The document discusses the keratometer, an instrument used to measure corneal curvature. It describes two main designs (Bausch & Lomb and Javal-Schiotz) and how they work. Proper alignment of mires is important for accurate readings. Readings provide information on corneal shape, astigmatism, and pathology. Sources of error include the instrument, operator technique, and patient factors. Attachments like the Lensco-Meter are used to calibrate the instrument and measure contact lens back optic zone radius.
Overview of keratometers: definitions, alignment, functions like measuring corneal curvature, astigmatism, and more.
Steps and techniques to perform keratometric readings, including accurate measurements, recording, and interpreting findings.
Identifies potential sources of inaccurate keratometric readings, addressing errors from instruments, operators, and patients.
Describes keratometer attachments, their functions like calibration and measuring curvatures, including Lens Co Meter and Topogometer.
Introduction to the Radiuscope, its advantages and disadvantages, and its applications for measuring rigid lenses.
Details about the relationship between MOR and contact lens prescriptions, various types of prescriptions, and relevant problems to calculate new powers.
Contact lens theory1 – Course 2
19/30/2020 Tatiana Mighiu
TOPIC
1. Instrumentation
1.1 Keratometer
1.2 Radiuscope
2. MOR as it relates to contact lens fitting
Readings:
N.Efron – Contact Lens Practice
Clinical instruments page 55-56
2.
Contact lens theory1 – Course 2
1.1 Keratometer ( Ophthalmometer )
The keratometer is a diagnostic instrument used to measure the central
curvature of the anterior surface of the cornea.
There are 2 different designs of keratometers on the market. Some are
based on Bausch & Lomb principles (Fig. 1) and the others are based on
the Javal-Schiotz principles (Fig. 2).
Fig. 1 Fig 2
29/30/2020 Tatiana Mighiu
Contact lens theory1 – Course 2
Keratometric mires alignment for the Javal-Schiotz keratometer
(www.ciom.it)
Aligned Misaligned
49/30/2020 Tatiana Mighiu
5.
Contact lens theory1 – Course 2
Keratometer Functions
a. Corneal apex measurement (aprox 3 mm in diameter)
- used to determine the contact lens base curve selection
- used to monitor any corneal changes
- detect contact lens surface irregularities or poor lens wetting
b. Amount of corneal astigmatism is determined
(as difference between the horizontal and vertical readings)
c. Nature and axis of astigmatism is determined
WTR – flatter meridian is in the horizontal meridian
ATR – flatter meridian is in the vertical meridian
Oblique – axes between 70°- 90° and 110°-160°
Irregular – axes are not 90° apart and can’t take accurate readings
59/30/2020 Tatiana Mighiu
6.
Contact lens theory1 – Course 2
d. Determine the nature of ametropia
- AXIAL - high myopia with low keratometric readings
- REFRACTIVE – high myopia with high keratometric readings
e. Assess corneal edema(mires will appear watery)
f. Assess dry eye (mires will appear broken, not clear)
g. Assessment of tear layer by evaluating the mires after blink
69/30/2020 Tatiana Mighiu
7.
Contact lens theory1 – Course 2
h. Assessment of the fit of a soft contact lens by evaluating the
mires after the blink
- clear mires – steep fit
- blurry mires – flat fit
i. Assessment of the flexure of a rigid contact lens
(rigid lens bends on the eye with blinking)
j. Measurement of a rigid lens curvature (BCOR, FCOR) with the
use of accessory devices ( E.g. : conta-check)
k. Diagnosis of pathology
(E.g. keratokonus – very steep curves, corneal ulcer, pterygium,
scarring – distorted mires)
79/30/2020 Tatiana Mighiu
8.
Contact lens theory1 – Course 2
B&L Keratometer parts and principle
Parts:
Lock
Focusing knob
Height elevation
knob
Canthus
marker
Meridian
axis drum
and scale
Horizontal
drum and
scale
Vertical
drum and
scale
Occluder
Chin rest
Head rest
Eyepiece
89/30/2020 Tatiana Mighiu
9.
Contact lens theory1 – Course 2
The B&L Keratometer is calibrated in diopters.
Range of the B&L Keratometer 36.00D to 52.00D.
B&L Keratometer assumed corneal refractive index of
1.3375.
