ophthalmic Lenses & Dispensing
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Ophthalmic Lenses & Dispensing
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Action of a prism
Now the prism has been rotated clockwise through 90°
WhenThis
the
Note
prism
is ahow
crossline
is the
rotated
horizontal
chart.
clockwise
Onlimb
thebefore
of
next
themouse
the
crossline
crossline
clickchart
you
chart
will the lines
The base setting
can
be marked
on the
it has
rotated to
from its
original
position.
Thelens
basewhen
lies on
the been
left and
also appear
placeappears
ato
prism
rotate,
to
held
be
always
with
displaced
its
displaced
base
towards
DOWN
in the
the
indirection
prism
front of
apex.
of
thethe
chart…
prism apex.
this position
where
a
continuous
appearance
of
the
vertical
limb
is
only the vertical limb is displaced towards the prism apex. obtained.
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Ophthalmic Lenses & Dispensing
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The transverse test - plus lens
.
been
movedtoslowly
downwards
TheThe
lenslens
hashas
nownow
been
returned
its original
positionbefore
beforethe
the
chart,
The
and
lens
the
hasthe
horizontal
now
been
limb
moved
appears
slowly
toto
move
the
right
upwards,
chart,
and
the On
limbs
move
back
their
original
positions
andagain
appear
next
mouse
will
place
abefore
Notice
that the
limbs
aretoinclick
theiryou
correct
position
thecontinuous
chart,
and
AGAINST
the vertical
the
movement
limb
appears
the
to lens.
move
to the
with
the
limbs
viewed
outside
the chart.
plus
sphere
centrally
inthrough
frontof
ofthe
the
chart...
but they
appear
magnified
lens...
left, AGAINST the movement of the lens.
MOVEMENT
is obtained
plusthe
lenses
in the transverse
test.
The AGAINST
optical centre
can be marked
on thefrom
lensall
over
intersection
of the crosslines.
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Ophthalmic Lenses & Dispensing
The transverse test - minus lens
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.
The lens
has
now
been
returned
to their
its
original
The
lens
has
slowly
downwards
Notice
that
the
limbs
are
in
correct
position
The
lens
hasnow
nowbeen
beenmoved
moved
slowly
toposition
the
rightbefore
beforethe
On
the
next
mouse
click
youappears
will
place
chart,chart,
and
limbs
move
to also
their
original
positions
and appear
and
the
horizontal
limb
appears
to
move
downwards,
but
they
appear
minified
through
the
lens...
thethe
chart,
and
the back
vertical
limb
also
toamove
to
minus
sphere
in front
of
chart...
continuous
with
thecentrally
limbs
viewed
outside
chart.
WITH
the
of
lens.
theagain
right,
WITH
themovement
movement
ofthe
thethe
lens.
The optical
can be marked
on the
lens
thelenses
intersection
of the crosslines.
WITHcentre
MOVEMENT
is obtained
from
all over
minus
in the transverse
test.
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Action of a plus cylinder
Rotating the cylinder back again causes the limbs to
SCISSOR
backon
to the
theirlens
original
The cylinder axis can
be marked
whenposition.
it has been rotated to
On
clockwise
This
Notice
is
a
crossline
rotation
that
Further
the
of
chart.
limbs
the
clockwise
cylinder,
appear
On
the
rotation
the
to
next
be
vertical
mouse
in
of
their
the
limb
click
original
cylinder,
rotates
youpositions
will
anticlockwise
place
this position where a continuous appearance of the crosslines
is obtained. and
the ahorizontal
but
plus
that
cylinder
just
limb
the
produces
held
rotates
vertical
with
clockwise
further
limb
its axis
is
SCISSORS
magnified
VERTICAL
towardsseen
itinMOVEMENT.
inthe
inaduring
front
SCISSORS
horizontal
ofthe
therotation
chart…
meridian.
MOVEMENT.
You
can
emulate
the
actual
movement
by
reversing four times through this sequence (right click and select previous).
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Ophthalmic Lenses & Dispensing
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Action of a minus cylinder
Rotating the cylinder back again causes the limbs to,
The cylinder axis
can be marked
theoriginal
lens when
it has been rotated to
SCISSOR
back to on
their
position.
On clockwise
Notice
On
rotation
that
the
next
the
Further
of
the
limbs
mouse
cylinder,
clockwise
appear
click
the
you
to
rotation
be
vertical
will
in
place
their
of
limb
the
original
a
also
minus
cylinder,
rotates
positions
cylinder
clockwise
and
this position where a continuous appearance of the crosslines
isbut
obtained.
the horizontal
that justlimb
the
held
rotates
vertical
produces
with its
anticlockwise
limb
axis
further
appears
VERTICAL
SCISSORS
towards
minified
in front
itinMOVEMENT.
inthe
of
a SCISSORS
horizontal
the chart…meridian.
MOVEMENT.
You can emulate the actual movement seen during the rotation test
by reversing three times through this sequence (right click and select previous).
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Ophthalmic Lenses & Dispensing
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Use of the focimeter
120
120
100
100
90
90
80
80
60
60
140
140
40
40
160
160
20
20
180
180
+
180
180
0.75
0.75
0.75
0.50
0.50
0.50
0.25
0.25
0.25
0.00
0.00
0.00
0.25
0.25
0.25
0.50
0.50
0.50
0.75
0.75
0.75
This is the circular target
which is brought into focus
by rotation of the dioptre
This is power
the protractor
knob. from
which cylinder axis and
base setting can be read.
This is the central target
area. The circular scales
are calibrated in prism dioptres
This
aand
typical
view adjustment,
of
thewhich
measuring
scales
If the
instrument
is
correct
when
there
no
The
target
The
vertical
mayisbe
ofinthe
horizontal
linear
type
crosslines
must
can be
first
rotated
beisseen
rotated
tolens
coincide
sounder
that the
when
you
look
a manually
operated
focimeter.
test,coincide
the the
target
should
beinto
seen
in sharp
focus
the
centre
ofoblique
the
lines
with
cylinder
with
the
axis
principal
direction,
meridians
or the
ofbase
an at
astigmatic
setting
of an
lens
under test.
andHere
the
power
scale
should
readmeridians,
zero,
case
here.
Inprotractor
the following
prism.
demonstration
they now
lie
we
along
will assume
the
the as
useis150
ofthe
aand
circular
60.
target.
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Ophthalmic Lenses & Dispensing
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Use of the focimeter
100
120
90
80
60
140
40
160
20
180
+
180
0.75
17.75
17.75
0.75
0.50
18.00
18.00
0.50
0.25
18.25
18.25
0.25
0.00
18.50
18.50
0.00
0.25
18.75
18.75
0.25
0.50
19.00
19.00
0.50
0.75
19.25
19.25
0.75
Then rotate the eyepiece
slowly back inwards until
the scales just come into
sharp focus. Stop as soon
as they come into focus.
In order to do this, begin by turning the power adjusting
Now rotate the adjustable eyepiece ring of the telescope to rack
Before
use end
a manually
operated
focimeter
knob
rightyou
to one
of its reading
range.
It doesyou
not
out
Youthe
should
eyepiece
now to
find
itsthat
fullest
theextent.
dioptricThe
scale
protractor
reads exactly
scale on
zero.
the
mustwhether
adjust its
focusing
your
ownrange.
use.
matter
it is
the pluseyepiece
or minusfor
end
of the
graticule
will
become
blurred
is no longer
in focus.
If it does
not
now read
zero,until
the itinstrument
needs
servicing!
You will notice that the green target is so much out of
focus that it can no longer be seen.
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Ophthalmic Lenses & Dispensing
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Use of the focimeter
120
120
100
100
90
90
80
80
60
60
140
140
40
160
160
20
20
180
180
The lens under test must
be a plano-prism since the
dioptre scale is reading zero.
+
180
180
0.75
0.75
0.50
0.50
0.25
0.25
0.00
0.00
0.25
0.25
0.50
0.50
0.75
0.75
The base
if thesetting
target
of
lies
anin
oblique
the position
prism
shown
will here
be here
found
and
easier
a left
toeye
read
If theFinally,
green
target
lies
infocimeter
the
position
indicated
itcan
signifies
that
theisoptical
Now
that
the
is
ready
for
use
we
consider
will
notice
that
theis
target
is
exactly
centred
over
thethat
middle
The
target
is displaced
upwards
and
its
under
if the
you
test,
rotate
the
the
reading
crosslines
3
which
base
UP
lie
@
along
150
the
which
90 &could
meridians
equally
bethe that
IfYou
green
target
lies
ingreen
the
position
indicated
here
it180
signifies
element
under
test
incorporates
4
base
IN
at
the
measuring
point,
assuming
We
will
begin
by
considering
how
the
focimeter
measures
prism
power.
how
it
is
used
to
read
the
powers
of
prisms
and
lenses.
of the
crosslines.
Nois
displacement
of
the
target
signifies
that there is
centre
seen
to
lie over
second
ring.
until
one
limb
passes
as
1.5
through
base
UP
the
and
centre
2.6
ofbase
the
target.
IN.measuring
optical
element
incorporates
2
base
UP
at
the
the lens
under
testexpressed
isunder
for
thetest
right
eye.
It would
be
4
base
OUT
if it were a point.
left eye.
no prismatic effect at the point on the lens which is being measured.
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Ophthalmic Lenses & Dispensing
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Use of the focimeter
120
120
120
140
140
140
90
90
90
100
100
100
80
80
80
60
60
60
40
40
40
160
160
160
20
20
20
180
180
180
180
180
180
+
4.75
6.75
4.75
0.75
0.75
4.50
6.50
4.50
0.50
0.50
4.25
6.25
4.25
0.25
0.25
4.00
6.00
4.00
0.00
0.00
3.75
5.75
3.75
0.25
0.25
3.50
5.50
3.50
0.50
0.50
3.25
5.25
3.25
0.75
0.75
Adjusttothe
position
of the
the target
lens toappears
centre the
target.focus
Continue
refocus
until
in sharp
willthe
now
consider
focimeter
islens
usedrest
In order
Here,
toWe
read
a the
spherical
back
lens
vertex
hasishow
been
power
placed
of
aalens
onadjusting
the
you
must
ensure
and that
Refocus
target
by
rotation
of the
power
knob.
(If
the
lens
under
test
to
frame,
it read
again.
The
power
of the
lensglazed
under test
can
noworbe
totarget
determine
the
of spherical
lenses.
the At
lens
the
is
green
placed
withhas
concave
disappeared.
surface
Itelement,
isblurred
intoo
contact
blurred
with
to the
be seen.
lens rest.
some
point
the
target
willpower
reappear,
and
off-centre.
incorporates
aitsstrong
it may
from the power
scaleprismatic
and is seen
to be -6.00.
not be possible to centre the target.)
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Ophthalmic Lenses & Dispensing
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Use of the focimeter
120
120
120
120
140
140
140
140
90
90
90
90
100
100
100
100
80
80
80
80
60
60
60
60
40
40
40
40
160
160
160
160
20
20
20
20
180
180
180
180
-++
180
180
180
180
1.25
0.25
1.25
0.25
0.25
0.75
0.75
1.50
0.50
1.50
0.50
0.50
0.50
1.75
0.75
1.75
0.75
0.75
0.25
0.25
2.00
1.00
2.00
1.00
1.00
0.00
0.00
2.25
1.25
2.25
1.25
1.25
0.25
0.25
2.50
1.50
2.50
1.50
1.50
0.50
0.50
2.75
1.75
2.75
1.75
1.75
0.75
0.75
Note that in whichever
thethe
prescription
the first reading is the
We canform
record
power of is
therecorded,
lens, either
When
aFurther
spherical
lens
isof
under
test
the
consists
of
acylinder
circle
When
Here
The
an
Here
the
readings
astigmatic
We
best
the
rotation
will
focus
best
are
now
lens
+1.00
focus
is
consider
the
is
obtained
under
power
is
when
obtained
how
test,
the
with
adjusting
vertical
the
each
the
with
focimeter
horizontal
dot
the
knob
lines
is
vertical
drawn
brings
are
is
lines
in
lines
out
the
of into
of ofadots.
line
sphere,
the
second
reading
the
of
the
sphere
the
power
...or,
/ -1.00
xtarget
90.
asreadings
+1.00
/ as
+1.00
xsum
180...
