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Visual Optics 2006/2007
Chapter 6
Astigmatism & Subjective Refraction
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Fig. 6.1 - Formation of focal lines by a sphero-cylindrical lens. For parallel incident
light the focal lines fall at the second principal foci .
Image produced by +/+ Spherocylinder Page 6.1
Astigmatism = 3 D
Dioptric
separation
of FLs = 3 D
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Spherical Equivalents to
Spherocylinders
Page 6.2
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• Spherical equivalent to an astigmatic lens produces a point image at
the dioptric midpoint of the (original) astigmatic image
• For parallel incident light average of astigmatic meridional powers
• For the above lens and parallel incident light:
Fig 6.1,
Page 6.1Page 6.2
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• The dioptric midpoint of the astigmatic image defines the COLC plane
• This is the plane of optimum image quality for an astigmatic lens or eye
• This is one of the main reasons that we are interested in spherical
equivalents
Fig 6.1,
Page 6.1Page 6.2
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The Astigmatic Eye and
Equivalent Spheres
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• The equivalent sphere to the full astigmatic correction places theCOLC on the retina, giving the patient best possible vision with a
spherical lens
• Call this lens the Best Vision Sphere (BVS)
• No other spherical lens will give the astigmat better vision, so vision
with BVS is as good as it gets prior to shrinking the Interval of Sturm
with cylinder
• Can find BVS power either from:
• the equivalent sphere to the full astigmatic correction
• the spherical lens power needed to move the COLC to the retina
of the uncorrected astigmatic eye
The Astigmatic Eye and Equivalent Spheres
Page 6.3
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Page 6.3
Take the eyes fromChapter 5 that we used
to define the five clinical
types of astigmatism and
find the BVS for each
Fig 5.24
Page 5.45
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Fig 5.24
Page 5.45
Full ametropic correction
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Fig 5.24
Page 5.45
Full ametropic correction
In terms of COLC position:
BVS = +4 D
FS = +4 D
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Page 6.3
Take the eyes fromChapter 5 that we used
to define the five clinical
types of astigmatism and
find the BVS for each
Fig 5.24
Page 5.45
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Fig 5.24
Page 5.45
Full ametropic correction
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Page 6.3
Take the eyes fromChapter 5 that we used
to define the five clinical
types of astigmatism and
find the BVS for each
Fig 5.24
Page 5.45
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Fig 5.24
Page 5.45
Full ametropic correction
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Page 6.3
Take the eyes fromChapter 5 that we used
to define the five clinical
types of astigmatism and
find the BVS for each
Fig 5.24
Page 5.45
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Fig 5.24
Page 5.45
Full ametropic correction
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Page 6.3
Take the eyes fromChapter 5 that we used
to define the five clinical
types of astigmatism and
find the BVS for each
Fig 5.24
Page 5.45
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Fig 5.24
Page 5.45
Full ametropic correction
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Examples of Equivalent Spheresusing ocular power and image
vergences
Page 6.4
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Fig. 6.2 - Reduced eye example of simple hyperopic astigmatism. Focal line
positions correspond to the uncorrected eye
Example 6.1: Uncorrected Simple Hyperopic Astigmatism
Page 6.4
Equivalentsphere?
+1.50 DS
LCOLC
= +58.5 D
+3
0
Full
correction
Femm = +60 D
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Example 6.2: Uncorrected Compound Myopic Astigmatism
Fig 6.3
Page 6.5
Equivalentsphere?
4.00 DS
6
2
Full
correction
Femm = +60 D
LCOLC
= +64 D
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Example 6.2: Compound Myopic Astigmat with BVS
Fig. 6.4 - Focal line positions for case of compound myopic astigmatism (Example
6.2) with 4.00 DS best vision sphere in front of eye .
Page 6.6
BVS produces
symmetrical
Mixed Astigmatism
2 D 2 D
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Example 6.2: Fully Corrected Compound Myopic Astigmat
Page 6.6
Full correction
produces apoint focus at
the retina
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Use of the BVS in Clinical Refraction
Page 6.7
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• Subjective methods must have verifiable outcomes
• BVS is verified by the patient‟s vision: “best vision” with a spherical lens
• Reason: the COLC is the most compact part of the astigmat‟s IOS
• Factor in accommodation by calling BVS the most positive (least
negative) sphere that gives the patient optimum vision.
• This is important because it is easy to inadvertently overminus a patient
if this “push plus” approach is not used
• By placing the dioptric midpoint of the IOS on the retina, BVS produces
symmetrical mixed astigmatism – this provides a common starting point
for all subjective astigmatic refractions
Page 6.7Sphere-only Refraction (Donder‟s Method)
NOTE: this is a fully subjective refraction. In practice, it is modified
because you start with retinoscopy/autorefraction (objective) findings.However, the principles behind each step remain the same.
