1. science
2. physics
3. optics

Course OPTO 253
(Ophthalmic Optics I)
Dr. Ashraf Eldakrouri
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Course Grades
Mid term 1
Mid term 2
Final
Quizzes
Attendance
Lab
total
20
20
40
5
5
10
100
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Course Index
Lecture Number
Brief outlines
Lecture 1
Introduction: Sign Convention; Nomenclature Notations
Lecture 2
Ophthalmic Lens Materials (1): Manufacture of optical Glass;
Lecture 3
Ophthalmic Lens Materials (2): Plastic Lenses; manufacturing processes for plastics
Lecture 4
Ophthalmic Lens Materials (3): CR39; Polycarbonates; Corlon lenses
Lecture 5
Power Specification and Measurement (1): Approximate power; Back vertex power and front
vertex power
Mid –Term Exam 1
Lecture 6
Power Specification and Measurement (2): Equivalent power; Effective power; Worked
problems; Correction of homework problems;
Lecture 7
Form of a lens: Flat Lens; Curved lens (meniscus lens); periscopic lens;
Lecture 8
Power Measurement
Lecture 9
Identification of Lenses
Lecture 10
Transposition: Rules transposition; worked problems
Mid –Term Exam 2
Lecture 11
Lens Power & Thickness: Sagitta Formula; Ophthalmic prisms and decentration (1):
Prentice's rule
Lecture 12
Ophthalmic prisms and decentration (2): Solved problems; Prismatic effects of cylindrical
lenses;
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Specification of Lens and Frame Sizes; Decentration; Risely and Fresnel prisms
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Lecture 13
Lecture 1
Introduction
• 1- Sign Convention
• 2- Nomenclature (naming System)
• 3- Notations
• 4- Ophthalmic lens materials
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1- Sign Convention
•
The sign convention rule that used in the optics field will be
1- incident light will be consider as traveling from left to right +
2- all distance that measured in the optical system concerned the following
a) if it is measured in the same direction of the incident light will be Positive
+
b) it is measured in the opposite direction of the incident light , it will be consider as
negative 3- Vertical distance above the optical axis is positive and the one below is negative
4- The angle between the ray and the optical axis is measured from the ray to the optical
axis
5- Angles of incidence, reflection, and refraction are measured from the normal to the ray
6- angle measured in the counterclockwise is positive and the one in clockwise is negative
7- An arrowhead on a line or curve fixing the limit of the distance or angle being measured
indicates the direction in which that distance or angle is being measured
8- Vergence is the spread of light rays at a specific distance from the focal point
9- light moving towards the focus is consider as a converging ( +)
10 – Light moving away from the focus is consider as a diverging (-)
11- the measuring unit of vergence is the Diopter. The vergence of a particular ray system
is the reciprocal of the distance from the wave-front to the center of curvature (focus),
in meter
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2- Nomenclature (naming System)
1- A ray
it is an imaginary line extending from the focus to the
wave-front. It represents the direction of propagation of
the wave-front.
2- A pencil of light
it is a bundle of rays emanating from a point source after
passing through a limiting aperture ( pinhole effect)
3- A beam of light
it is a collection of pencils arising from an extended
(infinite-sized) source, or from a source of finite size
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4- Object
it is a physical source of light, or no light, existing in
object space and it is divided to
a) real object is from which the light rays diverge or
are reflected from
b) Virtual object is one towards which light is
converging before interruption by the surface of an
optical system
5- Image
It is the projection of an object in image space. It is
formed by light traveling from an object, in image space,
after an optical system has acted on the light it is divided
to two different types; Real image and virtual image.
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6- Real image
It is formed by the actual convergence of rays reflected or refracted
by an optical system. A real image can by caught on a screen it the
screen placed in the image space ( the focus).
7- Virtual Image
it is formed by the light divergence from point in the optical system.
The virtual image can’t caught on the real screen until it changed to
a real image.
8- Object space
it is related to all the space in which light has traveled before being
interrupted by the optical system.
9- Image Space
This is the space within which light travels after being acted upon by
an optical system.
The Primary (object) applies to points in object space.