99/30/2020 Tatiana Mighiu
Contact lens theory1 – Course 2
Steps in taking K readings:
Adjust
the
eyepiece
Position
patient
- with the
chin in the
chin rest
and with
the head
firmly
against the
head rest
Position
yourself
Align the
instrument
in front of
the right eye
Occlude left
eye (if not,
the right eye
is not
looking
directly at
the
instrument
Instruct
patient to:
- keep eyes
wide open
and blink
normally
-do not move
or speak
-look at the
reflection of
own eye in the
instrument
Adjust
focusing
knob
119/30/2020 Tatiana Mighiu
Contact lens theory1 – Course 2
To accurately read central corneal curvature MUST:
1. Superimpose the doubling mire.
2. Rotate keratometer body until horizontal + signs
of lower and center mires are on the same
plane and read axis.
3. Adjust until + signs coincide and then read
power on the horizontal drum.
4. Adjust until “-” signs coincide and read power.
Re align instrument in front of the left eye and
repeat procedure.
139/30/2020 Tatiana Mighiu
14.
Contact lens theory1 – Course 2
Patient side Practitioner side
(www.dfv.com)
9/30/2020 Tatiana Mighiu 14
15.
Contact lens theory1 – Course 2
Horizontal mires in spherical vs astigmatic corneas
9/30/2020 Tatiana Mighiu 15
Horizontal mires Vertical mires
─ ─
+ ++ +
─ ─
- Vertical alignment of “+” signs
- Tips of “+” signs are on the same horizontal
line
Since the tips of the “+” signs are aligned the
axis can be read from the axis wheel
To read the horizontal meridian the horizontal
meridian drum has to be rotated as to
superimpose the 2 horizontal “+” signs
─
─
+ + +
+ +
─
─
- Vertical misalignment of “+” signs
- Tips of “+” signs are NOT on the same
horizontal line
Since the tips of the “+” signs are not aligned
the axis wheel has to be rotated until the tips
of the “+” signs align and then the axis can be
read from the axis wheel
To read the horizontal meridian the “+” signs
have to be now superimposed.
16.
Contact lens theory1 – Course 2
Superimposed horizontal and vertical mires
9/30/2020 Tatiana Mighiu 16
Spherical cornea Astigmatic cornea
Horizontal mire Doubling mire
─ ─
+ + +
─ ─
- Horizontal meridian drum has been rotated
and the “+” signs between the mires are
superimposed.
─
Vertical mire
+ + +
─
Doubling mire + +
─
- Vertical meridian drum has been rotated
and the of “- ” between the mires are
superimposed
17.
Contact lens theory1 – Course 2
Recordings and interpretation of findings
Normal corneal curvature readings are between
41.00 - 46.oo D
Average corneal curvature is between 43.00D - 44.00D
Associated
with myopia
Ex: 41.00D
STEEP CORNEAS
Associated
with
hyperopia
Ex: 46:00D
FLAT CORNEAS
179/30/2020 Tatiana Mighiu
18.
Contact lens theory1 – Course 2
Recordings and interpretation of findings
Recordings
a. Generally the horizontal meridian is recorded first at its axis
followed by the vertical meridian at its axis.
If astigmatism is regular horizontal meridian value is
recorded first and is followed by the vertical meridian value
at its axis.
b. Values can be recorded in diopters or millimeters.
Most common is to have them recorded in diopters as
42.75@180/43.75@090 or 42.75/43.75@090 or written in
millimeters as 7.89/7.71@090
For accuracy 3 readings MUST be taken and the mean
value recorded. The 3 readings should be within 0.25D in
each principal meridian.
9/30/2020 Tatiana Mighiu 18
19.
Contact lens theory1 – Course 2
Recordings
Writing the corneal astigmatism in sphero-cyl form
E.g. OD 40.50D @ 180 / 43.50@090
From the K readings, the difference between the horizontal meridian
and the vertical meridian represents the amount of corneal
astigmatism.
Corneal astigmatism is 3.00D
a. Minus cylinder (-)cyl – the axis is the axis of the lower dioptric
power
-3.00 x 180
b. Plus cylinder (+) – the axis is the axis of the highest dioptric power
+3.00 x 90
9/30/2020 Tatiana Mighiu 19
20.
Contact lens theory1 – Course 2
Interpretation of findings
209/30/2020 Tatiana Mighiu
E.g.1 42.00@180/43.75@090
- the flatter meridian is at 180°, therefore the nature of astigmatism
is WTR
- the amount of corneal astigmatism is 1.75D
- astigmatism is regular because the axes are 90° apart
E.g.2 44.62 @165/43.25 @075
- the flatter meridian is at 75°, therefore the nature of astigmatism is
ATR
- the amount of corneal astigmatism is 1.37D
- astigmatism is irregular because the axes are not 90° apart
E.g. 3 45.00/46.37@60
- the flatter meridian is at 150, therefore the nature of astigmatism is
Oblique
- the amount of astigmatism is 1.37D
- astigmatism is regular because the axes are 90° apart
21.