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• Diameter (h) of the COLC is directly proportional to the amount of
astigmatism
• Assuming constant pupil diameter (y), vision with BVS should be a
systematic function of the amount of astigmatism
• F1 and F2 are so much larger than the normal range of astigmatism that
(F1 + F2) in the denominator is not really a factor
• NOTE: BVS power and vision with BVS are totally unrelated. BVS
power simply moves the COLC to the retina. COLC size then depends
only on the amount of astigmatism (assuming constant pupil diameter, y)
Page 6.7Vision with BVS
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Predicted Vision in Uncorrected Ametropia and Astigmatism
Page 6.8
Table 6.1 - Predicted Vision in Uncorrected Ametropia and Astigmatism
REFRACTIVE ERROR (D)
VISION* SPHERICAL ¶ ASTIGMATISM (with BVS)†
20/20 small small
20/30 0.50 1.00
20/40 0.75 1.50
20/60 1.00 2.00
20/80 1.50 3.00
20/120 2.00 4.00
20/200 2.003.00 high
______________________________________________________________________________
* Vision for 4 mm pupil and serif letters (for smaller pupil vision better for a given levelof uncorrected ametropia).
Sanserif letters are easier to read vision at all levels of ametropia).
¶ Myopia or absolute hyperopia (uncompensated by accommodation).
† With best vision sphere (COLC on retina).
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Vision in Astigmatism (ŵ BVS) vs. Spherical Ametropia
Fig. 5.25
Page 5.48
Uncorrected
spherical myope
Uncorrected
astigmat with
COLC on retina
Vision in the uncorrected
2D myope is “identical” to
that of the 4 D astigmat
with COLC on the retinaCOLC size is the basis
for predicting magnitude
of astigmatism
Move the COLC to the
retina with sphere.
Worse vision correlates
with higher astigmatism
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Predicted Vision in Uncorrected Ametropia and Astigmatism
Page 6.8
Table 6.1 - Predicted Vision in Uncorrected Ametropia and Astigmatism
REFRACTIVE ERROR (D)
VISION* SPHERICAL ¶ ASTIGMATISM (with BVS)†
20/20 small small
20/30 0.50 1.00
20/40 0.75 1.50
20/60 1.00 2.00
20/80 1.50 3.00
20/120 2.00 4.00
20/200 2.003.00 high
______________________________________________________________________________
* Vision for 4 mm pupil and serif letters (for smaller pupil vision better for a given levelof uncorrected ametropia).
Sanserif letters are easier to read vision at all levels of ametropia).
¶ Myopia or absolute hyperopia (uncompensated by accommodation).
† With best vision sphere (COLC on retina).
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Predicted Vision in Uncorrected Ametropia and Astigmatism
Page 6.8
Table 6.1 - Predicted Vision in Uncorrected Ametropia and Astigmatism
REFRACTIVE ERROR (D)
VISION* ASTIGMATISM (with BVS)†
20/20 small
20/30 1.00
20/40 1.50
20/60 2.00
20/80 3.00
20/120 4.00
20/200 high
______________________________________________________________________________
* Vision for 4 mm pupil and serif letters (for smaller pupil vision better for a given levelof uncorrected ametropia).
Sanserif letters are easier to read vision at all levels of ametropia).
¶ Myopia or absolute hyperopia (uncompensated by accommodation).
† With best vision sphere (COLC on retina).
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Control of COLC Position during Refraction
Page 6.8
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Control of COLC Position during RefractionPage 6.8
After finding BVS, the clinician will use one of two approaches:
(a) JCC Method - maintain optimum vision throughout the cylinder part of the refraction by keeping the COLC on the retina for all
added cylinder powers, or
(b) Fan & Block Method – move the COLC in front of the retina so
that the posterior FL is on the retina, then add cylinder to move the
anterior FL back to the retina
• In either case, control of patient accommodation is the key to a
successful subjective refraction.
• Excess negative sphere, moving the COLC behind the retina
(JCC) or moving the posterior FL behind the retina (Fan & Block),means that the clinician no longer has control of patient
accommodation.
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Control of COLC: JCC Refraction Page 6.8
Cylinder determination starts from vision with BVS (COLC on retina)
Based on predicted astigmatism from vision with BVS, the clinicianadds cylinder (parallel to one of the ocular PMs) to the BVS:
• Added negative cylinder moves one FL backward, while the
other remains stationary
• Because the COLC is always the dioptric midpoint of the IOS,the COLC moves behind the retina
• Compensating sphere is then added to return the COLC to the
retina
• Question is, how much sphere is needed to return the COLC
to the retina?
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Pre-JCC Example: with BVS in place, clinician adds 2 DC 180
Page 6.9
How much sphere is needed to return the COLC to the retina?