The secondary (Object) applies to point in image space.
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• Ophthalmic Lens Materials
Before 300 years ago all lenses is made from glass. But from 300
year till 1938 the virtually single vision lenses were made from
particular variety of glass known as ophthalmic Crown glass which
has an index of refraction of 1.523.
For any refracting material with a uniform refractive index the power to
bend light rays increases with the thickness of the material. Also ,
assuming a uniform thickness of different refracting materials, the
material with the highest refractive index will refract light more
powerfully.
Other varieties of glass like flint glass were first used for special
purposes such as for making reading segments in bifocals.
Recently high index lenses have pervaded the market for general use in
single vision, bi and multi focal lenses.
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Chapter 2
Manufacture of optical glass and
lenses
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Lecture 2
•
•
•
•
•
•
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Manufacture of optical glass
Types of optical glass
Qualities of ophthalmic glass
Plastic lenses
Manufacture processes for Plastic
Optical and Physical properties of plastic
Ophthalmic lenses (CR-39)
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Optical glasses: fabrication and optical
properties
What is optical glass?
Optical glass is optically homogeneous glass, free from
defects such as striae and bubbles, which is used with
optical functionalities, for example in the form of lenses or
prisms.
Types of optical glass
The first optical quality (flint) glasses were developed by
Otto Schott (in Jena, Germany), around 1890, who also
invented Bacrown glass, enabling the fabrication of lenses
corrected for chromatic aberration.
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The compositions of the more traditional optical glasses are
usually based on multi-component silicates, including
heavy elements such as Pb, Ba, La, Gd, Ta and Nb. The
basic compositions usually fall into two categories:
(1) high dispersion flint glasses (normally containing PbO);
(2) low dispersion crown glasses (often containing Ba or
La).
Such optical glass series can be conveniently represented on
a plot of the refractive index (e.g. nd, the glass refractive
index for the d line of He at 587.6 nm, or nD, the index for
the D line of Na at 589.3 nm) as a function of dispersion
(or the change in index with the wavelength of light,
usually represented by the reciprocal dispersion or Abbe
number, νd= (nd-1)/(nF-nC), with F and C corresponding
to the F and Clines of hydrogen, at 486.1 nm and 656.3
nm, respectively). The refractive index difference (nF-nC)
is called the mean dispersion.
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The main Varieties of glass are:
1- Ophthalmic Crown
2- Flint Glass
3- Barium Crown Glass
1- Ophthalmic Crown is made of 70% Silica (sand), 14-16% Sodium Oxide,
11-13% Calcium Oxide and 1-5% of Potassium, borax, antimony and
arsenic
Ophthalmic Crown is used for the majority of single-vision glass lenses
available today and for the distance portion of most glass bi-and trifocal.
2- Flint Glass is made of 45-65% lead oxide, 25-45% silica and about 10%
mixture of soda and potassium oxide.
Flint glass has a higher refractive index than ophthalmic crown. It is used
mainly for bifocal segments in some fused bifocals.
3- barium Crown Glass is made of 25-40% barium oxide and the result is
silica and Potassium oxide.
The barium is increasing the refractive index like the lead oxide but does
not increase the chromatic dispersion as much as lead oxide does.
It is mainly used for the segment portion of a specific type of fused bifocal.
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• Table 2.1 optical properties of high index glass
as compared with ophthalmic crown
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Glass
Ref. Index
Ophthalmic
Crown
1.523
NU Value Specif.
Gravity
58.9
2.54
Dense Flint
1.616
38.0
3.53
Extra-dense
Flint
Barium Crown
1.690
30.7
4.02
1.701
31.0
2.99
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• How do you change the lenses color?
• Adding metallic oxide to the raw materials makes glass for
absorptive lenses, Example
1- Cobalt oxide results to a blue lens
2- Chromium oxide causes a green lens
3- magnesium oxide causes a violet lens
4- Uranium oxide causes a yellow lens
5- Cerium Oxide have UV absorption properties
6- Iron absorbs IR radiation
7- Photo-chromic lenses contain Silver halide crystal that
make the lens material in excited case by absorbed the UV
radiation so it change the lens to the dark color
the Silver halide will lighten the lens in absence of UV
excitation.