From these
two
we+2.00
can
deduce
the
powerand
of the
lens
under(the
test.
the
focus
which
focal
target
the
used
and
lines
target
iswhen
parallel
+2.00
to
inwhen
read
thewhen
with
other
reading
the
theone
the
power
reading
principal
horizontal
on
of the
of on
an
meridian
principal
power
the
astigmatic
lines
power
scale
are
meridians
into
scale
in
lens.
is
sharp
+2.00.
focus.
is
focus.
+1.00.
the lens.
of thefocus
cylinder
is
whatever
must
be
added
to
the
first
reading
toof
obtain
the
second) and the axis direction is the same as the lines in the second reading.
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Ophthalmic Lenses & Dispensing
Use of the focimeter
Click to return
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120
100
90
80
140
60
40
160
20
180
180
5.00
4.25
4.75
4.00
4.50
3.75
4.25
3.50
4.00
3.25
3.75
3.00
3.50
2.75
In the The
case
of
an
oblique
cylinder
should
rotate
the
other
power
principal
of the
the
meridian
lens
under
the you
lines
test
is,
come
therefore,
into focus
Notice
that
power
scale
reads
-4.25
vertical
and
horizontal
until
are
parallel
when
the
-4.25
power
/the
+0.75
adjustment
xcrosslines
150
(or
knob
-3.50
is turned
/ they
-0.75
tox -3.50.
60).
when
lines
lie along
the
60
meridian.
with the principal meridians of the lens under test.
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Ophthalmic Lenses & Dispensing
Use of the focimeter
Click to return
to CD contents
120
100
90
80
140
60
40
160
20
180
180
2.25
2.25
0.50
2.00
2.00
0.75
1.75
1.75
1.00
1.50
1.50
1.25
1.25
1.25
1.50
1.00
1.00
1.75
0.75
0.75
2.00
The power of the lens under test is -1.50 / +2.75 x 15
Try this one by yourself !
( or +1.25 / -2.75 x 105)
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Ophthalmic Lenses & Dispensing
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Use of the focimeter
120
100
90
80
140
60
40
160
20
180
180
4.00
1.50
1.00
1.50
2.00
1.25
4.25
2.00
2.25
1.50
4.50
2.25
2.50
1.75
4.75
2.50
2.75
2.00
5.00
2.75
3.00
2.25
5.25
3.00
3.25
2.50
5.50
3.25
Eitheris+2.50
/ -0.75
x 45
Add
+2.25!
Here
another
one
to
try
yourself
This
This
This
is
the
reading
is
one
second
reading
is
taken
reading
at
at
the
at
the
the
major
near
major
What is the power
of the lens?
or
This time
a progressive
power
lens
is under test.
reference
reference
point
point
inin
the
themouse
distance
near
portion.
portion.
Answer
given
on
next
click
+1.75 / +0.75 x 135 Add +2.25
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Ophthalmic Lenses & Dispensing
The correction of ametropia
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Vertex distance
Correction of hypermetropia
Correction of myopia
Effective power in distance vision
Effective power in near vision
Vergence impressed in near vision
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Ophthalmic Lenses & Dispensing
The correction of ametropia
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Vertex distance
vertex distance
BS 2738: Part 3: 1991 Method of presentation of prescription orders for spectacle lenses
BS 3.1
3521:On
Part
1991 Glossary
of terms relating
to the
ophthalmic
and spectacle
all 1:
prescriptions
and prescription
orders,
power oflenses
the sphere
(sphericalframes
power) shall be stated for each eye or lens.
vertexdistance
distance should
be from
indicated
by stating
01 205 vertex
Distance
the visual
pointthe
of anumber
lens to of
themillimetres
corneal apex
following
the prescription,
for example:
NOTE. If
the prescribed
power is sufficiently
high such that the vertex distance becomes
significant, e.g. if the power exceeds 5.00 D, then the distance at which the power was
+6.00/-0.50
90 at
12
measured should additionally be
recorded inx the
prescription.
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Ophthalmic Lenses & Dispensing
The correction of ametropia
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Correction of Hypermetropia
far point distance
k
M´
MR
In hypermetropia,
light from
a distant
object
is is
focused
behind
themacula.
retina. This may
There is a point,
behind
the eye,
which
conjugate
withofthe
If the
can make surfaces
sufficient effort too
of accommodation,
it may increase
be due
to eye
the
refracting
weak
refractive
error), the axial
Light
converging
towards thisbeing
point would
be(purely
focused
by the eye’s
power
to produce
a sharp(axial
image
of a distant
on thecase,
macula,
M´.
lengthitsof
the eye
beingattoo
error),
or, point
as isobject
usually
a combination
optical
system
theshort
macula. This
virtual
is
calledthe
the Far Point,
MR.
of these two factors (correlation ametropia).
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Ophthalmic Lenses & Dispensing
The correction of ametropia
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Correction of Hypermetropia
vertex distance
far point distance
k
d
M´
F´
MR
f ´V its second principal focus.
Light from a distant object is focused by the lens at
Since this
is conjugate
with thelens
macula,
the eye’s
ownits
optical
system can
In order
for a spectacle
to correct
an eye,
second
produce focus,
a sharpF´,focus
the distant
at the
principal
mustofcoincide
withobject
the eye’s
farmacula,
point MM´.
R.
TheThe
backspectacle
vertex focal
length
is made
the sum
lens,
therefore,
liesup
at from
its own
ofback
the vertex
d, and
pointfar
distance,
vertex
focal
fromthe
thefareye’s
point. k.
V distance,
V
V length
F´ f =
‘´ K==/ (1
kk +++dddK)
...but it is much easier to think of it terms of focal length!
This can be expressed in dioptres...
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Ophthalmic Lenses & Dispensing
The correction of ametropia
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Correction of Myopia
k
M´
F´
MR
The
far
point,
MRlight
, of the
eyeobject
lies Light
inisfront
of the
placed atby the
Myopia
In myopia,
is corrected
from
bymyopic
minus
a distant
focused
from
ad
distant
ineye.
frontAn
object
of object
the retina.
is focused
f ´Vlenses.
the lens
farThis
point
be principal
intosharp
focus at
the
macula
in the
at may
itswould
second
be due
the refracting
focus,
which
surfaces
lies inbeing
front
too
ofunaccommodated
the
strong
lens.(refractive
Since theeye.
second
principal
myopia),
focusthe
coincides
axial length
with of
thethe
eye’s
eye far
being
point,
toowhich
great is
(axial
conjugate
myopia),
with the macula,
orthe
a combination
eye can produce
of these
a sharp
two factors
focus of(correlation
the distantametropia).
object at the macula, M´.
f ´V = k + d
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Ophthalmic Lenses & Dispensing
Effective power in distance vision
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Hypermetropia
x
F´
f´Vf´V
new f ´lens
f ´V +anx eye is that the second
The condition for a spectacle
correct
V =toold
principal focus of the lens must coincide with the eye’s far point.
We will now consider
what happens
when
changes
are distance
made to the vertex distance.
To correct
the eye at
a greater
vertex
a plus
must be
made
weaker.
Thus if a plus
lenslens
is moved
away
from
the eye, its focal
length must be increased by the change in vertex distance.
Plus lenses moved away from the eye get stronger.
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Ophthalmic Lenses & Dispensing
Effective power in distance vision
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Myopia
x
F´
MR
f ´V
new f ´V = old f ´V + x
myopia,
the
pointaway
lies infrom
frontthe
of eye,
the eye.
If aInminus
lens
is far
moved
its focal
length To
must
be decreased
the change
in vertex
distance.
correct
the eye atby
a greater
vertex
distance
a minus lens must be made stronger.
Minus lenses moved away from the eye get weaker.
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Ophthalmic Lenses & Dispensing
Effective power in near vision
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stationary object
-3.00
0
B
-33.3 cm
+3.00
We arriving
will now at
consider
happens
vertexand
distance
of a thin
The vergence
the frontwhat
surface
of thewhen
lens the
is -3.00D
assuming
a lens is leaving
altered the
when
thesurface
the lenswill
is being
used
near
vision. the light.
lens, the vergence
back
be zero,
thefor
lens
collimates
Here, a +3.00D lens is being used for near vision at 33.3 cm in front of the lens.
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Ophthalmic Lenses & Dispensing
Effective power in near vision
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stationary object
x
-0.25
-3.25
B
l < 33.3cm
+3.00
Clearly,
The light
the
leaving
new
the is
lens
distance
is moved
nowwill
divergent
decrease
and
by
the
the
eye
movement
will need
oftothe
make
lens
an
Suppose
that
the object
lens
now
away from
the
eye,
(i.e.,
down
the
nose)
effort
andofthe
accommodation
vergence
arriving
(about
at the
0.25D)
lens
inwill
order
increase,
to view
theoriginal
to
near
-3.25D.
point
clearly.
towards
object, which,
in this
case,
has
remained
inhere
its
position.
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Ophthalmic Lenses & Dispensing
Effective power in near vision
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stationary object
x
B
-3.25
-0.25
l < 33.3cm
+3.00
It can be shown that, for small movements, x, the change in effective
power is given by -xF(2L1 + F ) where L1 is the original object distance
and F is the power of the lens. x is considered to be negative if the lens
moves to the left, away from the eye. A graph of this expression showing
how effective power varies with lenses of different powers is given later.
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Ophthalmic Lenses & Dispensing
Effective power in near vision
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object moves with lens
x
x
B
-3.00-3.000
B
0
-33.3
cm cm
-33.3
+3.00 +3.00
Under these circumstances it can be shown that the change in effective power is
2a
We
will by
now
consider
second
situation
where,
when
thethrough
lens is case
moved,
thethe
object
given
-xF(
Lthe
+ F)lens
. The
shown
above
iseye,
the
unique
when
termalso
Here,
hassituation
moved
away
from
the
a
distance,
moves
through
distance
asmoved
the
theby
object
distance
is, therefore,
constant.
in the bracket,
Lthe
+ same
F,object
is equal
zero,
so lens,
theaway
change
in effective
power
must
be
x, andthe
hastoalso
the
same
distance,
x. also
equal to zero. This result is indicated on the graph of effective power which follows.
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Ophthalmic Lenses & Dispensing
Effective power in near vision
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Change in effective power when lenses are used for near vision
at 33.3cm and subsequently moved 5 mm away from the eye.
+1.00
+0.80
+0.60
+0.40
Q = -x(L1+ F)2
+0.20
0.00
-0.20
Q = -xF(2L1+ F)
-0.40
-10.0 -8.0
-6.0
-4.0
-2.0
0.0 +2.0 +4.0 +6.0 +8.0 +10.0
Lens power
2 when
This is
is aa plot
plot of
ofNote
the
expression,
thatthat
Q =Q0 =for
Q
-xsingle
(LF1 =+1 +
case
F)F)
whenxx(2L
(L
==1-0.005m
++FF)) ==0.and
0. L11 = -3.00D.
This
the
expression,
Q
== -xF(2L
-0.005m
and
-3.00D.
Note
0 the
when
0,
or when
when
1
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Ophthalmic Lenses & Dispensing
Vergence impressed in near vision
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L1 = 0
= BVP
BVP
L´L´22 =
F´
The form
thevertex
lens ispower
immaterial.
Provided
that the
are the
The of
back
of a lens
represents
theBVPs
vergence
leaving
the back
surface
when
the incident
vergence
is zero.
same,
in distance
vision,
lenses
of different
forms
are interchangeable
.
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Ophthalmic Lenses & Dispensing
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Vergence impressed in near vision
Note that you must first find the front
curve before you can determine L´2.
F1 = +12.06
B
L1 = -3
L´2=2=+6.58
= +6.69
+6.87
L’L’
2
B´
B’B’
+10.00
if the
form
changed
equiconvex,
its
details
remaining
In Finally
near the
vision,
the
vergence
impressed
by a lens depends
not
only on
its BVP,
Now
lenslens
form
hasischanged
totoplano-convex,
its other
other
details
remaining
same,
for
near
object
position,
the vergence
leaving
the
butthe
also
upon
itsthe
form
andsame
thickness.
Here,
a +10.00D
made
with
a lens
-3.00
the
same,
and,
forsame
the
near
object
position,
thelens
vergence
leaving
the
Clearly,
in
near
vision,
lenses
of the
same
back
vertex
is
now
to
beto+6.87.