Equivalent sphere theory
tells us the required
compensating sphere power
• The equivalent sphere to 2.00 DC is 1.00 DS.• We therefore compensate with equal and opposite sphere power
• Adding +1.00 DS to the 2.00 DC returns the COLC to the retina
• The +1.00 DS is added to the BVS. If BVS = +3 D, new sphere = +4 DS
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Pre-JCC Example: with BVS in place, clinician adds 2 DC 180
Page 6.9+1 DS compensating sphere returns the COLC to the retina
We will prove that compensating sphere = 1/2 the added cylinder returns
the COLC to the retina, using image vergences through the astigmatic eye
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Proof that Sphere = ½ Cylinder Maintains COLC at RetinaPage 6.10
Use the CMA considered earlier to demonstrate the proof
Fig 6.3,
Page 6.5
BVS
4 DS
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Proof that Sphere = ½ Cylinder Maintains COLC at Retina
Fig. 6.4BVS puts COLC
on the retina
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Proof that Sphere = ½ Cylinder Maintains COLC at Retina
Fig. 6.5,
page 6.10
Now add 2 DC axis 180 to the BVS; COLC moves behind retina
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Proof that Sphere = ½ Cylinder Maintains COLC at Retina
Fig. 6.5,page 6.10
Page 6.11
L90 = L + F90 + FBVS + FCyl (90) = 0 + 66 4 2 = +60 D = focused at retina
L180 = L + F180 + FBVS + FCyl (180) = 0 + 62 4 + 0 = +58 D = 2 D behind retina
Compensate with +1DS:
+59 + 1 = +60 D = retina
New sphere = 4 + 1 = 3 DS
L = 0
PROOF: THE HARD WAY
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Clinical Subjective Refraction
(Astigmatic Patient)
Page 6.12
Page 6.12Fig 6 6
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gFig. 6.6
The clinician works entirely in diopters for the subjective refraction
At the very start of a fully subjective refraction, the clinician knows
nothing about the location of focal lines or COLC relative to the retina
Page 6.12Fig 6 6
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gFig. 6.6
Finding BVS fills in the first piece of the puzzle. The clinician knows that theCOLC is on the retina and the patient has symmetrical mixed astigmatism
BVS power tells the clinician where the COLC was in the uncorrected state
This is a common theme in subjective refraction: each step tells the clinician
more about the patient‟s uncorrected ametropic stateNote that BVS power gives no information about magnitude of astigmatism
Page 6.12Fig 6 6
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gFig. 6.6
Vision with BVS is the clinician‟s guide to predicting amount of astigmatism
A larger COLC means more astigmatism (constant y)
Vision with BVS is a guide to amount of astigmatism, but gives NO
information about focal line orientation
Page 6.12
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Example 6.4 - Clinical Subjective Refraction
E l 6 4 Fi t t BVS
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Example 6.4 - First step: BVS
• Start with large power increments (minimize number of steps)
• Refine with progressively smaller power increments
Page 6.13
Fig 6 7
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Fig. 6.7
Page 6.14
Vision worse
V much better
V better again
V better again
V unchanged ?
E l 6 4 St t ith BVS
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Example 6.4 - Start with BVS
• Start with large power increments (minimize number of steps)
• Refine with progressively smaller power increments
Page 6.13
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• Refine with progressively smaller power increments
Vision unchanged
Vision unchanged
Vision worse
Vision better
Marginal improvement
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• Refine with progressively smaller power increments
Vision unchanged
Vision unchanged
Vision worse
Vision better
Marginal improvement
• Step 9 indicates that 4 DS is the BVS• Now add +1 DS to BVS to deliberately “fog” patient. This should
reduce acuity ~4 lines and helps relax accommodation
P 6 15V if i BVS F D f
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Page 6.15
The patient is now fogged
+1 D over tentative BVSVision should decrease to
no better than 20/60
(vision with 1 D myopia)
For each 0.25 D defog,
the patient must be able to
read more letters on the
VA chart.
The endpoint of defog is
where the next 0.25 Dgives no improvement on
the VA chart
This procedure controls
accommodation
Verifying BVS: Fog-Defog
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Other Ways to Verify BVS
The Bichromatic (Duochrome) Test
Fig. 6.9
Bi h ti T tBichromatic Test assumes
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Fig. 6.9
Page 6.16Bichromatic Test
Longitudinal spread of red and
green in the eye is about 0.50 D
that the visual system
prefers to focus yellow
(570 nm) on the retina
Bichromatic Test: Emmetrope tries to focus yellow on retina
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Bichromatic Test: Emmetrope tries to focus yellow on retina
Adding +0 25 D to Emmetrope focuses Red on retina
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+0.25 DS
focuses red
on retina
Adding +0.25 D to Emmetrope focuses Red on retina
Adding 0 25 D to Emmetrope focuses Green on retina
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0.25 DS
focuses green
on retina
Adding 0.25 D to Emmetrope focuses Green on retina
Bi h ti T t Ch tPage 6.17
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Bichromatic Test Charts
Most projection systems allow red and green filters to be superimposed
over any slide
What does the appearance (left) mean?