Contact lens theory1 – Course 2
Sources of inaccurate readings
Instrument
• From instrument own construction
- uses para-axial theory
- assumes cornea is sphero-cylindrical
- assumes focal length = image distance
• Inadequate instrument calibration
- cross-reticle is of center – measurement taken will not be
of corneal apex
- the drum readings do not match steel ball readings –
instrument can be recalibrated or error be taken into
readings recordings
219/30/2020 Tatiana Mighiu
22.
Contact lens theory1 – Course 2
Operator
- uncorrected refractive error – will cause fluctuating
accomodation (check own vision and eyeglasses if done
properly)
- not focusing the eyepiece properly – can induce an error up
to 1.00D (make sure the focusing steps are done properly)
- incorrect measurement technique
- the tips of “+” signs are not aligned – axis off
- “+” signs not superimposed horizontal reading off
- “-” signs not superimposed – vertical readings off
- inaccurate readings (do not read measurement properly
from the drums or axis wheel)
229/30/2020 Tatiana Mighiu
23.
Contact lens theory1 – Course 2
Patient
- has fixation problem (ensure that the eye not measured is occluded)
- has corneal abnormalities
- irregular cornea (mires will not superimpose) – can’t take accurate
readings
- inadequate or excessive tear film (broken or watery mires) - ask
patient to blink several times before taking the measurement
- ointment on cornea
- eyelid or eyelashes interference (ask patient to open the eyes wider)
As a general rule the keratometer readings are taken at the beginning of
the pre-fitting protocol before bio-microscopy and ocular tests (tear film
evaluation and ocular staining)
239/30/2020 Tatiana Mighiu
24.
Contact lens theory1 – Course 2
4.Keratometer attachments
a. Lens Co Meter – is a steel ball of known radius
The steel balls have the following radii with the
corresponding K values:
Radii K
7.14 mm 47.25 D
7.54 mm 44.75 D
7.94 mm 42.50 D
8.38 mm 40.25 D
8.73 mm 38.62 D
9.13 mm 37.00 D
USES:
- to calibrate the instrument
- to measure the optic radius of a gas permeable lens
only
249/30/2020 Tatiana Mighiu
Contact lens theory1 – Course 2
279/30/2020 Tatiana Mighiu
Question 1
What will be the reading error of a keratometer,
if readings of 44.67@180/44.87@090 where
recorded when a 44.75D steel ball was
measured?
28.
Contact lens theory1 – Course 2
.
b. Con Ta Check
- is a mirror that
holds a lens
with a known
radius
• Used to:
- calibrate instrument
- check the front and
back curve of a rigid lens
289/30/2020 Tatiana Mighiu
29.
Contact lens theory1 – Course 2
c. Inns Disc
– keratometer attachment used to extend the range of the instrument
to +30.00 D….. +61.00D
How it works:
A spherical lens is placed over the aperture on the front of the keratometer
(that side facing the patient), the normal range of 36.00 D to 52.00 D can be
extended.
A +1.25 sphere extends the range of the keratometer 9.00 D to 61.00 D
A -1.00 sphere extends the range an additional 6.00 D flatter to 30.00D
299/30/2020 Tatiana Mighiu
30.
Contact lens theory1 – Course 2
d. Topogometer
- attachment used to measure larger areas of the cornea
- has a vertical and horizontal scale attached to the front of
the keratometer
- has been used in the analysis of keratoconic cornea
How it works:
- the patient looks on the target and the instrument is
focused on the central keratometry reading, the target
can be moved laterally along the track until the focused
reading begins to change
- an optic cap zone can be calculated and a nomogram is
used to assess the lens design
309/30/2020 Tatiana Mighiu
Contact Lens Theory1 Course 10
2.Radiuscope
(Optic Spherometer or Binocular Digital Radius Gauge)
Advantages - more accurate than the keratometer
- simple to use
Disadvantage - costly
32
Optical system used in conjunction with a
microscope to measure the curvature of a
surface in radius of millimeters
Uses Drysdale method
9/30/2020
33.
Contact lens theory1 – Course 2
Radial target as seen looking through the microscope
Objective lens
Real image
Aerial image Concave lens mount
339/30/2020 Tatiana Mighiu
34.