Again
youaxial
must
find
powers
lens
base
curve,
glass,
nbe
= 1.5
and
an
of
9mm,
iscurve
usedofforthe
near
lens
willfound
beinfound
+6.69.
Again
youthickness
must
findsurface
the
front
power
but
made
in
different
forms
are the
not
interchangeable.
before
tracing
from
the
near
object
point.
In this
case,
= Flens
= is
+4.92.
vision
attracing
-33.3cm.
The
leaving
the
surface
of
+6.58D.
before
from
thevergence
near
object
point.
Inback
this
case,
F1 F
is1 the
found
be
+9.43.
2 to
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Ophthalmic Lenses & Dispensing
Vergence impressed in near vision
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Near vision effectivity error
The difference between the actual vergence leaving the lens, L´2, and the
anticipated vergence on
lens
L1 the
= -3basis of thin L’
+6.58 has been called the
2 = theory,
error due to near vision effectivity (or near vision effectivity error, NVEE).
Foranticipated
example, in
the case(found
of the from
+10.00
lens
a -3.00
base
The
vergence
L´ =
L +made
F ) forasthe
+10.00
lens
For
this
form
the
error
due
to
near
vision
effectivity
is
-0.42
D.
meniscus
vergence
leaving
the lensiswas
found
to be =+6.58D.
forms
whichthe
have
just been
considered
-3.00
+ 10.00
+7.00D.
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Ophthalmic Lenses & Dispensing
Vergence impressed in near vision
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Near vision effectivity error
IfErrors
the
trial
lens
was
of
thelens
usual
plano-convex
form,
Suppose
due
that
toseen
near
thethat
trial
vision
used
to the
are
determine
a problem
the
We have
the effectivity
NVEE
of
final
lens
with
the
curved
surface
designed
to
face
the
eye,
near
with
vision
medium
prescription
to high-power
was
equiconvex
plus lenses.
in form.
form
which
is likely
to be
dispensed
is -0.42D.
the “error” would be even worse, almost 0.50D!
final lens
Its NVEE is seen to be only
-0.12D. Changing from this
form to the final lens form
without adjusting the power
of the lens would mean that
there is a loss in power of
about 0.3 D.
trial
lens of
symmetrical
common
form
trial lens
L´ 2 = +6.58
L´ L´
2 =2 +7.02
= +6.87
NVEE = -0.42
NVEE
NVEE= =+0.02
-0.12
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Ophthalmic Lenses & Dispensing
Vergence impressed in near vision
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Lenses of different forms are not interchangeable In near vision.
to CD contents
In practice, tables of correction factors are available giving compensation for NVEE.
Correction Factors
The lens is then said to be compensated for
errors due to near vision effectivity.
Typically, compensation is required for both
single vision lenses and for the near addition
of bifocal lenses.
Note that in the case of bifocal additions, the
compensation is also required for the near
addition when the DP precription is minus.
This correction factor is valid when the seg
is on the back surface of the lens.
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
When lenses are prescribed for near vision,
the form of the final lens is usually different
from that of the trial lens. In such cases the
back vertex power of the final lens must be
increased by the amount shown in the Table
opposite so that the effect of the final lens is
the same as that of the trial lens.
Near addition (D)
Lens
Power
-10.0
-8.0
-6.0
-4.0
-2.0
0.0
+2.0
+4.0
+5.0
+6.0
+7.0
+8.0
+10.0
+12.0
+14.0
37
-0.25
0.0
+0.25
+0.50
+0.75
38
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Ophthalmic Lenses & Dispensing
Centration of spectacle lenses
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Horizontal centration of lenses
Near centration distance
Obtaining the measurements
Geometrical insetting of bifocal segments
Specification of segment top position
Prismatic aspheric lenses
Vertical centration - the centre of rotation condition
The centre of rotation condition for near vision
Centration errors - dispersion - off-axis blur
Ghost images due to prism in a lens
Graphical construction to find prismatic effect
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Ophthalmic Lenses & Dispensing
Horizontal centration of lenses
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The type of centration
errors we could
make
if we just specified
a
Furthermore,
if progressive
lenses
were
without
The horizontal
centration power
specifications
whichdispensed
are actually
required
binocular
PDdistance
is illustrated
here.the
It is
assumed
that
the horizontal
centre
This
isasymmetry
called
interpupillary
distance
orthe
PD.
specifying
monocular
centration
distances,
their
corridors
clear
vision
are the
measured
fromof
centre
The
becomes
very
distance
of
the
frame
exactly
matches
the
PD,
so
that
no
horizontal
You
will
see
that,
really,
the PD
isshown
only
useful
as
aRcheck
wouldofbe
offset.
DoLook
you
very
notice
carefully
how
asymmetric
at
this
face.
it M
is?
the
bridge
of
the
frame.
They
are
here
as
and ML.
obvious
if
we
bisect
the
face!
decentration
needs
to
be
specified.
for our measurement of the horizontal centration distance.
MR
PD
ML
OC
These distances are equal.
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Ophthalmic Lenses & Dispensing
Horizontal centration
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Centration distance
Under
circumstances
lie where
visual
First,these
note that
we assumethe
thatcentration
the visualpoints
axes would
pass through
thethe
centres
axes
intersect
the
spectacle
plane.
Into
the
of rotation
prescribed
prism,
the
We
This
distance,
already
of
noted
course,
that
is
we
the
need
know
as absence
the
the
horizontal
distance
distance
from
each
between
centration
What
we
are
trying
to same
achieve
is
demonstrated
here.
ofhave
the
eyes’
pupils
and
through
the
eyes’
centres
and
that
these
optical
lensbridge
would
be
positioned
at
the
centration
point.
point
the
tomid-point
the
mid-point
of of
the
ofdistance
bridge
the
ofvision
theofframe
the
frame
andshown
the
which
eye’s
thecentre
subject
of is
rotation.
to wear.
axes
are centre
parallel
inthe
and
are
directed
towards
infinity.
Optimum position
for optical centre
spectacle plane
monocular
CD
.
R
mid-point of
frame bridge
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Ophthalmic Lenses & Dispensing
Horizontal centration
Near centration distance
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In
near
vision,
we
are interested
in
the
Notice
Thethat
near
this
centration
distance
distance
is not the
issame
seen
l
If monocular
we know the
reading
distance,
l,
and
the
near
centration
distances
as the
to NCD
be
distance
a function
between
of thethe
distance
pupil centres.
CD.
=
CD.
centre
of rotation
then the NCD
measured
in thedistance,
spectacles,
plane.
l
+
can be expressed in terms of thesCD.
l
Remember, that it is the monocular
NCDs which should be recorded.
Optimum position
for near optical centre
NCD
spectacle plane
centres of
converging pupils
s
CD
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Ophthalmic Lenses & Dispensing
Horizontal centration
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Obtaining the measurements
The following routine will be found to provide
accurate and consistent results.
• Fit the frame
.
.
• Attach tape
- if empty frame
• Mark centre of bridge
• Dot pupil centres
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Ophthalmic Lenses & Dispensing
Horizontal centration
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Obtaining the measurements
The monocular centration distances can now be measured and recorded.
.
Left eye value
.
Right eye value
Monoc CDs are recorded as follows: 32 / 35.
The right eye value is always written first.
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Ophthalmic Lenses & Dispensing
Horizontal centration
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Bifocal inset
Suppose
in
the
diagram
below
thatthe
thenear
bifocal
segments
seen
only
by Ldo
eye
Bifocal
segments
areeye
usually
inset
to bring
fields
into
coincidence.
The
fields
ofonly
view
through
the
right
and
left
would
have
seen
byobtained
R
Ifapertures
the
near
fields
notthe
coincide
areas
simply
apertures here
in otherwise,
opaque,
occluders.
same shape
the apertures,
supposed
to be D-shape,
flat-top
segments.
there will be areas which fall
only within the field of one eye.
To make the fields coincident
they should binocular
overlap exactly
field
in the near point plane.
segment
aperture
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Ophthalmic Lenses & Dispensing
Bifocal segment insetting
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The following method ensures that the segment
insetting brings the near fields into coincidence.
B
This
shows
the distance
InNow,
order
todiagram
obtain
the
field of view.
we
will
place
amaximum
bifocal
lens
portion
a plus
bifocal
lens
the
centre
ofofthe
bifocal
segment
should be
whose
distance
prescription
is which
Now,
a plus
lens which
is correctly
centred
has
been
correctly
centred
for
placed
at
the
point
where
the
visual
invision
front of
the
other
eye. inaxis
fornegative
distance
has
been
placed
front
It goes
without
saying,
that
distance
in front
of we
the want
eye.
intersects
the vision
spectacle
plane.
of the
andofitthe
is seen
that,aperture
owing toto
the
the eye
centre
segment
Noteout
that
the minus
lens the
exerts
base
prism
exerted
lens,
the eye
lie on when
the
visual
axis by
in order
for the
Clearly,
the
distance
prescription
is
prism
base in more
at thetonear
visual
must
converge
view
the
near
object.
eye tothe
obtain
the maximum
field of
view.
positive
segment
must of
be inset
more
point, relieving
the effort
than
we would decentre
convergence,so
minus single
bifocalvision lenses
forlenses
near vision.
should be inset less
If there were no spectacle lens in
front of the eye, it would rotate into
this direction in order to view the
near object point, B, on the midline.
and
inset
so placed
its centre
lies
It ...
has
now
been
in position
Othe
converging
visual axis.
inon
the
spectacle
plane...
D
D
than single vision lenses.
spectacle plane
This is the bifocal segment
mid-line
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Ophthalmic Lenses & Dispensing
Geometrical insetting to bring
the near fields into coincidence
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monoc CD
=p
R
s
OS
distance OC
It
can be shown
thatfor
theL geometrical
Substituting
-3.00D
and +37.00Dinset,
for Sg,
for
distance
lens
of power,isF,27mm)
mounted
(D)
(soathe
lens-eye
separation
weSobtain
The
following
tablecentre
of geometrical
insetting
inthe
front
of the
eye’s
rotation
and
L (D)
useful
average
rule
forofgeometrical
inset:
has been
prepared
from is
this
expression
from the
near point
given
by:
g=
g p.L
= 3.p
/ (L
/ (40
+ F-- F)
S)
g
l
Visual
axis
+8.00
+4.00
0.00
-4.00
-8.00
Table of geometrical insetting
monocular centration distances
28 29 30 31 32 33 34 35 36
2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4
2.3 2.4 2.5 2.6 2.7 2.8 2.8 2.9 3.0
2.1 2.2 2.3 2.3 2.4 2.5 2.6 2.6 2.7
1.9 2.0 2.0 2.1 2.2 2.3 2.3 2.4 2.5
1.8 1.8 1.9 1.9 2.0 2.1 2.1 2.2 2.3
Tables such as this may be provided in
practice in order to assist bifocal fitting.
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Ophthalmic Lenses & Dispensing
37
3.5
3.1
2.8
2.5
2.3
Specification of segment top position
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segment
top position
44 HCL
23
22
If theAlthough
final
frame
issegment
the
height
can
measured
with
a23simple
For
example,
iffitted,
the
heights
are
measured
as
mm, ruler.
Note,
Bifocals
however,
thefor
general
thatsegment
segment
heights
purpose
height
could
usebe
are
is
be
defined
specified
usually
as
fitted
as
the
measured,
so
distance
that
it is
Remember
thehorizontal
other
eye
also.
from
the
better
the
segment
segment
to give
topthe
top
istosegment
tangential
tomeasure
the lower
top
with
position,
the lower
which
tangent
edge
is of
the
tothe
the
vertical
iris.
lens
and
vertical
dimension
the
frame
isfor
44
mm,
distance
periphery
With
most
ofthe
the
and
subjects,
segment
shouldbox
this
be
top,
measured
coincides
above orof
with
asbelow
illustrated
the
the
linehorizontal
of
the
the
lower
right
centre
lid.
eye.line.
then the segment top position = 1 above HCL.
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Ophthalmic Lenses & Dispensing
Horizontal centration
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Prismatic aspheric lenses
An aspherical surface such as the
ellipsoid shown here has a pole.
s there is a further consideration.
When dispensing aspheric lenses which incorporate
prism,
A1
x
P
The amount of decentration
can be found as follows.