Add PLUS
g
Bi h ti T t Ch tPage 6.17
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Bichromatic Test Charts
One problem with the Bichromatic Test is the fact that the eye is more
sensitive to green than red. A theoretical “equal” appearance may
therefore be interpreted by some patients as clearer on green
g
Another drawback is the eye‟s use of depth of focus (acceptable focusing
error in the retinal image) to economize on “accommodative change”
The eye appears to favor focusing longer wavelengths on the retina for
distance vision (overaccommodating), changing to shorter wavelengths in
near vision (progressively underaccommodating)
Bi h ti T t Ch tPage 6.17
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Bichromatic Test Charts
The Bichromatic Test is most useful to verify that a patient is not
substantially overminused (much clearer on green), not as a test of final
BVS or final sphere
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Subjective Refraction using the
Jackson Cross Cylinder (JCC)
JCC ft Obj ti S bj ti R f tiPage 6.17
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JCC after Objective vs. Subjective Refraction
• Routine clinical practice – retinoscopy or autorefractor gets the
clinician close to the patient‟s final correction in most cases
• Typically a sphere check (modified BVS) followed by JCC is then
used to refine the correction. Reasons:
• Retinoscopy and autorefraction rely on patient cooperation (esp. fixation)
• Some patients do not fully relax accommodation during objective refraction
• Subjective methods can locate ocular PMs more accurately
• Objective refraction is prone to aberration effects, especially for patients
with larger pupils
• For a fully subjective refraction, the JCC approach includes additional
steps, e.g. estimation of total magnitude of astigmatism from visionwith BVS and “axis determination from scratch.” Neither of these
steps is typically required after objective refraction unless the
patient‟s vision is significantly worse than expected
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Fig 6.9: A ±0.25 D Jackson Cross Cylinder. Cylinder orientation is specified
by the axis meridian. Opposing cylinder axes are set 90 apart, each at a 45 angle to the cross cylinder handle.
Page 6.19
Numbers on the JCC indicate cylinder axis
The JCC consists of two plano-cylinders of
opposite sign with axes 90 apart
The lens cross for a JCC shows actualpowers in actual “meridians”
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Page 6.20
The equivalent sphere to the JCC is (0.25 + 0.25)/2 = Plano
what effect will the JCC have on COLC position? _____________
The JCC is actually manufactured as a spherocylinder with power +0.25 DS 0.50 DC axis . This gives it better optical performance
than a true “crossed cylinder” combination .
Use 2 4 180 CMA to demonstrate JCC after retinoscopy
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Page 6.20
6
2
Full
correction
Use 2 4 180 CMA to demonstrate JCC after retinoscopy
Fig 6.3
Page 6.5
Assume retinoscopy was “off” for cyl giving 3 DC axis 160
Full correction in SC notation: 2 4 DC axis 180
Using the JCC to Refine Cylinder Axis after Retinoscopy
Page 6.20
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Using the JCC to Refine Cylinder Axis after Retinoscopy
Focal line positions with 3 DC axis 160 in front of patient‟s eye
The patient has 1 D residual astigmatism (ignoring the 20 axis error)
The clinician then does a modified BVS procedure to move COLC to retina
The patient‟s vision with COLC on retina will be a little worse than for a 1 D
astigmat because of the 20 axis error (slightly irregular COLC)
Using the JCC to Refine Cylinder Axis after Retinoscopy
Page 6.20
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Using the JCC to Refine Cylinder Axis after Retinoscopy
Check that the “partial correction” does maintain COLC on retina
The equivalent sphere to the partial correction should equal the
equivalent sphere to the full correction (4 DS) BVS
* again, we are ignoring the 20 axis discrepancy
Page 6.20
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Refining Cylinder Axis using
Obliquely Crossed Cylinders
Refining Cylinder Axis using Obliquely Crossed Cylinders
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Refining Cylinder Axis using Obliquely Crossed Cylinders
Page 6.20
• Optometrists use negative cylinders for refraction
• Two negative cyls crossed at an oblique angle produce a resultant
cyl with intermediate power meridian
• Clinicians “think” axis during refraction (trial cyl, JCC, etc.)
• We can consider obliquely crossed negative cylinder axes, becausethe resultant cylinder axis will be correct (rotated 90 from the
resultant power meridian)
Refining Cylinder Axis using Obliquely Crossed Cylinders
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Refining Cylinder Axis using Obliquely Crossed Cylinders
Page 6.20
Obliquely crossedcylinders of the same sign
will produce a resultant
cylinder with an axis
between the two
Like an airplane‟s paththrough the air with wind
direction at an acute angle
NO WIND
Refining Cylinder Axis using Obliquely Crossed Cylinders
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Refining Cylinder Axis using Obliquely Crossed Cylinders
Page 6.20
Obliquely crossedcylinders of the same sign
will produce a resultant
cylinder with an axis
between the two
Like an airplane‟s paththrough the air with wind
direction at an acute angle
resultant
direction
Obliquely Crossed Cylinders (same sign)
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Obliquely Crossed Cylinders (same sign)
Fig 6.12 - Two negative cylinders with axes crossed at an oblique angle
produce a resultant negative cylinder with an intermediate axis.