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• Desirable Qualities of Ophthalmic Glass
1- Homogeneity in both chemical and physical composition
2- Correct refractive index and chromatic dispersion values
3- freedom from color
4- A high degree of transparency
5- A high degree of chemical and physical stability
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Manufacture of Optical glass
• The glass is melting at high temperature so it is need a very careful
technique to get the lens at the end. The important thing is that
1- the whole glass showed reach the melting point at the same time
2- the glass showed start to cooling until reach the cooling temperature at
the same time
3- the glass ingredient almost oxides or salts of metals, including silica,
sodium, potassium, calcium and aluminum.
Types of manufacture techniques
1- continuous flow process is the nowadays technique.
2- batch process technique is the old one
1- continuous flow process
In this method, the glass is not poured into sheets but is automatically
extracted by a continuous process, and pressed into molds that form
the rough blanks.
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2- the batch process technique:
1- the ingredient are put into a large melting pot.
2- An addition ingredient cullet ( which is waste glass from
previous melts) is added to preserve valuable raw materials
and to protect the inside of the pot from the corrosive
molten glass
3- the pot temperature is raised to between 800oC and 1000oC
and is kept at that temperature for 3-5 days.
4- the pot is then glazed (protected) by using small pieces of
cullet.
5- The various ingredient ( depend on the type of glass) are
then added at fixed intervals until the temperature of the pot
has risen to about 1400oC.
6- Bubbles of gas escape at these temperature and impurities
such as stones float to the surface of the molten glass and
21 can then be sieved off. The process takes several hours.
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7- the remaining molten glass is stirred constantly by hand or
by a mechanical arm.
8- the molten glass is allowed to cool slowly to a temperature
of 1200oC, then it is poured and rolled into sheets of
various thicknesses.
9- Each sheet is then placed in an oven where it is gradually
cooled to room temperature.
10- The glass is pressed or molded into rough blanks.
11- the rough blanks are inspected and then the first surface
is ground and polished
12- shortly after another inspection, the second surface is
also ground and polished to create an ophthalmic lens of a
particular power.
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Plastic materials
Plastic lenses are generally made from two different
materials. They are:
1. Original plastic lens made of (PMMA) Polymeric materials
( usually organic)
2. Modern hard resin lens from ally1 diglycol carbonate
(CR 39) which is harder and more resistant to scratches than
other plastic lens materials.
Plastic lenses are made from a very high quality material as
glass. Plastic lenses are about half the weight of glass and
are highly impact-resistant. With a center thickness of
3.0mm without special hardening process. Plastic lenses
have a thicker profile than glass, get scratches more easily
and do not protect the eye from UV rays unless properly
tinted. Glass lenses unlike plastic, must be treated to resist
breakage. They can be hardened by chemical or heat
23processes.
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Optical and physical properties of plastic ophthalmic
lenses
• We star with CR39 type
1- CR-39 has a half weight of ophthalmic crown glass with similar prescription and
of identical size
2- they are fairly impact resistant in their natural state
3- CR-39 are very inert and are resistant to almost all solvent and chemicals
except perhaps, highly oxidizing chemicals
4- CR-39 is more resistant than glass to pitting from small hot substances.
5- CR-39 has much lower thermal conductivity than glass and less prone to
fogging
6- Cr-39 lenses can be tinted to almost any color
7- reduces the manufacturing price than glass forms as a result of the material
nature.
Disadvantages
1- it is soft and easy to scratches
2- thicker than crown glass the has the same power although it have fairly low r.i
They have inferior photo-chromic qualities when compared with glass lenses
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• Polycarbonates
• Advantage
1- they are vastly superior to ophthalmic glass and CR-39 in term of
impact resistant
2- it have high R.I (1.586)slightly higher than the ophthalmic crown glass.
3- it have a specific gravity of 1.20 (as compared with 1.32 for CR-39) and
therefore lenses made of this material is the lightest spectacle lenses in
production
4- these lenses are easily tented and an abrasion resistant coating wich
also absorbs uv radiation is applied to both front and back surface.