Contact lens theory1 – Course 2
Radiuscope uses
349/30/2020 Tatiana Mighiu
a. Measures the base curve of rigid lenses
(using the concave lens mount)
b. Measures the convex radius of a spherical rigid lenses
(using the concave lens mount)
c. Measure of a secondary (peripheral) curve
d. Lens inspection ( edge thickness, scratches)
e. Determine lens warpage
35.
Contact lens theory1 – Course 2
Verification of a rigid contact lens
359/30/2020 Tatiana Mighiu
Contact lens theory1 – Course 2
2. MOR as it relates to contact lens fitting
Types
379/30/2020 Tatiana Mighiu
1. Rx is spherical
MOR is spherical
2. Rx is sphero-cylindrical
MOR is spherical
3. Rx is sphero-cylindrical
MOR is sphero-cylindrical Axes 90 apart
4. Rx is sphero-cylindrical
MOR is spher0-cylindrical Axes NOT 90° apart
38.
Contact lens theory1 – Course 2
1. RX is a spherical prescription
MOR is a spherical prescription
The MOR is added algebraically added to the Rx
E.g.1 Rx +2.25 D E.g.2 Rx -4.00 D
MOR +0.50 D MOR +0.75 D
______________ _____________
New Rx + 2.75 D New Rx -3.25 D
389/30/2020 Tatiana Mighiu
39.
Contact lens theory1 – Course 2
2. Rx is a sphero - cylindrical prescription
MOR is a spherical prescription
The MOR is added algebraically to the spherical
portion of the Rx
E.g.1 Rx -3.25 – 0.50 x 90
MOR +0.75
___________________
New Rx -2.50 -0.50 x 90
399/30/2020 Tatiana Mighiu
40.
Contact lens theory1 – Course 2
3. Rx is a sphero – cylindrical lens
MOR is a sphero-cylindrical lens
Axes 90° apart
The RX and MOR are transposed so that both axis are
the same and then the prescriptions are added
algebraically
Step 1. Transpose MOR so that axis is the same
with Rx
Step 2. Add Rx prescription to the transposed
MOR
409/30/2020 Tatiana Mighiu
41.
Contact lens theory1 – Course 2
E.g.1 Rx -2.00 -1.25 x 180
MOR +0.25 -0.50 x 90
Step 1 Transpose MOR axis at 180 as original
prescription
-0.25 + 0.50 x 180
Step 2 Add Rx with transposed MOR
Rx - 2.00 - 1.25 x 180
New MOR - 0.25 + 0.50 x 180
_______________
New Rx -2.25 – 0.75 x 180
419/30/2020 Tatiana Mighiu
42.
Contact lens theory1 – Course 2
4. Rx is sphero-cylindrical lens
MOR is a sphero-cylindrical lens
Axes NOT 90° apart
Step 1 -Transpose Rx and MOR into a “+” cyl form
Step 2 - Prescription with the axis closest to “0” is A
Step 3 - Determine δ as the difference of the 2 axis
NEW CYLINDER
Step 4 - Calculate the resultant cylinder with the formula:
__________________________
Rcyl = √ A2
cyl + B2
cyl + 2Acyl Bcyl cos 2δ
429/30/2020 Tatiana Mighiu
43.
Contact lens theory1 – Course 2
NEW SPHERE
Step 5 – Calculate the added sphere with formula:
Acyl + Bcyl – Rcyl
s = ---------------------
2
Step 6 – Calculate the new sphere with formula:
New sphere = A sph +B sph + s
439/30/2020 Tatiana Mighiu
44.
Contact lens theory1 – Course 2
NEW AXIS
Step 7 – Determine added axis φ from the following
formula
Bcyl sin 2δ
sin 2φ = ──────
Rcyl
Step 8 – Determine New axis with formula:
New axis = Acyl axis + φ
Step 9 – Write the new Rx in (-) cyl form
449/30/2020 Tatiana Mighiu
45.
Contact lens theory1 – Course 2
Homework 2 MOR Problems
1. A patient has the following spectacle prescription refracted at 10 mm
Rx OD - 2.75 + 1.00 x 045
OS - 3.25 + 1.00 x 065
He is fitted with contact lenses and the best visual acuity was
achieved when the following MOR was performed
MOR OD -0.50 + 0.75 x 135
OS +0.50 – 0.75 x 155
Calculate the new power required to fit this patient with contact
lenses. Give your answer in (-) cyl form and round to 1/8 of a
diopter.
459/30/2020 Tatiana Mighiu
46.