Page 6.21
Resultant cylinder axis between twoobliquely crossed cylinder axes
Resultant axis will be closer to the
axis of the higher power cyl
Trial cyl axis (TCA) 90
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Page 6.19
For JCC axis
refinement, we place
the handle parallel to
the TCA
This producesobliquely crossed
negative cylinders
The resultant axis is
in between, and
closer to the higher
power cyl (axis)
Obliquely crossed
negative cylinders with
axes 45 apart
Resultant axis
Refining Cylinder Axis for Our CMA
Page 6.20
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Refining Cylinder Axis for Our CMA
Required correcting cylinder axis is 180
We currently have the trial cylinder axis (TCA) set to 160
To refine axis, we set it to the 160 (that we found with retinoscopy),
place the JCC handle along 160 and present “first” and “second”
views with obliquely crossed cylinders 45 either side of 160
Fig. 6.13
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JCC:
Refining Cylinder Axis
g
Page 6.22
Fig. 6.13
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JCC:
Refining Cylinder Axis
g
Page 6.22
First and second views are
equivalent to rotating theTCA clockwise then
counterclockwise from 160
The advantage of the JCC is
that the patient sees instant
comparisons, not a gradualchange in axis
The axis “rotation” is also
identical between first and
second
Fig. 6.13
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JCC:
Refining Cylinder Axis
g
Page 6.22
The patient prefers “second”
because the resultant cylinder axis is closer to 180
This prompts the clinician to
rotate the TCA from 160 toward
180, e.g. to 170
JCC handle is now aligned with
170. First and second? Patient
prefers the view with the
resultant rotated toward 180
Refining Cylinder Axis using Obliquely Crossed Cylinders
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Refining Cylinder Axis using Obliquely Crossed Cylinders
Page 6.22
• What happens when trial cylinder axis reaches 180?
• First and second should be the same and both should be blurry
because they both move the resultant cyl axis away from 180
• Here you should reassure the patient that this is normal
• Further refine by rotating beyond 180
• The patient should “push” you back toward 180
• From this point it is a matter of fine-tuning to get the exact axis
• For a 3 D (eventually 4 D) cyl, axis should easily be set to an
accuracy of 1
• For an 0.50 D cyl, axis cannot be set as accurately
Page 6.23
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Refining Cylinder Power using the
Jackson Cross Cylinder
Page 6.23Refining Cylinder Power using the JCC
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Page 6.23
• Easier to consider power refinement using actual cyl powers in
actual meridians because we are now moving the focal linesrelative to the retina
Refining Cylinder Power using the JCC
JCC: Refining Cylinder Power Page 6.23
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Fig 6.14 - To refine trial cylinder power, the cross cylinder is placed with its (a)
axes, and therefore also (b) principal meridians parallel to / perpendicular to the
trial cylinder principal meridians
g y
JCC power meridians
are 90 from their axes
Negative axis
parallel and
perpendicular to
TCA for power
refinement
Negative PMs are
always 90 away
(from axis)
Fig. 6.15 Refining Cylinder Power – JCC Power Meridians Shown
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Page 6.24
First view moves both FLs closer to the retina. This makes COLC smaller
Second view moves both FLs away from the retina. The COLC gets larger
JCC axes parallel and perpendicular to TCA for power refinement
Fig. 6.15 Refining Cylinder Power – JCC Power Meridians Shown
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Page 6.24
Patient prefers the view with the negative JCC power meridian parallel to
the trial cylinder power meridian (both 90)
The clinician thinks of this as negative JCC axis 180; trial cyl axis 180.
Patient prefers minus on minus; therefore add more minus cylinder power.
Change the 3.00 DC axis 180 to e.g. 3.50 DC axis 180. Compensate??