Disadvantage
1- it has a low nu value ( dispersion or Abbe value) and hence gives rise to
a higher amount of chromatic dispersion than glass or Cr-39
2- the surfaces of polycarbonate lenses are such that it is difficult to mold
them such that imperfections are completely eliminated.
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• Corlon lenses
1- it is a specific type of lens made from plastic and glass
lens
2- the front is glass and the back is plastic
3- these lenses are manufactured as C-Lite lenses.
The advantage
1- it is 25% thinner than conventional lenses.
2- it is 25% lighter than all-glass lenses.
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Manufacturing processes of plastics
• The plastic is separate to two groups depend on the physical properties
of the finished product
1- Thermoplastic Materials
these soften when heated and therefore can be remolded.
2- thermosetting Materials
Once hardened, these plastics can be softened, even at high
temperatures.
1- manufacturing of Thermoplastic
it is called the injection molding
When the thermoplastic heated, it is stretched, pressed or molded into
complex shapes with no apparent chemical change
When it is cooled, it is retain the shape of the container in which ther were
heated
Example: Plexiglas, Lucite, PMMA, cellulose,…etc
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2- manufacturing of Thermosetting
The manufacturing process distinguishing factor from the injection
processing is that the hardening of thermosetting materials is an
irreversible process.
Example: epoxy resins, phenolics (Bakelite) and CR-39 (diglycol
carbonate).
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Chapter 3
Power measurements
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Power Specification and measurements
• The way of an ophthalmic lens, or lens system, can be specified in
many different ways.
1- Approximate Power:
It is specified according to its front and back surface power, without
regard to its thickness
2- Back Vertex Power and Front Vertex Power
BVP and FVP specify power according to the change in the vergence
of rays coming out of the back surface or the front surface of the elns
3- Equivalent Power
it is specified the power of a thick lens system in terms of the power
of a single thin lens.
4- Effective Power
this relates to the change in the power of a lens as it is moved closer,
or further away, from the patient’s eye.
Only BVP used routinely in lab and practitioners. The lensometer is the
measured device for the BVP
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• 1- Power specification
The refracting power is define as the change in vergence that
occurs when light passes through a lens. The unit for
Power measurement is the Diopter.
The term Diopter is used to describe
1- The curvature of a surface
Where the Diopter = 1 / radius of curvature (meter)
2- the curvature of the wave front at a specific distance (r)
from its point source. In this case 1/r is referred to as
vergence.
3- the reduce distance means the actual distance (L) divided
by the refractive index of the medium within which the
distance is measured
Reduce distance R = L/n (m)
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• From 3 point we have
Reduce vergence = 1 / reduce distance
= n/L (m-1)
The Refractive power F is
F = L’ - L
Where L’ : reduce vergence of the object
L : reduce vergence of the image
So
F = n’ /l - n /l = (n’-n) / l
For an object at infinity, l’ = f’
the image neglected
So
F = n’ / f’ = (n’ –n)/r
For image at infinity l = f
F = - n / f = (n’ – n) /r
So
F = n’ / f’ = - n/f
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• From all we define the relation between the surface power , radius of
curvature and the refractive index in
F = (n’ – n) / r
Where n’ is the refractive index of the medium that cause refraction
n is the medium that the light pass through before reach the surface of
the refractor.
In air case the n for air = 1 so
F = (n’ -1) / r
The total approximate power:
the total power will be the power of front surface addition to the power
of the back surface
F1
F = F1 + F2
F2
Where F1 is the front surface
F2 is the back surface
Bothe power measured by the lenso-meter
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The summary
• The equivalent power F is the reciprocal of the focal length measured
in metres. Like the equivalent power of an optically effective surface,
the equivalent power of a spectacle lens is given in dioptres (D).
The surface power is determined by the ratio of the difference
between the refractive indices of two media to the radius of curvature
of this surface. The two surface powers F1 and F2 yield the equivalent
power F of a lens, taking into account the centre thickness t.
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• Back Vertex Power
It is define as the reciprocal of the reduce distance from the back pole of
a lens to its secondary focal point.