Contact lens theory1 – Course 2
2. A patient has the following spectacle prescription refracted at 10 mm
Rx OD - 5.75 - 2.00 x 180
OS - 6.25 - 1.75 x 168
He is fitted with contact lenses and the best visual acuity was
achieved when the following MOR was performed
MOR OD -0.75 + 0.75 x 090
OS +0.25 + 0.75 x 078
Calculate the new power required to fit this patient with contact
lenses. Give your answer in (-) cyl form and round to 1/8 of a
diopter.
469/30/2020 Tatiana Mighiu
47.
Contact lens theory1 – Course 2
3. A patient has the following spectacle prescription refracted at 10 mm
Rx OD + 3.75 + 1.00 x 045
OS + 6.25 + 1.00 x 065
He is fitted with contact lenses and the best visual acuity was
achieved when the following MOR was performed
MOR OD -0.50 + 0.75 x 80
OS +0.50 – 0.75 x 120
Calculate the new power required to fit this patient with contact
lenses. Give your answer in (-) cyl form and round to 1/8 of a
diopter.
479/30/2020 Tatiana Mighiu
48.
Contact lens theory1 – Course 2
4. A patient has been fitted with a contact lens with the following
power +15.75 -3.00 x 180. His visual acuity was not satisfactory with
this contact lens and he was over refracted and found that his
VA will be substantially improved if a contact lens that will carry an
additional power of plano +1.75 x 140 will be ordered.
What would be the power of the contact lens that has to be
ordered?
489/30/2020 Tatiana Mighiu
Editor's Notes
#3 Bausch & Lomb Keratometer
- one position instrument with variable doubling system
the object has a fixed size and the doubling system is varied until the image is displaced through its exact height
reflected rays are passed through a disc with 4 apertures
two prisms aligned perpendicular to the other will allow the measurement of the major and minor axis powers independently without adjusting the orientation of the instrument
depending on the model the readings are available in:
- dioptric form
- millimeters and dioptric form
Javal-Schiotz Keratometer
two position instrument with a fixed doubling system
the predetermined amount of doubling is incorporated and the mire moved until the image produced is of the predetermined height
measure the corneal curvature in only one meridian at a time and needs to be rotated by 90o to measure the second principal meridian
the mires are of two different colors so that any overlapping of the mires produce a change in the mire color
#10 Cornea acts as a highly convex mirror.
The reflective properties of the cornea are used to measure its radius of curvature.
By altering the focal length of the eye piece a very accurate reading of the apex of the cornea can be taken.
The mire pattern is tripled by the optical system of the keratometer to appear as 3 rings.
The focusing knob moves the keratometer closer or farther from the cornea to reach a fixed distance.
Lower right ring is doubled when out of focus, when the ring becomes single and in focus it is compared to the size of the image reflected from the corneal surface.
Mires superimpose by turning the horizontal and vertical drums.
If horizontal and vertical signs are superimposed no corneal astigmatism is present on the cornea.
For an astigmatic cornea the horizontal and vertical signs do not superimpose at the same setting.
The flatter the cornea the longer the radius of curvature (the mires will appear larger) resulting in a lower power for the eye optical system.
The steeper the cornea the shorter the radius of curvature (the mire will appear smaller) resulting in a higher power for the eye optical system.
#33 Drysdale method
- the image formed by a curved mirror is in the same plane as the object when the object is at the center of curvature of the surface (because
the reflected light returns along its own path)
an image may also be formed on the surface and the distance between the 2 images is equal to the radius of the surface (can be measured)
Nidek Radiuscope
The microscope projects an image of a radial line pattern target to a position about 1 cm below the microscope objective (this position coincide with the position at which the object must be, to be seen clearly by the observer).
When the microscope is focused on the concave surface of a rigid contact lens, first position, the observer will see both the surface of the lens and the target that is projected through the microscope in focus.
Moving the microscope down, a second position is found at which the projected target is again in focus.
This happens when the rays of the projected target are reflected back along their own paths. Another image called “aerial image” is formed.
The distance that the microscope must be moved from the first focus on the lens surface to the second “aerial image” equals to the radius of curvature of the lens surface.
Other radiuscope models work in reverse. The real image is when the radiuscope table is in a lower position and the “aerial Image” is closer to the objective lens.
#34 How the concave radius of curvature of a spherical hard contact lens is measured?
Procedure is given for the NIDEK radiuscope used in the contact lens lab.