Fig. 6.15
P 6 24
Refining Cylinder Power – JCC Power Meridians Shown
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Page 6.24 Change sphere from 2.50 DS to 2.25 DS
First shrinks the IOS to zero, so this view is preferredClinician again guided by negative JCC axis on negative TCA; therefore add
more minus
Next combination would be 2.00 DS to 4.00 DC
First and second would produce “equally bad” response. Try 4.25 DC, then
3.75 DC.
Page 6.25 Refining Cylinder Power
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When changing cyl from 4.00 DC to 4.25 DC, theoretically compensate
with +0.125 DS. Smallest phoropter increment is 0.25 DS. So, what do
we do?With COLC on retina, adding 0.25 DC moves the COLC 0.125 D behind
the retina. This is fine, because the patient can accommodate the
0.125 D to return the COLC to the retina
Adding +0.25 DS would move the COLC slightly in front, giving the
patient no way to return the COLC to the retina
Page 6.25 Final Sphere Determination
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Same procedure as for BVS verification
Fog the patient +1 D. Change phoropter sphere from 2.00 DS to 1.00
DS. This should make them 1 D myopic and drop vision to 20/60Defog in negative 0.25 DS steps
Expected vision:
1.00 DS (+1.00 D fog) 20/60
1.25 DS (+0.75 D fog) 20/401.50 DS (+0.50 D fog) 20/30
1.75 DS (+0.25 D fog) 20/25 or better
2.00 DS (Zero fog) 20/20 or better (optimum visual acuity)
Patient must be able to read MORE letters down the chart to give them
each 0.25 DS defog
No improvement means no more minus
P 6 26
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Example 6.5
Jackson Cross Cylinder Procedure as “Seen” by the Clinician
Page 6.26
Patient for Full Subjective Refraction; BVS/JCC: ax = 23.39 mm
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Fig. 6.16 - Application of the ametropia equation in lens cross format to show the
patient‟s required ametropic correction for Example 6.5.
Page 6.26
Use Donder‟s Method to find BVS Page 6.27
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Clinician systematically adds plus or minus spheres starting with
larger increments, refining to progressively smaller increments
Page 6.27
Vision with BVS Page 6.27
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Page 6.27
3.5 DS
Dioptric separationof FLs = 5 D
Vision Astigmatism
with BVS
20/20 Small
20/30 1.00
20/40 1.50
20/60 2.00
20/80 3.00
20/120 4.00
20/160 – 20/200 5.00Based on table 6.1, page 6.8
Assume that the patient has
smaller pupils and gets 20/120;
so 4 D astigmatism is predicted
Fig 6.17, Page 6.27Initial Cylinder Axis Determination
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g , gy
A successful JCC procedure consistently maintains the COLC on the retina.
the most appropriate fixation target for the patient is a circular target
Why? Because a circular target cannot give the patient any preference for a
focal line on the retina over the COLC
Initial axis DeterminationPage 6.28
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The choice of JCC method for initial axis determination will depend on
the predicted amount of astigmatism, and on vision with BVS
For predicted astigmatism of 0.50 D or less, two choices:
• Axis search (no trial cylinder in phoropter)
• Power search (0.50 DC trial cylinder in phoropter)
g
Page 6.28Initial axis Determination – Axis Search Method
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g
Flip
1st 2nd
BVS ONLY in Phoropter
Page 6.28Initial axis Determination – Axis Search Method
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Flip
2nd 1st
1st 2nd
Initial axis Determination – Axis Search Method
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Page 6.29
1st 2nd 2nd 1st
Starting TCA
1st 2nd
Initial axis Determination – Axis Search Method
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Page 6.29
1st 2nd 2nd 1st
Because the 0.25 D Jackson Cross Cylinder is, in spherocylindrical
notation, a +0.25 DS 0.50 DC , “Axis Search” is asking the question:
“Do you want a sphere-compensated 0.50 DC axis 180, axis 90, axis
45 or axis 135?”
Initial axis Determination – Power Search MethodPage 6.28
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For the Power Search Method and low predicted astigmatism, a 0.50 DC
is added to the BVS and rotated e.g. to 180. The BVS is changed by
+0.25 DS to compensate for the added cylinder
The JCC handle is rotated to 45 (or 135) so JCC axes are at 90 and 180
First and second is asking the question, “Do you accept negative cylinder
axis 180?”