F1
A1
A2
\From the figure we have
BVP = 1 / A2F1
There are two equations to calculate BVP
t
FV = [F1 / (1 –t F1 /n) ] + F2 ---------- (1)
Equation 1 is the exact formula for computing BVP
FV = F1 + F2 +F12 t /n ------------- (2)
Equation 2 is the simplified approximate formula for computing BVP
To calculate F1 best use equation 1 to calculate Fv batter use equation 2
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Equivalent, Front vertex, or Neutralizing
Power
• It is defined as the negative of the reciprocal of the
distance from the front pole of the lens to the primary focal
point. It is the FVP of a lens that is neutralized during
“Hand neutralization” of a lens.
• The FVP can be calculated from the following formula
• FN = [F2 / (1 –t F2 /n) ] + F1 -----------------------(3)
• FN = F1 + F2 +F22 t /n ----------------------------- (4)
Equation 3 is the exact formula for computing FVP
Equation 4 is the approximately formula for the FVP
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examples
• 1 ) Given a lens where F1 = +8D, F2 = -9D, thickness = 3mm and
refractive index = 1.6, Find FN, Fv, and FA?
Solution:
FA (approximate power) = F1 + F2
FA = 8 -9 = -1D
FV = F1 + F2 +F12 t /n ---FV = 8 – 9 + (64 x 0.003 / 1.6)
FV = -1 + 0.12 = -0.88D
FN = F1 + F2 +F22 t /n -----FN = 8 – 9 + (81 x 0.003 / 1.6)
FN = -1 + 0.15 = -0.85D
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The equivalent focal power in thick lens
• Sometimes the lens is thick and the two surface is separated by
another medium. This lead us to have a two thin lens.
• Because the separated medium that have different refractive index,
the focal length of the thin lens which will produce the same image
size and image position as the two refracting surfaces is called the
equivalent focal length. This equivalent focal length is define by
FE = 1 / f’E
• Where
FE is the equivalent focal power
f’E is the equivalent focal length (meters)
And because the two surface the equivalent power no more the sum of
F1 and F2 but it has a new relation that
FE = F1 + F2 – (d/n) F1F2
This is the formula for the equivalent focal power for both thin and thick
lenses
Where d is the separation distance between the refractor surface
n is the refractive index of the medium separated them
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• examples
• 1- Given two lenses; +7.5 D and +10D separated by a distance of
14.5mm and the separator Refractive index is 1.336. Find FE, FV, FN
and the position of the principal planes?
• Solving
• FE = F1 + F2 –d/n F1F2
= 7.5 + 10 – (7.5 x 10) x 0.0145 / 1.336
= 17.5 -0.81 = 16.69 D
To find Fv we use
FV = F1 + F2 + F21 t/n
= 7.5 + 10 + (7.5)2 x 0.0145 /1.336
= 18.1 D
FN = F1 + F2 + F22 t/n
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= 7.5 + 10 + (10)2 x 0.0145 /1.336
= 18.6 D
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• you notice that Fv almost equal FN
• to find the position of the principal planes we need to
know the equivalent power
• FE = 1/fE’
fE’ = 1/FE
= 1/16.69 = 0.06 m = 6 cm
fE = - 1/FE = - 6 cm
So we can get
fV = 1/FV = 1/18.1 = 0,055cm = 5.5 cm
fN = -1/ FN = 1/18.6 = 0.054 = -5.4 cm
if e is the distance from the +7.5 D lens to P primary point
and e’ is the distance from +10D lens to P’ Secondary
point
e = fN –fE = -5.4 –(-6) = 0.6 cm
e’ = fV – fE = 5.5 – 6 = -0.5 cm
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• Forms of a lens
• the form of a lens refers to the relationship between the
front and back surface power of a lens
• Assuming that we want to make a +8.00D lens
• we should have one of the following
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F1
F2
F = F1 + F2
+4
+4
+8
+6
+2
+8
+8
0
+8
+10
-2
+8
+12
-4
+8
+14
-6
+8
+16
-8
+8
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Flat Lens
• It is a lens that has both surfaces that are either positive
or negative or one of the surfaces is plano.