Step 1. Set radiuscope voltage at 5.0 V
Step 2. Prepare the lens for measurement
- clean well and dry the contact lens
- place a drop of water or saline in the depression of the concave lens mount
- gently place the lens on the concave lens mount
Step 3. Turn instrument ON.
Step 4. Fully lower the microscope objective using the adjustment knob while moving the stage so that the light coming from the microscope is
centered on the contact lens
Step 5. Fully rise the objective
- looking into the eyepiece will observe instrument light filament and then the radial target
- bring the target into its sharpest focus using the focusing knob
Step 6. When target is sharp in focus set the instrument gauge to “0”
Step 7. Slowly lower the instrument
- the instrument filament will be seen again, continue lowering the instrument until the radial target is seen again
Step 7. Turn the focusing knob until the second radial target is clear and sharp in focus
Step 8. Read the radius of curvature on the instrument gauge
E.g. First setting (real image) index line 0.00
Second setting aerial image) index line 6.42
Radius of curvature 6.42
Step 9. For accuracy take 3 reading and record the mean as your final answer.
#35 To measure the convex radius of a rigid lens same procedure as for concave surface is used, but the positions of the real and aerial images are reversed.
The radiuscope measures the apparent thickness (real thickness = apparent thickness x index of refraction)
The procedure for measuring toric base curves is slightly different
Start by focusing the real image and then the table is lowered until one meridian is seen.
The lens mount is then rotated slowly until one meridian is sharp in focus
After that the instrument is raised again, focused on the real image and dial gauge set to “0”.
The instrument is lowered again until the first line meridian is seen sharp in focus and the value on the gauge is
recorded
Continue lowering the instrument until the second meridian line comes in focus. Note that this line is 90 degrees to the
first one. Record second reading.
The lowest reading will indicate the steepest curve, the higher reading will indicate the flattest curve.
#42 E.g. 2
A patient receives the following prescription for new eyewear
OD - 1.75 -2.25 x 65
OS - 2.00 -0.75 x 124
After the glasses were made patient complains of visual discomfort. He is sent to his doctor and comes back with the following adjustment to the prescription
MOR OD -0.25 - 0.75 x 155
OS +0.25 + 0.50 x 34
Determine what is the new prescription that has to be filled for this patient.
Step 1. Transpose MOR to the axis of the RX
OD - 1.00 + 0.75 x 65
OS + 0.75 - 0.50 x 124
Step 2 Add MOR to the Rx
RX OD -1.75 - 2.25 x 65 OS -2.00 - 0.75 x 124
MOR OD -1.00 +0.75 x 65 OS +0.75 - 0.50 x 124
_________________ _________________
OD -2.75 -1.50 x 65 OS -1.25 - 1.25 x 124
New Rx OD -2.75 - 1.50 x 65
OS -1.25 -1.25 x 124
#45 E.g. Rx +9.75 -2.50 x 180
MOR -0.50 +0.50 x 80
Step 1. Transpose both Rx and MOR in (+) cyl form
Rx + 7.25 + 2.50 x 90
MOR -0.50 + 0.50 x 80
Step 2. Choose prescription with lower axis as A
A -0.50 + 0.50 x 80
B +7.25 +2.50 x 90
Step 3. δ = B axis – A axis
= 90° - 80° = 10°
2δ = 2x10° = 20°
Step 4. Determine resultant cylinder
_____________________________
Rcyl = √(+0.50)2+(+2.50)2 +2(0.50)(2.50)cos20
____________________
= √+0.25 + 6.25 + 2.5 cos20
____________________
= √+6.50 +2.5(0.93969262)
__________
= √8.849231552
Rcyl = +2.975 D ~ +3.00D
Step 5. Calculate the added sphere with formula Acyl + B cyl – Rcyl +0.50 +(+2.50) – 2.975 +0.025
s = ---------------------- = ----------------------------- = --------
2 2 2
s = +0.0125 D
Step 6. Calculate the new sphere
New sphere = A sph + B sph + s
= - 0.50 +7.25 +0.0125
= + 6.7625 D
New sphere = + 6.75 D
Step 7 Determine added axis φ
B cyl sin 2δ +2.50 sin20° +0.855050358
sin2φ=---------------- = --------------- = ----------------
Rcyl +2.975 +2.975
sin2φ = 0.287411885
2φ = 16.70°
φ = 8.35°
Step 8 Determine the new axis
New axis = A axis + φ
= 80°+ 8.35°
= 88.35°
New axis =88.35°~ 88°
Step 8. Write the new prescription in (-) cyl form
+6.75 +3.00 x 88
+9.75 -3.00 x 178