A1 = pole of aspherical surface
s = centre of rotation distance
P = prismatic To
effect
ofWhen
lens
obtain
the best
frominthe
prismperformance
is incorporated
theaspheric
lens, thedesign,
visual the
In order
coincide
with
the the
visual
thevisual
pole of
the
pole
of axis
thetoaspherical
surface
should
lieaxis,
on
axis.
is
deviated
towards
the
apex
of the
the
prism.
aspherical surface must be decentred towards the prism
The apex,
pole
theis,
aspherical
surfacedirection
noxlonger
on =
the0.3
visual
inofthe
opposite
to lies
the
prism
base.
Theofthat
amount
decentration
= P.s
/ 100
P axis.
So when the prism power is 3, the necessary decentration is about 1mm.
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Ophthalmic Lenses & Dispensing
Vertical centration of spectacle lenses
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The centre of rotation condition
pantoscopic angle
visual axis
Typically the pantoscopic angle is 100.
optical axis
optimum position
optimum
for
optical position
centre
for optical centre
However,
spectacle for
frames
are normallytilt
toshown,
compensate
the pantoscopic
ItInisorder
easily
from
the
geometry
of the
fitted
socentre
that
the
front
is parallel
with
the
The
optical
axis
of
the
lens
then
continues
If
the
spectacle
frame
is
fitted
like
this,
the
the
optical
of
the
lens
must
be
lowered
0
figure,
that
for
each
1
pantoscopic
angle,
the
line
joining
thebefore
supra
-orbital
ridge
and
the
to
pass
through
the
eye’s
centre
of
rotation.
optimum
position
for
the
optical
centre
would
from
its
position
the
pupil
centre.
The
optical
centre
should
be
lowered
by
0.5
mm
i.e.,the
front
tilted
before
thepupil.
eyes.
bechin,
directly
in front
ofisthe
centre
of the
amount
depends
upon
the
pantoscopic
angle.
The degree of tilt is called the pantoscopic angle.
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Ophthalmic Lenses & Dispensing
Vertical centration of spectacle lenses
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Required position
of optical centre.
HCL
..
.
Taking
notecentre
of
thegive
angle,
the vertical
required
height
the
optical
The
ofpantoscopic
rotation
condition
for
centration
is
easily
or, better
still,
the required
heights
of the OC
from of
the
HCL.
centresatisfied
can be obtained
pupil centre
heightoffrom
by fitting by
themeasuring
frame andthe
marking
the position
the the
lower horizontal
tangent
thehead
lensisperiphery
and
simplyposition.
subtracting
pupil centres
whentothe
held in the
primary
0.5mm from this measured value for each 1º of pantoscopic tilt.
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Ophthalmic Lenses & Dispensing
Vertical centration of spectacle lenses
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The centre of rotation condition for near vision
D = distance visual point
Primary visual
axis for DV
R = eye’s centre of rotation
O = optical centre of lens
D
R
O
This figure indicates that the centre of rotation
condition has been satisfied for distance vision.
We see that in satisfying the centre of rotation condition for distance
vision, the requirement for near vision is satisfied at the same time!
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Ophthalmic Lenses & Dispensing
Centration errors
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.
For
Theexample
most obvious
if plus problem
lenses are
which
not
decentred
arises from
inwards
incorrectly
for near
centred
vision
In addition to problems with binocular vision, the prism which is introduced by poorly
lenses
there
is will
thatbe
unprescribed
base out prism
prismatic
centred lenses may produce other noticeable effects which are a source of complaint.
effect
exerted
is introduced
at the nearbefore
visual the
points.
eyes.
.
Errors in the vertical meridian of the lenses may give
rise to intolerable vertical differential prismatic effects.
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Ophthalmic Lenses & Dispensing
Centration errors
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dispersion by a prism
incident white light
is dispersed by a prism into its
monochromatic constituents.
The angle between the emergent red and blue
ends of the spectrum represents the angular
dispersion or chromatic aberration of the prism.
The chromatic aberration exhibited by a plano prism of power, P, made in
a material whose V-value or Abbe Number is denoted by vd , is given by:
P
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chromatic aberration =
Ophthalmic Lenses & Dispensing
vd
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Centration errors
dispersion by a lens
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incident white light
is dispersed by a lens into its
monochromatic constituents
c
OC
lens power = F
transverse chromatic aberration
c.F the dispersion being due
The same effect occurs with lenses,
In theSo,
case
lens,
the
isTCA
known
aslens
transverse
TCA.
Patorepresents
the effect
prismatic
exerted
bychromatic
the
the
in of
the
case
of
a effect
lens,
where,
c.F
is
theataberration,
prismatic
effect.
=effect
the prismatic
of the
at the
point
oflens
incidence.
point of incidence and is given vby Prentice’s rule, P = c.F.
d
P
TCA = v
d
just as in the case of a plano-prism.
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Ophthalmic Lenses & Dispensing
Centration errors
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effects of dispersion
When
the
prism
is turned
through
90º,
Now
consider
the low-contrast
When
viewed
through
a through
prism whose
When
viewed
through
a prism
whose
When
the
prism
is turned
90º,
Consider
first
a
high
contrast
target
The effectbase-setting
of transverse
chromatism
upon
the wearer
depends
upon
the object
being
viewed.
however,
coloured
fringes
may
be
seen
target
the
right.
coincides
with
the
base
setting
coincides
the
lines,
however,
theillustrated
edges
of on
the
bars
oflines,
the
such as
the one
shownwith
on the
left.
on
edges
bars
the
target.
no effect
can
be seen
on the acuity.
target.
no the
effect
can of
bethe
seen
onof
the
target.
target
appear
blurred,
reducing
high-contrast target
low-contrast target
This effect is sometimes described as off-axis blur and is due to the
dispersion caused by the prism along its base-setting. It is minimized, by
using lens materials with the highest possible V-value, or Abbé Number.
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Ophthalmic Lenses & Dispensing
Centration errors
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effects of poorly centred lenses
This experiment demonstrates another effect of poorly centred lenses.
Notice that the spot appears
Rotate
prism
and
notice
On
the the
next
mouse
click
youhow
displaced
towards
the
prism
the
ghost
image
alsoabove
rotates.
will
introduce
asitting
low-power
apex
and that
the
It
always
appears
displaced
prism
(say
½ see
 ) base
DOWN
spot you
can
a ghost
image
towards
the
prism
apex.
in
frontisofinthe
spotlight...
which
focus,
like the spot.
A
A
H
H E
E
D
DX
XR
RC
C
spot spot
Click here to turn on >>
the muscle spotlight.
Now click here to >> room room
turn off the room light.
EGSKBY
EGSKBY
TQPKLNVDXA
TQPKLNVDXA
Once you have located this
ghost in a darkened consulting
room, switch the room light on
again and see that the ghost is
still visible, although somewhat
more difficult to discern.
The optics of this ghost image
are considered in the next slide.
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Ophthalmic Lenses & Dispensing
Centration errors
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effect of poorly centred lenses
Ghost
image
Dioptric
image
requirements
areprism
all met
by prisms
of the
low intensity
power!
If theThese
refractive
index of the
material
is 1.5
In order for The
a ghost
image
to be
troublesome,
three
conditions
dioptric
image
produced
byofthe
prism
isimage,
seen inmust
this be
direction.
This
shows
the
formation
the
ghost
which
is satisfied.
of this ghost image is only 0.15%. Despite its dimness, you will
1) The ghost should
be bright
enough
to bereflection
noticeable.
produced
by total
internal
at the lens surfaces.
This
ghost
image
is experiment
often complained
of quite
by wearers
of low-power
prisms,
have
seen
in the
that it is
noticeable,
even when
2) The vergence of the ghost
should beofsimilar
to thatdof= the
The deviation
this image,
(n -lens.
1)a
by subjects
who are
are switched
wearing multifocals
have been
prism-thinned
the lights
back on in which
the consulting
room.
The vergence of The
this ghost
canof
bethis
shown
to beimage
(3n-1).F
(n-1).
n = 1.5, this
deviation
catoptric
is /(3n
- 1)When
a
and those who are wearing low-power, poorly centred lenses.
turns out to be 7F. For a plano-prism its vergence is zero and it is in sharp focus.
3) The ghost must lie close to the fixation line (but not superimposed).
A multi-layer anti-reflection coating reduces the intensity of the image, almost to zero.
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Ophthalmic Lenses & Dispensing
Graphical construction
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to find prismatic effect on an astigmatic lens
Example: find the vertical and horizontal prismatic effects at a point
which lies 10mm down and 4mm inwards from the optical
centre of the lens R +4.00 / +2.00 x 30.
Begin by finding the prism due to the sphere.
Notice
theThis
cross-sectional
ofof
the
lens
iseffect
the optical
the
The prismatic
due shape
tocentre
the sphere
region
of meridian,
R. In the
vertical
spherical
+4.00
component.
isthe
found
from
Prentice’s
law,
P meridian
= cF.
Ininthe
horizontal
the
cross-sectional
the lens
shape resembles
a prism
base
UP.
shape
resembles
a
prism
with
its
base
OUT.
Thismeridian,
is point atcwhich
In the vertical
= 1cmwe are
findingmeridian
the prismatic
effect.
In the horizontal
c = 0.4cm.
Hence:
.
OC
.
R
PV = 1 x 4 = 4 base UP
PH = 0.4 x 4 = 1.6  base OUT
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Ophthalmic Lenses & Dispensing
Graphical construction
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to find prismatic effect on an astigmatic lens
Example: find the vertical and horizontal prismatic effects at a point
which lies 10mm down and 4mm inwards from the optical
centre of the lens R +4.00 / +2.00 x 30.
There is no power along the axis
meridian of a plano-cylinder, hence
the cylinder can exert no prismatic
effect
along +2.00
its axisxmeridian.
Now we must consider the prism due to the
cylinder
30
+2.00 x 30
All the power of a cylinder lies at right
angles to its axis, i.e., along its power
meridian, so a cylinder exerts prismatic
effect only along its power meridian.
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Ophthalmic Lenses & Dispensing
Graphical construction
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to find prismatic effect on an astigmatic lens
Example: find the vertical and horizontal prismatic effects at a point
which lies 10mm down and 4mm inwards from the optical
centre of the lens R +4.00 / +2.00 x 30.
P
The cylinder can only produce a prismatic
We will first consider how to find the baseeffect
direction
the
prismtothe
due
to thei.e.,
cylinder.
at right
angles
its prismatic
axis,
along
In
order
toofdetermine
effect
themust
120 meridian
of the
lens.and
at R, we
resolve the
vertical
R
horizontal
decentration
alongpart
the
Now
notice
This find
iswhere
the
point
the at
thickest
which
we
ofpower
the
We
must
the
perpendicular
distance,
meridian
of
theprismatic
are
finding
cylinder
lies
with
respect
toeffect.
point,
R. axis.
It is
PR,
of the
point
Rcylinder.
from the
cylinder
up and out along 120 with respect to R.
+2.00 x 30
.
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Ophthalmic Lenses & Dispensing
Graphical construction
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to find prismatic effect on an astigmatic lens
Example: find the vertical and horizontal prismatic effects at a point
which lies 10mm down and 4mm inwards from the optical
centre of the lens R +4.00 / +2.00 x 30.
Evidently, P lies above R and on its
Then
mark
the
position
of
the
point,
First,
construct
and
Next,
determine
theorigin
base
direction
of R,
Next
draw
indetails
the an
cylinder
axis
along
The simplest method is to use a 30º
graphical construction,
of
which
follow.
temporal
side.
When
thehere
cylinder
is
to
scale
on
the
diagram,
10mm
mark
the
nasal
side
of
the
lens
the
prismatic
effect
at
R.
Ask
yourself,
If
the
cylinder
had
been
negative
in
sign,
P
its
prescribed
axis
direction,
here,
30º.
Now
drop
a
perpendicular
from
R
Does
P
lie
above
R
or
below
it?
P
N
positive
sign ,inas
in this
down
andin4mm
from
theexample,
origin.
“where
does
Paxis
lie with
respect
wouldDoes
represent
thethe
position
of theof
prism
apex.
to
thePcylinder
meeting
at
lie
on
side
RtoP.
orR?”
does
P represents
the nasal
position
of itthe
prism
The base
would
been side
DOWN
& IN
it lieso
onhere,
thehave
temporal
R?
base,
the base
is say,
UPof&10:1.