• it have three types
• 1- equi-convex
• 2- biconvex
• 3- Plano-convex
Curved Lens (Meniscus Lens)
• It is one that has one positive and one negative surface.
• Qualities of image produced by a curved lens are better
than that produced by flat lens.
• The greater majority modern positive spheres are made
up in curved or meniscus form.
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• Periscopic lens
1- Special type of curve lens
2- A lens that has a surface power equal to +1.25 or -1.25
3- The periscopic form always has a 1.25 base curve
• Best Form lens
A best form lens which has had its surface powers carefully
computed to eliminate or at least minimize the various
peripheral defect or aberration is called a best form
spherical lens.
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Identification of Lenses
• Lenses may be identified according to the following:
1- The type of curve surface
- spherical
- Cylindrical
- Sphero-cylindrical
2- Power
- Magnification $ sign (+ or -)
3- If the lens is astigmatic then we need to specify the axis
direction of the cylindrical component in degrees
• Lenses can be identify with
1- lensometer, lensmeter, focimeter
2- hand neutralization
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Rotation Test
• In this test, the lens is rotated in front of the eye and any
apparent break or discontinuity in the observed line is
noted.
• To do the test follow the following:
1- Hold an unidentified lens close to the eye
2- Observe an optical cross target
3- Rotate the lens
4- Observe portion of the target seen within the outline of
the lens
5- If the lens appear broken, then the lens is astigmatic
6- If there is no apparent break in the line, then the lens is
not astigmatic but must be spherical.
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Astigmatic lenses
(Cylindrical lens or Sphero-cylindrical lens)
• In order to identify an astigmatic lens, we have to
determine whether:
1- The lens is cylindrical or spherical
2- determine the power(s) along the major meridians
3- Determine the axis of the cylindrical component
• To identify an astigmatic lens:
1- do the rotation test
2- determine the major meridians the astigmatic lens
- the astigmatic lens has 2 power meridians: the meridians of highest
powers and lowest powers. Usually both meridians are 90o apart
i) hold the lens before the eye
ii) observe the target
iii) if there is an apparent break in the target, then we are not looking
through the meridians of the lens
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• Follow the identify of the astigmatic lens
iv) Slowly rotate the lens until the line is perfectly vertical or horizontal
v) Mark the position of the line target on the lens
vi) This represents 1 of the major meridians
vii) the other meridian will be 90o away from this position
3- Do the transverse test
i) Do the transverse test as describe above
ii) If there is no power along the l of the meridians, then the astigmatic
lens is a cylindrical lens.
iii) If there is power along both meridians, then the lens is spherocylindrical lens.
• Identification of sphero-cylindrical lens
1- Do the rotation test to identify the lens as astigmatic lens
2- Mark the major meridians of the lens
3- Do the transverse test
4- If there is apparent movement along both principle meridians, then the lens
must be Sphero-cylindrical
5- Do the rotation test to determine the power along the 1st principle meridian.
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• Determination of the cylindrical power
1- Hold the lens close to the eye, so that the major meridians are vertical
and horizontal
2- Move the lens vertically or horizontally along the power meridians
3- Observe the type and magnitude of the apparent movement
4- Select a cylindrical lens of opposite power
5- Align the axes of the 2 lenses
6- Report the transverse test
7- Increase the power of known cylindrical lens until movement in step 6
is neutralized
8- The power of the known cylinder is the same but opposite to that
known cylinder lens.
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• Crossed Cylinders
• The Crossed- Cylinder Form
1- A crossed cylinder lens is one having a plus cylinder
ground on the front surface and a minus cylinder ground
on the back surface, with the axes of the two cylinders
being 90o apart
2- In optometric practice, crossed cylinders are used in
refining the axis and power of the patient’s cylindrical
correction, and are also used for near-point testing (for
example, to determine the power of a tentative bifocal
addition)
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Properties of crossed cylinders
1- 2 cylinders placed together with their axes parallel to one another, can
be replaced by a single cylinder whose power is equal to the sum of
the 2 cylinder powers.
e.g
+1.00DC x 90 +2.00DC x 90 = +3.00DC x 90
2- 2 cylinders of equal power but oppiste sign placed together with their
axes parallel neutralize one another
e.g.