2nd 1st
Trial cylinder
0.50 DC axis 180
Trial cylinder
0.50 DC axis 180
Initial axis Determination – Power Search MethodPage 6.28
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If first (below) is preferred, the patient is definitely “accepting” because
minus on minus means they want MORE negative cyl
If second is preferred, the patient is “rejecting” because plus on minus
means they want LESS negative cyl
A neutral response (no difference) means either that the cylinder axis may
be within 45 of 180, or that the patient may have very low astigmatism
2nd 1st
Trial cylinder
0.50 DC axis 180
Trial cylinder
0.50 DC axis 180
Initial axis Determination – Power Search MethodPage 6.28
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For a “rejection” (preference for second) or neutral response, the trial
cylinder axis is rotated to 45 and first and second are presented with
JCC handle at 180 (axes 45 and 135)
2nd 1st
Trial cylinder
0.50 DC axis 180
Trial cylinder
0.50 DC axis 180
Initial axis Determination – Power Search MethodPage 6.28
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Trial cylinder
0.50 DC axis 45
Trial cylinder
0.50 DC axis 45
1st 2nd
If again rejected or neutral, TCA is rotated to 90, then 135 until an
acceptance (or non-rejection) is obtained
Two “non-rejections” e.g. at 45 and 90, with rejections at 135 and 180
suggest that the TCA should be set between 45 and 90 for refinement
For a “rejection” (preference for second) or neutral response, the trial
cylinder axis is rotated to 45 and first and second are presented with
JCC handle at 180 (axes 45 and 135)
Page 6.30Power Search for Predicted Astigmatism > 1 D
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The added trial cylinder prior to axis search should be 0.50 D to 1.00 D less
than the predicted astigmatism
For patients with astigmatism of e.g. 2 D or more, power search is easy
because it becomes very obvious to the patient when the trial cylinder axis
approaches its correct orientation
Our example patient, with estimated 4 D astigmatism, would indicate a
starting cylinder of 3.00 DC. This is compensated with +1.50 DS over BVS
Our patient, with full correction 1.00 DS 5.00 DC axis 110, will see much
better when the TCA reaches 90 (20 off-axis). It will appear similar at 135
(25 off-axis).
We will assume a starting TCA of 90
JCC Axis Refinement
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JCC Axis Refinement
Axis refinement is used after “axis” or “power” search, or
following objective refraction (retinoscopy)
Figure 6.20
Page 6.31
Resultant cylinder axis
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g
Axis refinement
with TCA 90
Axis Shift for JCC with Handle Parallel to Trial Cylinder Axis
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Table 6.2
Page 6.32
Trial Cylinder Power (D) 0.25 DC JCC 0.50 DC JCC
0 45 45
0.50 22.5 31.5
1.00 13.5 22.5
1.50 9 17
2.00 7 13.52.50 5.5 11
3.00 4.5 9
4.00 3.5 7
5.00 3 5.5
6.00 2.5 4.5
Axis Shift
Resultant cylinder axis
3.5 from
90 = 86.5
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Axis refinementwith TCA 90
y
+3.5 from
90 = 93.5 Axis error = 16.5
Figure 6.20
Page 6.31
Axis error
= 23.5
Outcome: rotate
TCA counter-
clockwise. Wewill rotate to
112.5 (midpoint
of 90 and 135)
Page 6.33
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Fig. 6.21 - TCA and correcting cylinder axis orientation for the second stage of
axis refinement
We are now only
2.5 away from the
required correcting
cylinder axis
Fig 6.22
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Page 6.33
1 axis
error
6 axiserror
Rotate TCA clockwise from 112.5. The
patient will be less certain about the
difference between 1st and 2nd above
indicating that we are close to CCA
Fig 6.23
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Page 6.35
Continue refining until
“equal” blur response
with TCA at CCA (110)
3.5 axis
error
3.5 axis
error
Page 6.35JCC Power Refinement
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Rotate JCC handle through 45 so the JCC axes are aligned with 20 and
110. The actual handle orientation will be 65 (or 155)
Fig 6.23 (top)
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Page 6.36
Minus on
minus Plus on
minus
Remember: the patient‟sfull cylinder correction will
be 5.00 DC axis 110
Fig 6.23 (bottom)
Page 6.36
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Smaller IOS means smaller
COLC means clearer
vision for the patient
Larger IOS means larger
COLC means worse
vision for the patient
Patient wants MORE minus cyl
Fig 6.23 (bottom)
Page 6.36
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Smaller IOS means smaller
COLC means clearer
vision for the patient
Larger IOS means larger
COLC means worse
vision for the patient
Patient wants MORE minus cyl
Fig 6.23 (top)
P 6 36
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Page 6.36
Minus on
minus Plus on
minus
Remember: the patient‟sfull cylinder correction will
be 5.00 DC axis 110
Fig 6.24 (top)
P 6 38
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Page 6.38
Minus on
minus
Remember: the patient‟sfull cylinder correction will
be 5.00 DC axis 110
Plus on
minus
Fig 6.24 (bottom)
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Reducing a 0.50 D IOS to
zero means a point focus
1.0 D IOS means a “1 D”
COLC which means worse
vision for the patient
Patient wants MORE minus cyl
Fig 6.25 (top)
Page 6 39
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Page 6.39
Minus on
minus
Remember: the patient‟sfull cylinder correction will
be 5.00 DC axis 110
Plus on
minus?????