OUT.
Choose
a large
scale,
.
R
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Ophthalmic Lenses & Dispensing
Graphical construction
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to find prismatic effect on an astigmatic lens
Example: find the vertical and horizontal prismatic effects at a point
which lies 10mm down and 4mm inwards from the optical
centre of the lens R +4.00 / +2.00 x 30.
P
Q
N
.
R
The vertical prismatic effect at R due to
the cylinder is given by:
PQPR,
(cm)
xvertical
Fcyl. and
Since
we
the
PQ
QR
isdistance,
the
the require
effective
effective
decentration
decentration
of
of the
the
Theis
represents
the
horizontal
prismatic
can
plano-cylinder
in theeffects
vertical
horizontal
meridian.
meridian.
effective decentration
of thewe
planonow
resolve
PRitsinto
vertical
and
cylinder
along
power
meridian.
horizontal
components,
andatQR.
The horizontal
prismaticPQ
effect
R due
to the cylinder is given by:
QR (cm) x Fcyl.
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Graphical construction
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to find prismatic effect on an astigmatic lens
Example: find the vertical and horizontal prismatic effects at a point
which lies 10mm down and 4mm inwards from the optical
centre of the lens R +4.00 / +2.00 x 30.
In this example:
by measurement: PQ = 9.2mm
QR = 5.3mm
P
N
Hence the prism due to the cylinder is:
Q
.
R
PV = 0.92 x 2.00 = 1.84 base UP
PH = 0.53 x 2.00 = 1.06  base OUT
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Ophthalmic Lenses & Dispensing
Graphical construction
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to find prismatic effect on an astigmatic lens
Example: find the vertical and horizontal prismatic effects at a point
which lies 10mm down and 4mm inwards from the optical
centre of the lens R +4.00 / +2.00 x 30.
Prism due
to sphere
OC
.
.R
So we have found:
Prism due to sphere = 4 
base UP & 1.6  base OUT
Prism due to cylinder = 1.84 base UP & 1.06  base OUT
Prism due
to cylinder
P
Q
N
Total prismatic effect = 5.84 base UP & 2.66  base OUT
.R
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Ophthalmic Lenses & Dispensing
Lens thickness and weight
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Edge thickness of a minus lens
Thickness of plus lens
Variation in thickness of aspheric lens
Astigmatic prismatic lenses
Graphical construction for thinnest point on edge
Lens weight
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Lens thickness
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Edge thickness of minus lens
t
This is a cross-sectional
view of a plano-concave lens
e
s
y
Sag 10.00 at 60, n = 1.56
e is the edge thickness
We have: y = 30, r = 56
r
t is the
centre
thickness
First,
find
the
radius
of
surface
r sag
= 1000(n
- 1) / Curve
Suppose
wethe
wanted
to from:
find the
of a 10.00D
curve at 60
2
2
The the
semi-diameter
of the
is 60
/ 2 = 30mm
diameter,
of lens
the lens
being 1.56.
y refractive index
30material
s is the sagsof=the concave surface =
= 8.71mm.
Centre
of surface
= 1000(1.56
- 1)2 /of10curvature
2
r +  r2 - y2
56 +  56 - 30
From the geometry of the
figure
= 56mm
e = t+s
The quantity, s, is calculated from the sag formula, s =
y2
r +  r2 - y2
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Ophthalmic Lenses & Dispensing
Lens thickness
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Edge thickness of minus lens
t
s1
This is a cross-sectional
view of a curved minus lens
s2
e
e is the edge thickness
t is the centre thickness
s1 is the sag of the convex surface
s2 is the sag of the concave surface
From the geometry of the figure:
so
t + s2 = e + s1
e = t + s 2 - s1
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Ophthalmic Lenses & Dispensing
Lens thickness
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Edge thickness of minus lens
Consider a -6.00 lens, made in glass, n = 1.523, with +4.00 base and centre thickness of 1.0mm.
7.0mm
5.0mm
3.5mm
At diameter
diameter is
60mm:
If the
reduced to 40mm:
50mm:
s1 = 3.5
s1 = 1.5
2.4
s2 = 9.5
s2 = 4.0
6.4
e = te+s
s12 - s1
= 2t -+s
= 7.0mm
= 3.5mm
5.0mm
-6.00 at 40 edge subs = 3.5 mm
-6.00atat60
50 edge
edgesubs
subs==7.0mm
5.0mm
-6.00
The cross-sectional shape of a minus lens reminds us that
the smaller the lens diameter, the thinner will become the lens.
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Ophthalmic Lenses & Dispensing
Lens thickness
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Edge thickness of minus lens
Consider a -6.00 lens, made in glass, n = 1.523, with +4.00 base and centre thickness of 1.0mm.
Note: If the overall diameter of the lens is 50mm but it has been decentred
4mm inwards, the edge thickness would change as follows:
This
Thisisisthe
theoptical
geometric
centre
centre
of the
of the
lens
lens
..
25
29 50
25
21
The edge thickness on the
temporal side of the lens, eT,
is that of a 58 diameter lens.
The edge thickness on the
nasal side of the lens, eN,
is that of a 42 diameter lens.
eN = 3.7mm
eT = 6.2mm
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Lens thickness
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Thickness of plus lens
This is a cross-sectional
view of a plano-convex lens
s
e
t
e is the edge thickness
t is the centre thickness
s is the sag of the convex surface
From the geometry of the figure
t = s+e
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Ophthalmic Lenses & Dispensing
Lens thickness
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Thickness of plus lens
This is a cross-sectional
view of a curved plus lens
t
s1
s2
e
s1 is the sag of the convex surface
s2 is the sag of the concave surface
e is the edge thickness
t is the centre thickness
From the geometry of the figure:
so
t + s2 = e + s1
t = e + s1 - s2
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Lens thickness
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Thickness of plus lens
If edged
down
to the
smaller
diameter
40mm with
the
edge
increases
even more.
Consider
a +6.00
uncut,
CR 39,
n of
= 1.498,
-4.00thickness
base
andthickness
edge thickness
of 0.5mm.
When
this uncut
ismade
edgedindown
to a
diameter
of 50mm
the
edge
increases.
At diameter 50mm:
65mm:
F1 = +9.52 t = 7.5mm
7.5mm
s1 = 4.0
11.3
6.4
s2 = 2.5
1.6
4.3
e = t - (s1 - s2)
= 5.1mm
0.5mm
3.6mm
+6.00 at 40
65
50
edge subs = 5.1mm
0.5mm
3.6mm
In order
Thisto
edge
obtain
thickness
a reasonable
is unacceptable
edge thickness,
and it is
plus
quite
lenses
clearshould
that plus
be lenses
surfaced
downover
to aabout
suitable
+2.00D
diameter
should
fornot
thebe
shape
edged
when
down
all to
themuch
prescription
smaller details
sizes. are known.
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Lens thickness
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Thickness of plus lens
The problems are even greater with plus astigmatic lenses
Consider the specification +3.00 / +2.00 x 180 which is to be edged to a 48 x 40 oval shape.
1.5
e thin
mm
1.5
mm
e thick
1.6mm
1.6 mm
The thickest points on the
edge of the lens lie at each end
of the horizontal meridian.
The centre thickness
will then be 3.5 mm.
+3.00
48
The
Thehorizontal
horizontaldiameter
power
of
of the
the lens
lens is
is 48mm
+3.00
40
+5.00
The
The
vertical
vertical
diameter
power
It will The
be realised
that
the
edge
substance
ofto
this lens
thinnest
points
on
the
edge
the
lens
lie varies
We will
custom-design
theoflens
of
of
the
the
lens
lens
is
is
40mm
+5.00
from at
only
to at
1.6mm
round
edge
the1.5mm
extremities
of the
vertical
meridian.
give
1.5mm
this
point
onthe
the
edge.of the lens.
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Lens thickness
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Thickness of plus lens
The problems are even greater with plus astigmatic lenses
Now consider the specification +3.00 / +2.00 x 90 which is to be edged to the same oval shape.
The thickest points on the edge
of the lens now lie at each end
of the vertical meridian.
e thick
3.3
mm
3.3mm
The centre thickness
will then be 4.5 mm.
+5.00
48
e thin
1.5mm
The
Thehorizontal
horizontaldiameter
power
of
of the
the lens
lens is
is 48mm
+5.00
40
+3.00
The
The
vertical
vertical
diameter
power
Not only is Itthe
lens
1.0mm
thicker
inon
the
centre,
thethe
edge
from 1.5mm
The
thinnest
points
the
edge of
lensnow
nowvaries
willcustom-design
be realised
that
edge
substance
We will again
thethe
lens
to give
1.5mmof
atthis
thislens
pointnow
on the edge.
of
of
the
lens
lens
is
40mm
+3.00
at the thinvaries
edge,
at the
thick
edge
simply
because
the
axis lies at 90.
lieto
at3.3mm
the1.5mm
extremities
of is
the
horizontal
meridian.
from
to 3.3mm
round
the edge
of the
lens.
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Lens thickness
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Variation in thickness of aspheric lens
Aspheric lenses have the advantage that they are flatter and thinner than
spherical lenses so that when edged down the edge thickness is not so great.
65mm:
At diameter 50mm:
Spherical lens
F1 = +9.52 t = 7.5mm
7.5
6.4
Aspheric lens
F1 = +6.80 t = 6.4mm
65
+6.00 uncuts at 50
edge thickness
=
Spherical
Aspheric
0.5
3.6
0.5
2.8
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Lens thickness
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Astigmatic prismatic lenses
In the generalWe
case,
will now
a plus
consider
lens may
thehave
thickness
spherical,
of circular
cylindrical
plus and
lenses
prismatic power.
which incorporate both cylindrical and prismatic power.
This is the spherical component of the lens. It
This
This is
is athe
plano-cylindrical
prismatic component
component
with its
with its axis
may be considered to incorporate the bending of the
baseatDOWN
90. Note
(at 270).
that Note
this component
that this component
has zero edge
lens. Note that if the element is centred, its edge
hasthickness
zero edge
at thickness
the extremities
at its apex
of the(at
180
90).
meridian.
thickness will be the same all round the periphery.
cylindrical
spherical
prismaticelement
element
Variation in edge thickness of circular lenses
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Lens thickness
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Astigmatic prismatic lenses
The thickness of a plus sphero-cylindrical lens which incorporates prism (or decentration)
is seen to be made up from the thickness of each of these three individual components.
spherical element
cylindrical element
prismatic element
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Lens thickness
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Astigmatic prismatic lenses
Consider the prescription R +2.00 / +4.00 x 90 with 4 base OUT
which is to be produced with an uncut diameter of 60mm and zero edge thickness.
The spherical element
is +2.00
The cylindrical element
is +4.00 x 90
The prismatic element
is 4 base OUT
The centre thickness
of this component is
1.9mm
The centre thickness
of this component is
3.6mm
The centre thickness
of this component is
2.4mm
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Lens thickness
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Astigmatic prismatic lenses
Consider the prescription R +2.00 / +4.00 x 90 with 4 base OUT
which is to be produced with an uncut diameter of 60mm and zero edge thickness.
The thickness of the specification is made up as follows:
The spherical element
The prismatic element
4 base OUT, tC = 2.4
+2.00, tC = 1.9
Note that the edge thickness
of this lens is zero at the nasal edge.
The total centre thickness of
the lens is seen to be 7.9mm.
The cylindrical element
+4.00 x 90, tC = 3.6
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Lens thickness
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Astigmatic prismatic lenses
Now consider the prescription R +2.00 / +4.00 x 90 with 4 base DOWN
also to be produced with an uncut diameter of 60mm and zero edge thickness.
The spherical element
is +2.00
The cylindrical element
is +4.00 x 90
The prismatic element
is 4 base DOWN
The centre thickness
of this component is
1.9mm
The centre thickness
of this component is
3.6mm
The centre thickness
of this component is
2.4mm
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Lens thickness
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Astigmatic prismatic lenses
R +2.00 / +4.00 x 90 with 4 base DOWN
60mm and ethin = 0.
The thickness of the specification is made up as follows:
Note that the minimum edge thickness
of the lens is no longer zero. Both
prism and cylinder contribute some
thickness to the thinnest point on the edge.