+2.00DC x 90 - 2.00DC x 90 = infinty
3- 2 identical cylinders placed together with their axes at right angles to
one another are equivalent to a sphere whose power is equal to either
of the cylinders
e.g. +1.00DC x 90 +1.00DC x 180 = +1.00DS
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4- Any single cylinder can be replaced by a sphere of the same power as
the cylinder combine with a cylinder of equal but opposite power to
that of the original cylinder with its axis perpendicular to the axis of the
first
e.g.
+2.00DC x 90 = +2.00DS / -2.00DC x 180
5- 2 unequal cylinders placed together with their axes at right angles to
one another can be replaced by a sphere and a cylinder.
e.g.
+2.00DC x 90 +4.00DC x 180 = +2.00DS +2.00DC x 180
(Plus sherocyl form)
+4.00DS - 2.00DC x 90
(minus sherocyl form)
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Transposition
- Cross-Cylindrical prescription can be written in its equivalent spherocylindrical form
- The process of changing from one form to another is known as
transposition
• Rules of Transposition
1- Sphere-Cyl from cross-cyl
- Given: cross cyl form: +1.00DC x 90 + 4.00DC x 180
required: transpose to alternate sherocyl form
Procedures:
a) write either cross cyl as the sphere. +1.00DS
b) subtract the cylinder chosen as the sphere from other cylinder to find the
cylinder power. 4 – 1 = +3.00DC
c) Axis of the cylinder is the same as the axis of x-cyl that was not chosen as
the sphere.
Axis : 180
d) The sphero-cyl form is : +1.00DS +3.00DC x180 or
+4.00DS -3.00DC x 90
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2- Cross Cyl from Sphero-cyl:
- Given: either of the sphero-cyl form (plus or minus)
+1.00DS +3.00DC x 180
- required: transpose to x-cyl form
Procedures:
a) 1st x-cyl = sphere of the sphero-cyl Rx written as a cylinder
with axis at right angle to axis of cyl in sphero-cyl form:
+1.00DC x 90
b) 2nd x-cyl = sum of sphere and cyl from sphero-cyl rx, written as
a cyl with axis the same as cyl in sphero-cyl form:
+1 +3 = +4.00DC x 180
c) x-cyl form:
+1.00DC x 90 +4.00DC x 180
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Chapter 4
Lenses power and the thickness
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Relation between the power of lenses and its
thickness
1- If the power of the lens is above +4.00D the center and
the edge (polar) thickness become important
2- The concave lens (minus) is thick at the edge but the
convex lens (plus) is thick at the center
3- Thick lenses make spectacles look uglier addition to that
the thick centered plus lens (convex) is much heavier.
4- We can avoid the thickness and the heavier by using the
plastic lenses or the high refracted lenses respectively.
So high index plastic lens is ideal fro the lenses that have
power more than 4.00D
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The Sagitta Formula
• The sagitta formula is a means of specifying the curvature of a
surface.
h
h is the chord of the surface
C is the center of curvature
C
s is the sagitta ( distance from any point
On the circle and the midpoint of the chord
r is the radius of the lens curvature
s
The relation between r , s and h math is
r
s = r m (r2 –h2)1/2
(1) Exact formula
s = h2 / 2r
(2) approximate formula
Notice: the approximate formula shouldn’t use with the contact lens
From the power formula
F = (n-1) / r
3
If we replace r in equation 2 by equation 3 we get
s = F h2 / 2(n-1)
4
F = 2(n-1) s / h2
5
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• Sagitta is a measure from the refracting
surface to the chord. It is positive or negative
depend on the low of optics
• If we have a lens with two refractive surface
this means we have two sagitta s1, s2 and d (
chord diameter) and F1 and F2 the
approximate power. So
tc –tp = s1 –s2
Where tc is the center thickness
tp is the edge thickness
S1 and s2 the sagitta of first surface and
2nd surface respectively
From approximate power law F = F1 + F2
We get
tc - tp = FAh2 / 2(n-1)
The following example demonstrates the use of
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this formula
tc
tc
tp
tp
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Ophthalmic prism and descentration
• As we now:
1- Ophthalmic lenses are used to correct anomalies of refraction (
myopia, hyperopia and astigmatism). This occurs by changing the
vergence of light incident on their front surface.
2- in some cases, the prism is used to correct the binocular anomalies (
such as uncompensated exophoria and hyperphoria) . This occurs by
changing the direction of incident light without affecting its vergence.
3- the prism incorporated into the lens by placing its base apex meridian
in the desired direction
A prism may also be introduced by decentering a lens. This is why it is
necessary to measured the Pupillary distance PD accurately so as to
avoid inadvertent lens decentration causing the patient not to look
through optical center of the lens and therefore experience a
disturbing prismatic effect.
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4- In ophthalmic optics, only thin prisms, those of small apical angle, are
important and only rays incident nearly normally are considered. That
simplifies the problem of tracing rays through the prism a lot. The
diagram below shows such a prism. We want to calculate the
deviation, e, of a ray passing through the prism.
5- Let's simplify the calculation by having the ray incident normally on the
first face of the prism. It is not, then deviated by the first face and
strikes the second face such that it makes an angle α with the normal.
It leaves the prism at an angle θ' with the normal. From Snell's law,
n sina=n’sinb
n’
a
n a≅n’b
1
But the angle of deviation e is related to θ' by
b
a
e
b=a+e
2
n
Eliminating θ' from (1) and (2),
e=[(n/n’ )-1]b .
But in the prism case n’ =1 because the front face of the prism in air
e = [n - 1 ] b
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• Notice that
1- the light rays are refracted towards the base but the apparent
displacement of objects is towards the apex
2- the refractive angle is equal to twice the angle of deviation
3- the unit of b can be degrees or radians. E is usually specified in prism
diopters.
Relationships
For small angles , an angle in degrees may be converted into prism
diopters and vice-versa with very little error.
1o = 0.0175 radians = 1.75 centrads
1o = 1.75 D (prism diopters)
1D = 1 centrad
1D = 0.57o
For prism power of 10D or less, it is safe to make the assumption above.
Above 10D it is no longer safe to assume that:
1D = 1 centrad
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Prentice’s Rule
• We can think of a lens as a stack of prisms, each with slightly different
power. Not surprisingly, then, extra-axial points behave as if they had
a prism power as well as a lens power.
We can calculate that prism power from
the diagram below.
Consider a parallel bundle of rays striking
a lens of power F a distance d from the
optical axis. Rays converge to
the secondary focal point. The ray bundle is rotated through an angle e
where
e=−d/f'= d F.
To get the prismatic deviation, remember that prism power P is one
hundred times the angle of deviation in radians so
P=100e=100dF.
If we give d in centimeters we can drop the factor of 100 and write simply
P=d F
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• The following 4 figures show two different system of specifying the
base of a prism induced at an off-center point in an ophthalmic lens.
UP
60
120
UP UP
30
150 out in
120
150
UP 60
UP UP
in
out 30
IN IN
Out
Out
Right eye
Left eye
Down Down
Down
330
Down330
210out
210
in
in
out300
240
240 Down300
Down
• Fig (1) A circle for specifying the base of a prism can be divided into
four quadrant
UP
UP
120
UP
150 out
60
UP
30
in
IN
Out
Right eye
Down Down150
in
30 out
60Down 120
120
150
IN
UP
in
60
UP
30
out
Out
Left eye
Down Down
150
30 in
out
60
120
Down
Fig (2) the engl;ish system for prism base notation using two semicircles
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• Notice:
Induced prisms are important consideration in ophthalmic prescriptions in
the following two circumstance:
1- When single vision lenses are not properly centered so that the patient
doesn’t look through the optical center of the lens
2- In bifocal prescription, the lenses are centered for distance. Since the
PD must decrease for near work, there is an induced prism when the
patient tries to perform near work. This induced prism is base-out for
convex (plus) lenses and base-in for minus lenses
Review the example from the text book
Specification of lens and frame size -----with discused in the lab
Decentration ---- discused in the lab
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