The prismatic element
4 base DOWN, tC = 2.4
The spherical element
+2.00, tC = 1.9
If this lens is to have zero edge
thickness it is seen that the centre
thickness must be reduced.
The cylindrical element
+4.00 x 90, tC = 3.6
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Lens thickness
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Astigmatic prismatic lenses
R +2.00 / +4.00 x 90 with 4 base DOWN
60mm and ethin = 0.
To obtain zero edge thickness, the centre thickness can be reduced by 2.0mm.
The spherical element
Nowthickness
The
the edge here
thickness
can
beofreduced
the lensby
is 2.0mm
zero.
The prismatic element
4 base DOWN, tC = 0.4
+2.00, tC = 1.9
To obtain zero edge thickness
the centre thickness of the lens
need be only 5.9mm.
The cylindrical element
+4.00 x 90, tC = 3.6
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Lens thickness
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Astigmatic prismatic lenses
R +2.00 / +4.00 x 90 with 4 base DOWN
60mm and ethin = 0.
position
onpoints
the edge
of the
lens
where
the
edge
thickness
zero.
InNote
fact,the
there
are two
on the
edge
where
the
edge
thickness
is is
a minimum.
emin
emin
160
20
160
20
180 meridian
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Lens thickness
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Astigmatic prismatic lenses
The position on the edge of an astigmatic, prismatic lens where the thickness
is a minimum can be determined by means of a graphical construction.
Note first, that the thinnest point
on the edge of the cylinder lies at
When these two components are
the extremities of the minus cyl axis.
combined, the thinnest point on the
edge of the combination must lie
somewhere
between
thethinnest
prism
Also note
that the
apex point
and the
cylinder
axis.
on minus
the edge
of a plano
prism lies at the prism apex.
prism apex
emin

minus cyl axis
The
The prismatic
cylindricalelement
element
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Lens thickness
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Astigmatic prismatic lenses
The position on the edge of an astigmatic, prismatic lens where
the thickness is a minimum can be determined as follows.
The angle Next,
between
the edge
the angle,
ruler (line
EFD) andthe
thebase
basesetting
line AB,
FEB in
calculate
the of
acute
, between
of (angle
the
place
a ruler
on the
construction
and adjust
itsdraw
position
until
the
the Finally
figure)
givesand
the
angle,
, between
the
minus
cylinder
axis adirection
and
the lies
point
prism
the
minus
cylinder
axis
direction
and
line
from
B,zero
200P
Next,
draw
aof
horizontal
Then,
line,
AB,
construct
10
units
perpendicular,
to
represent
BC,
the
from
minus
B from
cylinder
axis
direction.
First,
calculate
thethe
quantity:
z =a long
onthe
line
AB,
the
edge
passes
through
point
Dwhere
and BD
the
distance
to the
on
edge
of
astigmatic,
prismatic
the
thickness
isbelow).
a zero
minimum.
length,
z,
inclined
at angle,
, dF
tolens
AB,
(line
in
the
figure
BC, ismeasured
exactly 10inunits.
(EF =angle
10 units
in thethe
diagram
Noteperpendicular,
the angle is always
the acute
between
minusbelow.)
cylinder axis
direction and the prism base setting, in the direction towards the prism apex.
where
and
C
P is the prism power
d is the lens diameter
F is the power of the cylinder
D
z

A

F
B
E
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Lens thickness
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Astigmatic prismatic lenses
By way of example, take the prescription R +2.00 / +4.00 x 90 with 4 base DOWN
which is to be produced with an uncut diameter of 60mm and zero edge thickness.
Next,
acute
angle,
, between
setting
of B
the
prism,
which
lies
Next,
drawcalculate
aplace
horizontal
line,
Then,
AB,
construct
10 units
along
perpendicular,
to the
represent
the
from
minus
cylinder
axis
direction.
Finally
athe
ruler
onBy
the
construction
and
adjust
itsBC,
position
until
the zero
lies
measurement
angle
base
= 20º.
where
P is the
prism
power,
4. in
aton90,
and
axis
direction,
is atdistance
180.
The
angle
, ,
isthe
90º
line
AB,the
theminus
edgecylinder
through
Dwhich
and
the
from
zero
toeach
Remember
that
when
passes
= 90 there
are point
two minima
on the dedge
of
the
lens,
200P
is
the lens
diameter,
this
example,
we
must
draw 10
a line
B,=of10
length,
3.33
units,
inclined
at 90º 60
to AB
First,
calculatesothe
quantity:
zunits.
= from
perpendicular,
BC,
is
exactly
(EF
units
in
the
diagram
below.)
symmetrical with the minus cylinderdF
axis on and
the side of
the
prism
apex.
(line BD in the figure below). F is the power of the cylinder, 4
z =
200x4
60x4
= 3.33
C
D
F z = 3.33
 = 90

A
B
E
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Lens weight
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Density
One of the physical properties which is published by lens
material manufacturers is the density of the material.
Glasses
Plastics
Material
nd
Density
White 15
White 16
White 17
White 18
White 19
1.523
1.600
1.701
1.802
1.885
2.54
2.63
3.21
3.65
3.99
1.500
1.557
1.586
1.595
1.670
1.710
1.32
1.23
1.20
1.36
1.32
1.40
CR 39
mid-index
Polycarbonate
high index
high index
high index
The density is expressed in
grams per cubic cm (g/cm3)
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Density
10mm
Water
CR 39has
material
a density
has aofdensity
exactlyof1.0
1.32.
10mm
3 of water
This means
so 1cmthat
1cm3 of
weighs
CR 391gram.
weighs 1.32g.
10mm
Density expresses the weight in grams of one cubic centimetre of the material.
1cm33 of crown glass weighs 2.54g so
1cm of CR 39 weighs 1.32 grams so
this glass is 2.54x heavier than water
CR 39 is 1.32x heavier than water.
and about twice as heavy as CR 39!
Note that the weight is found by multiplying the volume by the density of the material.
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Density
But, in reality
Naturally,
we cannot
we want
justspectacle
comparelenses
the densities
to be asoflight
the materials
as possible.
since higher
The
density
of
plastics
materials
is
about
half
that
of
glass
so
refractive index materials will have less volume, owing to the fact that the same
that
plastics
lenses
areofabout
half on
theamust
weight
glass
lenses.
curve
Thiswill
means
produce
thatathe
higher
density
surface
the
power
material
higher
beofrefractive
as
low as
index
possible.
material.
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Lens weight
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Weight of plus lens
y
Consider,The
first,
the cylindrical
plate
weight
of a circular
spectacle lens is founde by multiplying
the volume of the lens by the density of the lens material.
The volume of this plate is .y2.e
spherical
cap…
…combined
withup
a cylindrical
plate. components.
A plano-convex lensacan
be considered
to be made
from two separate
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Lens weight
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Weight of plus lens
y
s
Now consider the spherical cap
y
r
The volume of the cap is .s2(3r - s) / 3
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Weight of plus lens
The volume of a plano-convex lens is the sum
the of the
The of
volume
The volume of the cap
2.e
can- be
that if the
lens is of
the 2usual
curved
form
necessary
2(3r
theplus
cylindrical
spherical
cap
plate
2 itisis.y
2
isSo
.sItthe
s) /seen
3volumes
volume
of a plusofmeniscus
lens isplate
.(s1and
(3rthe
1 - s1) / 3 - s2 (3r2 - s2) / 3 + y .e)
to subtract the spherical cap which forms the concave surface from the sum
2the
of the convex cap and
the plate
thickness.
. which
(s2 and
(3r represents
- ss) and
/ 3 +r yrelate
.e). edge
where s1 and r1 relate toi.e.,
thevolume
convex =
surface
to the concave surface.
2
2
spherical
cap cylindrical
The volume
of a plano-convex
lens isplate
the sum of the
Note that thevolumes
density ofofthe
material is
normally
in gramscap.
per cubic centimeter
thelens
cylindrical
plate
and quoted
the spherical
so the volume of the lens must be calculated in cubic centimeters, by substituting s, r and
y in cm into the above formula. Also, the formula relates only to the volume of a round lens.
The weight of the lens is found by multiplying its volume by the density of the lens material.
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Weight of minus lens
e
So
A plano-concave
the volume of alens
plano-concave
can be considered
lens is the
to consist
volumeofofathe
thick
plate
cylindrical
which
represents
plate of thickness,
the edge e,
thickness
from which
minus
a spherical
the volume
capofhas
thebeen
spherical
removed.
cap.
The volume of the plate is .y2.e and the volume of the cap is .s2(3r - s) / 3
hence, the volume of the lens is .(y2.e - s2(3r - s) / 3)
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Lens weight
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Weight of minus lens
2 (3rvolume
the case
a curved
form minus
of -the
… so the In
volume
of aof
minus
meniscus
lens islens,
.(s1the
s22convex
(3r2 - s2) / 3 + y2.e)
1 - s1) / 3
spherical cap which represents the front surface must be added...
where s1 and r1 relate to the convex surface and s2 and r2 relate to the concave surface.
This is exactly the same result as that obtained for plus meniscus lenses.
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Weight of minus lens
.s12 (3r1 - s1) / 3 + .y2.e - .s22 (3r2 - s2) / 3
The total …the
volume
volume
of…minus
a curved
of a flat
the
lens
cylindrical
volume
is made
ofplate
the
up from
concave
which
therepresents
volume
spherical
of the
cap.
the edge
convex
thickness...
spherical cap...
This statement is true for both plus and minus lenses.
The volume of meniscus lenses is .(s12 (3r1 - s1) / 3 - s22 (3r2 - s2) / 3 + y2.e)
Remember that the volume must be calculated in cubic centimetres by substituting s, r and
y in cm into the above formula. Also, the formula relates only to the volume of a round lens.
Once again, the weight of the lens is found by
multiplying its volume by the density of the material.
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Lens weight
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Weight of minus lens
As an example, consider a -6.00D lens made in spectacle crown glass, n = 1.523, D = 2.54,
with a +4.00D base curve, a centre thickness of 1.0mm and edged to a 60mm diameter.
r1 = 13.075cm
s1 = 0.349cm
The convex spherical cap has a radius of 130.75mm
and a sag at ø60 of 3.49mm.
edge thickness
of the
lens
is 6.97mm
TheThe
concave
spherical cap
has
a radius
of 52.3mm
and a sag at ø60 of 9.46mm.
r2 = 5.23cm
s2 = 0.946cm
e = 0. 697cm
y = 3.0cm
The volume of the lens is .(s12 (3r1 - s1) / 3 - s22 (3r2 - s2) / 3 + y2.e)
= .(0.3492 (3x13.075 - 0.349) / 3 - 0.9462 (3x5.23 - 0.946) / 3 + 32x0.697)
= 10.85cm3
Weight = volume x density
= 10.85 x 2.54 = 27.56g.
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Lens design and performance
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Off-axis performance of spectacle lenses
Field diagrams
Best form lenses - point focal lenses
Best form lenses - Percival lenses
Best-form lenses - Minimum T-Error lenses
Aspheric spectacle lenses
Tscherning’s Ellipses
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Lens design and performance
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Off-axis performance of spectacle lenses
The
back
of a lens
is the vergence
leavingoff-axis
the
The
eyevertex
is notpower
stationary
but rotates
to view through
back surface
is zero,these
the light
portions
of thewhen
lens. the
Theincident
effect ofvergence
the lens under
conditions
Whenvaries
the eye
rotates
40ºobject.
the
effect
of the
is effect
+4.00/+1.25.
emanating
from
athe
distant
It expresses
the
the
with
ocular
rotation
and
thelens
form
of
the of
lens.
lens
the eye20º
looks
optical
When
thewhen
eye rotates
the along
effect the
of the
lensaxis.
is +4.00/+0.25.
The refracted pencil is afflicted with aberrational astigmatism.
+4.00 / +1.25
+4.00 / +0. 25
+4.00
40º
20º
+4.00
The form of this lens is quite shallow,
the back surface power is only -1.50D.
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Lens design and performance
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Field diagrams
In practice, the off-axis powers are measured from the vertex sphere,
an imaginary spherical surface concentric with the eye’s centre of rotation.
+4.00 / +1.25
+4.00 / +0. 25
+4.00
40º
20º
vertex sphere
+4.00
For a 40º rotation of the eye,
the sagittal oblique vertex sphere power is +4.00
and the tangential oblique vertex sphere power is +5.25
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Lens design and performance
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Field diagrams
ocular
rotation
The off-axis performance is usually shown in the
form of a field diagram where oblique vertex sphere
powers are plotted against ocular rotation.
+4.00 / +1.25
400
.S
.T
..
For 40º rotation the
For 0º
rotation the
effect
is +4.00/+1.25.
effect is +4.00.
For 20º rotation the
effect is +4.00/+0.25.
300
200
+4.00 / +0. 25
+4.00
40º
20º
100
.
00
+3.0 +4.0
oblique vertex
sphere powers
+5.0
FIELD DIAGRAM
vertex sphere
+4.00
S = plot of sagittal powers
FIELD DIAGRAMS FOR SPECTACLE LENSES
Tangential & sagittal oblique vertex sphere
powers
T = plot of tangential powers
4.00
2.00
0
5
10
15
20
25
30
35
0.00
40
oblique vertex
sphere powers
6.00
ocular rotation in degrees
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In practice, field diagrams
are plotted by the computer.
Ophthalmic Lenses & Dispensing
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Lens design and performance
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Best form lenses
T&S
FIELD DIAGRAMS FOR SPECTACLE LENSES
Tangential & sagittal oblique vertex sphere
powers
400
4.00
2.00
0
5
10
15
20
25
30
35
0.00
40
oblique vertex
sphere powers
6.00
ocular rotation in degrees
0
The first 30
best-form
lenses were quite steeply curved
and were designed to be free from oblique astigmatism.
-6.00
+4.00
Point focal lens
200
The
fieldcurve
diagram
for a point focal
A +4.00D lens would need an
inside
of -6.00D.
0
10
lens would look like this.
00
+3.0 +4.0
+5.0
FIELD DIAGRAM
Point focal lenses are free from oblique astigmatism but suffer from mean oblique error;
the mean oblique power of the lens decreases as the eye rotates away from the axis.
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Lens design and performance
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Best form lenses
MOP = BVP
S
T
A second
400type of best-form lens was introduced which was
flatter in form and designed to be free from mean oblique error.
300
A small amount
of oblique astigmatism was tolerated providing
that the disk of least confusion of the astigmatic pencil fell on the
0
retina. This20followed
a suggestion made by the ophthalmologist,
Thesubsequently
field diagramnamed
for a Percival
Dr A. Percival and the design was
after him.
0
10
form lens would look like this.
A +4.00 Percival form lens would need an inside curve of -4.00D.
FIELD DIAGRAMS FOR SPECTACLE LENSES
Tangential & sagittal oblique vertex sphere
powers
4.00
2.00
0
5
10
15
20
25
30
35
0.00
40
oblique vertex
sphere powers
6.00
ocular rotation in degrees
-4.00
+4.00
Percival lens
00
+3.0 +4.0
+5.0
FIELD DIAGRAM
The mean oblique power, (MOP) is seen to be the same as the back vertex power
of the lens, the mean oblique error is zero.
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Lens design and performance
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Best form lenses
FIELD DIAGRAMS FOR SPECTACLE LENSES
Tangential & sagittal oblique vertex sphere
powers
6.00
oblique vertex
sphere powers
400
S T
4.00
2.00
0.00
0
5
10
15
20
25
30
35
40
Modern best-form lenses are designed with a compromise
0
bending30so that the tangential power is the same as the back
vertex power. They are free from tangential error and known as
0
Minimum20T-Error forms. They exhibit a small amount of oblique
The field diagram for a Minimum
astigmatism,
but only about half that of a Percival design.
0
10
T-Error form would look like this.
ocular rotation in degrees
-5.00
A +4.00D
lens would need an inside curve of -5.00D.
0
0
+4.00
Minimum T-Error lens
+3.0 +4.0
+5.0
FIELD DIAGRAM
Minimum T-Error forms have the advantage that they
perform well over a wide range of vertex distances.
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Ophthalmic Lenses & Dispensing
Lens design and performance
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400
Best form lenses
S T
FIELD DIAGRAMS FOR SPECTACLE LENSES
Tangential & sagittal oblique vertex sphere
powers
4.00
2.00
0
5
10
15
20
25
30
0.00
35
oblique vertex
sphere powers
6.00
40
Effects of changes in vertex distance
with Minimum T-Error forms
ocular rotation in degrees
T&S
S
400
400
300
300
300
200
200
200
100
100
100
00
+3.0 +4.0
+5.0
Minimum T-error
at design vertex distance
00
+3.0 +4.0 +5.0
Point focal at long
vertex distance
00
+3.0 +4.0
T
+5.0
Percival at short
vertex distance
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Ophthalmic Lenses & Dispensing
Lens design and performance
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Aspheric spectacle lenses
1.0mm
-5.25
70
6.6mm
The flatter a spectacle lens is made, the thinner it may
become. Best-form lenses made with spherical surfaces
are usually quite steeply curved and therefore thicker
than if made in flatter forms. For example, a point focal
+4.00Dlens made in CR 39 material, would have back
curve of -5.25, and if the uncut diameter is 70mm and
the edge thickness is assumed to be 1.0mm, then the
centre thickness of the lens would be 6.6mm and the
weight of the uncut lens would be 20.3 grams.
+4.00
Point focal lens
made in CR 39.
Weight = 20.3g
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Lens design and performance
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Aspheric spectacle lenses
T&S
1.0mm
400
300
200
FIELD DIAGRAMS FOR SPECTACLE LENSES
Tangential & sagittal oblique vertex sphere
powers
2.00
0
5
10
15
20
25
0.00
40
oblique vertex
sphere powers
6.00
4.00
30
70
6.6mm
35
-5.25
ocular rotation in degrees
100
+4.00
Point focal lens
00
+3.0 +4.0
+5.0
FIELD DIAGRAM
Weight = 20.3g
The field diagram for this point-focal +4.00 design would look like this.
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Lens design and performance
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Aspheric spectacle lenses
1.0mm
400
T
300
FIELD DIAGRAMS FOR SPECTACLE LENSES
Tangential & sagittal oblique vertex sphere
powers
2.00
0
5
10
15
20
25
0.00
30
oblique vertex
sphere powers
6.00
4.00
40
70
If the +4.00D lens is now flattened so that its back curve
is only -1.50D,
the centre thickness will reduce to 6.0mm
200
and the weight of the lens will reduce by some 2 grams.
35
-1.50
6.0mm
S
ocular rotation in degrees
100
+4.00
-1.50 base curve
00
+3.0 +4.0
+5.0
FIELD DIAGRAM
Weight = 18.1g
The field diagram for this flatter form +4.00Dlens would look like this.
The off-axis performance of this flatter curved form is unacceptable!
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Lens design and performance
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Aspheric spectacle lenses
T&S
1.0mm
400
FIELD DIAGRAMS FOR SPECTACLE LENSES
Tangential & sagittal oblique vertex sphere
powers
2.00
0
5
10
15
20
0.00
25
oblique vertex
sphere powers
6.00
4.00
40
70
30
5.4mm
35
-1.50
If the front, spherical curve of this flatter form lens is now
replaced
a suitable aspherical surface, the negative
0
30by
surface astigmatism which is inherent in the aspherical
surface20
can
neutralise the astigmatism of oblique incidence.
0
Furthermore, since the sag of the aspherical surface is less
0
than the10sag
of a spherical surface of the same power, the
centre thickness of the lens will reduce even further to 5.4mm.
The weight
00 of the aspheric lens will reduce to just 16 grams.
ocular rotation in degrees
+4.00
-1.50 base curve
Weight = 16.0g
+3.0 +4.0
+5.0
FIELD DIAGRAM
for aspheric form with convex
hyperboloidal surface, p = -1.8.
The field diagram for this aspheric +4.00D lens would look like this.
The off-axis performance is the same as the steeper curved lens with spherical surfaces!
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Ophthalmic Lenses & Dispensing
Lens design and performance
Tscherning’s Ellipses - point focal lenses
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Back (F )
2
curve
According to third-order theory, lenses
of power F made in a material
of refractive
-50 -45
-40 -35 -30 -25 -20 -15 -10
-5
0 +5 +10
Lens power (F)
index 1.5 and
mounted
26.67mm
front
Before
the advent
of theincomputer,
accurate trigonometric ray-tracing had to be performed by
of the eye’s
centre
of rotation,
will be freelogarithm tables. The procedure was-5lengthy and to save time,
hand,
using
six or seven-figure
from astigmatism
for equations
distance vision
approximate
were when
employed to provide a starting point for the design. These so-called,
-10B Airy (1825), and later by
the insidethird-order
curve, F2 equations
is given by:
for spectacle lenses were first investigated by G
-12.25
F Ostwalt and M Tscherning towards the end the 19th century. The latter
published comprehensive
2)} / 28
of the forms in 1904. The
equations are quadratic in type and-15
plot as ellipses. These were
F2 = {14Fdetails
-375±(22500-2100F-140F
plotted and described by A Whitwell earlier this century who called them the Tscherning’s Ellipses.
-20
-10.00D lenses
+2.25
- 12.25
+14. 50
- 24. 50
-24.50
-25
Ostwalt
point-focal
form
Wollaston
point-focal
form
-30
It can be seen from the graph that there
-35 is a certain range of powers
which can be made free from oblique astigmatism and that within this
range there are two forms for each power.
The shallower form, which
-40
is the one used in practice, is named after Ostwalt and the steeper form
after W H Wollaston who had proposed such forms early in the 19th C.
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Lens design and performance
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Tscherning’s Ellipses - point focal lenses
Back (F )
2
curve
For example, lenses made in a material
-45 -40
0 +5 +10
of refractive index 1.5 and-50
mounted
26.67-35 -30 -25 -20 -15 -10 -5
Lens power (F)
mm in front of the eye’s centre of rotation,
-5
will be free from astigmatism for near
ellipses
caninside
be constructed
specified working distance,
visionSimilar
at 25cm
when the
curve , F2for point-focal, near vision lenses at a-9.10
-10
andby:
also for Percival lens forms or minimum tangential error forms again, for either distance or near
is given
vision. Naturally, the ellipses differ in size and position in each of these different circumstances.
-15
F2 = {14F -335±(36100-2660F-140F2)} / 28
-20
-25
-30
-35
It is seen from the graph that Ostwalt near vision forms are somewhat shallower
than the forms required
for distance vision.The Wollaston NV forms are virtually the same. The Ostwalt near vision design for a
-40
-10.00D lens required for near vision at -25cm would be biconcave in form.
In practice, the eye does not
demand optimum acuity in near vision and best form lenses are invariably designed for distance vision.
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Lens design and performance
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Tscherning’s Ellipses - point focal lenses
Back (F )
2
curve
If we
assumesothat
lenses
are mounted
26.67mm
frontinofathe
eye’s centre
of
The ellipses
illustrated
far the
have
assumed
that the lenses
are in
made
material
of refractive
index 1.5.
rotation, we
obtain
thematerial
following
ranges ofthe
powers for lenses which can
When the refractive
index
of the
increases,
canbe
bemade
made free from
-22.22 range of lenses which +7.23
+7.66
-31.36
free from oblique
astigmatism,
according
to
when
in refractive index,
oblique astigmatism
also
curiously,
in -15
the minus
range.
-50increases,
-45 -40 but
-35
-30 -25only
-20third-order
-10 theory,
-5
0Whatever
+5made
+10 the
Lens power (F)
of different
refractive
indices:
plus lensesmaterials
over about
+7.75 cannot
be made
free from astigmatism when restricted to spherical surfaces.
-5
n
Fellipses,
Fminlenses made in a material of refractive index, n,
It can be shown that the limits of Tscherning’s
for
max
1.5
+7.23
and mounted L´2 dioptres in front of
the eye’s
centre -22.22
of rotation are given by:
-10
1.6
+7.50
-26.77 1.50
-31.36 3
-15
2L´21.7
(n - 1) +7.66
n
1.8
+7.74
Fmax =
(n -1) --35.97 1.70
2-3n
-20
n+2
1.9
+7.77
-40.60
-25
Although based upon
approximate
equations, these
limits do give
a good indication
2L´
3
2 (n - 1)
n
of the ranges
lenses which can (n
be -1)
made
F minof =
+ free from astigmatism
-30for different media.
2-3n
n+2
-35
-40
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Ellipses - minimum tangential error forms
Back (F )
2
curve
Similar equations to those given for point-focal lenses can be derived for
-50 -45 -40 -35 -30 -25 -20 -15 -10
-5
0 +5 +10
Lens power (F)
third-order, Minimum Tangential Error forms. Assuming the same details
as those used for the point-focal designs, namely, n = 1.5 and the lenses
-5 that lenses will
mounted 26.67mm in front of the centres of rotation, we find
exhibit minimum tangential error when their inside curves
are given by:
-10
-11.88
F2 = {49F -1125 ± (275625-17850F-1295F2)}-15
/ 88.
This equation also plots as an ellipse with limits +9.24
-20and -23.02.
-10.00D lenses
+1.18
- 11.88
-24.83
-25
Ostwalt
Min T-error
-30
-35
+14. 83
- 24. 83
Wollaston
Min T-error
-40
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Ophthalmic Lenses & Dispensing
Iso -V-prism theory
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Spherical lenses
Plano-cylindrical lenses
Sphero-cylindrical lenses
Iso-V-differential prism zones
Graphical construction for iso-V-prism zones
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Ophthalmic Lenses & Dispensing
Iso-V-prism zone theory
Spherical lenses
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Consider the prescription R -2.00
L -2.00/-2.00 x 180
iso-V-prism
zone
is acan
zone
on 1cm
a lens
where
prismatic
effect
does 2 
In theeye,
case
spherical
lenses
the
iso-V-prism
zones
are
simply
InAnthe
right
theofeye
roam
from
the vertical
optical
centre
before
it meets
exceedeffect
a stipulated
amount.
effect islaw
ignored.
horizontal
bands,
their cwidth
behorizontal
calculatedprismatic
from Prentice’s
P = c.F.
ofnot
prismatic
(from
= P /can
F).All
In the left eye, the vertical power of the lens is -4.00, so the eye can roam 0.5cm
Hence
the 2
iso-V-prism
horizontal
bands.
from the optical
centre
before
it meets zones
2  of are
prismatic
effect.
R 20 mm wide
L 10 mm wide
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Ophthalmic Lenses & Dispensing
Iso-V-prism zone theory
Plano-cylindrical lenses
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Inthe
the1
case
plano-cylindrical
lenses
zones
are
power
of
iso-V-prism
aofcylinder
lies
atisright
athe
band
angles
20mm
toiso-V-prism
its
wide
axis
along
meridian
the
60º
and
meridian.
If Hence
theThe
vertical
prismatic
effectzone
is denoted
by iso-V-prism
PVthe
then
the
oblique
prism,
PitR,iswhich
For example,
suppose
it is
required
to
find
1
zone
for
the
cylinder
+2.00 x 60.
From
the
decentration
relationship,
the
eye
can
roam,
2
/
2cm,
or
10mm,
still rise
bands
but
they
parallel
to
the the
axis
meridian
of theisthe
cylinder.
necessary
determine
how
far
along
power
meridian
eye from:
can
gives
totoP
the
power
meridian
of
the cylinder,
found
V, along
Thelie
power
meridian
lies
along
150.
along
the
150
meridian
before
it
meets
2
base
150
or
1
of
vertical
prism.
roam before
itprism
encounters
Thealong
result150
the
could
vertical
bedetermined
depicted
prismatic
as
effect
follows:
which is is:
stipulated.
Their
dimensions
can
be
as
follows.
The
which
gives
rise
to
1
vertically
1 base UP
is produced by 2 base 150
JPR = PAV / sin (90 + )
PR = PV / sin (90 + )
1 / sin 150 = 2 base 150.
K = direction
Where

is
the
axis
of theconstruction
cylinder.
This could have been determined by a graphical
as follows.
2
1 iso-V-prism zone for +2.00 x 60
Power meridian
1 is a band, 20mm wide, lying along 60.
J´
A´ K´
20mm
Note that along JJ´ the prism base is DOWN
whereas along KK´ the prism base is UP.
Along the axis meridian, AA´,
the prismatic effect is zero.
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Iso-V-prism zone theory
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Sphero-cylindrical lenses
From
These
In
Since
the
Choosing
In
two
decentration
case
all
the
points
other
boundary
ofto
asphero-cylindrical
suitable
cases
are
plotted,
of
the
the
scale,
band
zone
one
will
the
lenses
on
is
anot
each
eye
J,
straight
can
be
the
can
principal
parallel
iso-V-prism
be
roam
line,
plotted
it2
meridian
with
is
/2
on
necessary
cm
the
zone
the
will
10mm
30
thetolens,
UP
ItConsider
is
essential
check
the
base
direction
along
each
principal
meridian
We
the
must
1
iso-V-prism
now
determine
zone
how
forlens.
far
the
lens
eye
-2.00
can
/+3.50
roam
xorof
30.
Consider
first
the
30 relationship,
meridian
ofpoint,
the
The
prism
along
30
which
along
be
be
meridian
parallel
the
able
cylinder
the
30
to
meridian
to
same
of
locate
the
axis
method
axis
lens
two
before
but
only
10mm
points
will
which
when
lie
in
up
was
order
the
along
just
cylinder
some
to
base
30be
described
other
30,
axis
the
(or
to
meridian.
lies
for
construct
optical
1
atplano-cylinders.
of
90
centre
or
the
180.
prism).
O.
tousing
ensure
that
the
vertical
prism
are
both
base
UP
orline.
both
along
the
30
meridian
it2
meets
2
base
UP
at
30.
will
give
rise
tothe
1
base
UP
,itbefore
ismeets
1along
/components
sin
30
= from
2able

base
UP
atvertical
30.
base
DOWN
Failure
to is
do
this
willThe
result
in30
the
band
90º off!
The principal
The
powers
power. of
along
the lens
30
are
-2.00.
-2.00D
along
prism
along
and
+1.50D
30being
is 2.
along
120.
.
J
1
base UP
10
-2.00
2 base UP at 30
O
+1.50
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Iso-V-prism zone theory
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Sphero-cylindrical lenses
Choosing
a suitable
scale,
point,
J´,far
can
beeye
plotted
on the 120
WeNote
must
nowthe
determine
how
the
can roam
that
eye must
rotate
DOWN
along
Note
that
the
vertical
prismatic
effect
at roam
any
point
on
this
line
is which
base DOWN
UP.
From the
Consider
decentration
now
the
relationship,
120
meridian
theof
eye
can
lens.
The
1.15
prism
/ .1.5
along
120
= O.
7.7mm
meridian
of
the
lens,
7.7mm
down
from
the
optical
centre,
along
the
120
itthe
meets
1.15
base
UPcm
at
120.
120
inmeridian
order
tobefore
encounter
prism
base
UP
We
can
now
construct
the
1
base
UP iso-V-prism line through the points JJ´.
alongwill
the
give
120
rise
meridian
toalong
1 base
before
meets
is 1 / sin
1.15
120prism
base
= 1.15
120,
 base
(or
of at
vertical
120. prism).
The
power
120UP
isit,+1.50.
The
along
30 1
isUP
1.15.
1 base UP
1
-2.00
J
base UP
.
1.15 base
UP at 120
O
7.7
.
J´
+1.50
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Iso-V-prism zone theory
Sphero-cylindrical lenses
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It we
willmeasure
be
realised
that
when
the
eye
views
through
anybe
point
Finally,
Assuming
a right
eye,
the
bandwidth,
thethe
base
direction
which
isofthe
thiseffect
perpendicular
prismatwill
distance
IN at any
Note
that
vertical
prismatic
We
can on
also
construct
1
base
iso-V-prism
line
through
the points
KK´.
We
can
now
draw
aorientation
line,DOWN
HH´,
through
O parallel
todirection
JJ´.
this
line
itthe
will
encounter
onlyKK´
horizontal
prismatic
effect.
between
point
JJ´on
the
and
line
KK
segment,
´,any
and
the
OH
of
at
the
any
point
on
i.e.,the
the
segment
of HH
OH´.
´.
point
onand
the OUT
line
is band,
base
DOWN
. line
Note that OK = OJ, and OK´ = OJ´, so that JJ ´ and KK´ are equidistant from HH´.
The result could be depicted as follows.
H 1 base UP
K
J
K´
If the-2.00
eye remains within the band
J
it will not encounter more than
1 of vertical prismatic effect.
.
67.6º
67.6º
O
K´
K
J´
1 base
DOWN
.
J´
1 iso-V-prism zone for -2.00 / +3.50 x 30.
By measurement, the band is 12.2mm
wide and lies along the meridian, 67.6º.
12.2mm
H´
+1.50
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Ophthalmic Lenses & Dispensing
Iso-V-prism zone theory
Iso-V-differential-prism zones
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The
zone
for
a -2.00D
horizontal
band
10mm
wide.
The
zone
If 1
theiso-V-prism
issubject
not very
had
wide.
beenIn
dispensed
the
verticalalens
meridian
pairisofsimply
bifocal
the a
eyes
lenses,
can the
only
segment
roam
5mm
zone
from
which
the optical
incorporates
centres before
the is
reading
they meet
prescription
of vertical
may not
differential
evenlens
lie within
prismatic
effect!
The differential
prescription
simply,
how1
much
stronger
one
is thanthe
theband!
other.
For example, consider the prescription
R -2.00
L-2.00 / -2.00 x 180.
In thisThese
case,
where
the
powers
of theapplication
lenses
known
in the
vertical
Perhaps
the
most
important
of
iso-V-prism
zone
is
The
iso-V-differential-prism
zonesare
are
simply
the
iso-V-prism
iso-V-differential-prism
zones
represent
the
areas
on theory
ameridians
pair of
(we are
only
interested
vertical
prismatic
effects),
power
of10mm
the
left
lens
in the
to enable
us to in
locate
thefor
areas
a pair ofthe
spectacles
within
which
spectacles
within
which
comfortable
binocular
vision
is most
likely
to
occur.
zones
plotted
the on
differential
prescription.
vertical meridian
is -4.00,
so the left
eyedoes
is stronger
than the
right eyeamount.
by -2.00D.
the vertical
differential
prism
not exceed
a stipulated
The eye must remain within this zone so as not to
encounter more than 1 of vertical differential prism.
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Ophthalmic Lenses & Dispensing
Iso-V-prism zone theory
Iso-V-differential-prism zones
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In these circumstances, the differential prescription can be obtained by
It was
stated example,
earlier
thatRthe
differential
prescription
is simply,
much
In the
previous
-2.00
L-2.00
/ -2.00
x 180,
changing
signstronger
of the sphere
changing
the signs
of
the
sphere
and
the cylinder
in onehow
eyethe
(usually,
iseye
than
theadding
other. the
In
the
general
with
astigmatic
lenses
whose
inone
thelens
right
and
result
toadding
thecase,
leftthe
eye
prescription
results
in -2.00axes
x 180,
choosing
the
weaker
lens)
and
two
prescriptions
together,
may is
not
bedifferential
parallel,using
the
difference
indecomposition
power
between
eyes
may not2.00D
be obvious.
which
prescription.
differential
power,
is therefore,
along 90.
ifthe
necessary,
astigmaticThe
orthe
Stoke’s
construction.
-2.00
Differential prescription
0.00
-2.00 x 180
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Ophthalmic Lenses & Dispensing
Iso-V-prism zone theory
Iso-V-differential-prism zones
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Consider the prescription:
R +1.50 /+2.00 x 135
L +3.50 / +2.00 x 105
The differential
is found,
before,
by/ changing
the sign
We find:
-1.50 / -2.00
+ +3.50
+2.00
Soprescription
the differential
Rxx 135
= as
+1.00
/ +2.00
x 75 x 105
of the power in one eye and then adding the two prescriptions together.
the general
case,
thedescribed
direction
the iso-V-differential
prism zones
Using the In
graphical
construction,
earlier,
for
locating iso-V-prism
= +2.00
x 45 + of
+2.00
x 105
band
may not
with either
cylinder
we find in this
instance
thatcoincide
the 2 zones
are bands
32axis
mmdirection.
wide lying along 24º.
= +1.00 / +2.00 x 75
24º
32mm
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Ophthalmic Lenses & Dispensing
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Ophthalmic lenses and dispensing
This presentation was created by Professor Mo Jalie
© Reed Educational and Professional Publishing Ltd 1999
© Original articles, Optician
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Ophthalmic Lenses & Dispensing