Fig 6.25 (bottom)
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The JCC changes a point
focus to a 0.50 D IOS with
anterior FL oriented at 20
The JCC changes a point
focus to a 0.50 D IOS with
anterior FL oriented at 110
Patient likes 5.00 D cyl
Page 6.39
Fig 6.26
Page 6.40
Fine-tuning 0.25 DC steps around 5.00 DC
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The JCC changes anterior
and posterior FL orientation
but retains a 0.25 D IOS
The JCC increases the IOS to
0.75 D
Patient wants more minus cyl
Fig 6.27
Page 6.41
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The JCC changes anterior
and posterior FL orientation
but retains a 0.25 D IOS
The JCC increases the IOS to
0.75 D
Patient wants less minus cyl
Spherical Equivalents in Partial Astigmatic Correction
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Page 6.42
• Some patients can only tolerate partial astigmatic correction (e.g.due to excessive spatial distortion with full correction)
• When prescribing partial correction patient has residual
astigmatism, complete with IOS
• Partial correction must place COLC on retina
• equivalent sphere to partial astigmatic correction must equal
BVS (equivalent sphere to full correction)
Spherical Equivalents in Partial Astigmatic Correction
P 6 42
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Page 6.42Equivalent sphere to partial astigmatic correction must
equal BVS (equivalent sphere to full correction)
Example: full correction = 2.00 4.00 axis 180
Patient can only tolerate ()2.50 of cylinder
Effectively, we have REMOVED 1.50 DC from the full correction
DS F F Cyl
S 75.02
50.1
2
To compensate for the 1.50 DC REMOVED, add 0.75 DS to Rx sphere
Original correction = 2.00 4.00 axis 180
New partial correction = 2.75 2.50 axis 180
DS F S 00.42
75.225.5
Equivalent sphere to
partial correction:
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Negative JCC Axis
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Positive JCC Axis
If we are refining
TCA
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If we are refining
axis, where is the
TCA?
(a) 180
(b) 90
(c) 45
(d) 135
If the patient prefers
TCA Resultant of obliquely crossed TCA and JCCnegative axis
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If the patient prefers
this view, what do we
do next?
(a) cyl power 0.5 D
(b) cyl power 0.5 D
(c) change TCA to 125
(d) change TCA to 145
If we are refining
TCA
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g
cyl power, where
is the TCA?
(a) 90 or 180
(b) 45 or 135
TCA
OR
If TCA is 180 and the
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patient prefers this
view, what do we do
next?
(a) cyl power 0.5 D
(b) cyl power 0.5 D
(c) change TCA to 125
(d) change TCA to 145
TCA
TCA
If TCA is 90 and the
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patient prefers this
view, what do we do
next?
(a) cyl power 0.5 D
(b) cyl power 0.5 D
(c) change TCA to 125
(d) change TCA to 145
Rationale of “Power Search” (Full Subjective JCC) Pp 6 29 30 Lab step 4 p 5
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Pp 6.29, 30 Lab step 4 p. 5
• Vision with BVS provides estimate of amount of astigmatism
• e.g. vision with BVS = 20/60 predict 2.0 D astigmatism (Table 6.1)
• If our prediction is correct, we will end up with XX DS 2.00 DC axis
• What our power search is doing is giving us an approximate value or
“range” for
• The most efficient method for 2.0 D predicted astigmatism is to insert a
sphere-compensated cyl that falls short of 2 D, so the JCC can make up
the difference ( 0.25 D JCC +0.25 DS 0.50 DC axis )
• So, for our 2 D “predicted” astigmat, we add 1.50 DC axis 180 (totally
arbitrary starting axis) to the BVS. We compensate by changing sphere+0.75 DS from BVS power
Rationale of “Power Search” (Full Subjective JCC) Pp 6 29 30 Lab step 4 p 5
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Pp 6.29, 30 Lab step 4 p. 5
• We set the JCC axes 90/180. If 180 just happens to be the patient‟s axis,
when the negative JCC axis is at 180:
1.50 DC axis 180 0.50 DC axis 180 (JCC) 2.00 DC axis 180
• The patient is fully corrected, so they “accept” minus on minus
• If they “reject” the extra 0.50 DC from the JCC (prefer plus JCC axis 180),
they want less than 1.50 DC axis 180, so 180 is unlikely to be the axis
• A reject, means try again at 45. Another reject means try 90. Reject means
try 135
• Neutral at any of 180, 45, 90, 135 means we may be close to the axis.
• Two neutrals, or a neutral and accept 45 apart suggests an in between axis
•So, for our 2 D “predicted” astigmat, we add 1.50 DC axis 180 (totally
arbitrary starting axis) to the BVS. We compensate by changing sphere+0.75 DS from BVS power
This would be a
TCA
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“Power Search”
accept with TCA
set at 90, IF thepatient prefers
this view
This would be a
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“Power Search”
reject with TCA
set at 180, IF thepatient prefers
this view
TCA
Rationale of “Power Search” (Full Subjective JCC) Pp 6.29, 30 Lab step 4 p. 5
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Pp 6.29, 30 Lab step 4 p. 5
• After power search, we put the patient‟s full estimated cylinder in the
phoropter (sphere-compensated) using the axis or axis range from Power Search
• Next step, refine axis (obliquely crossed cyls)
• Subsequent step, refine power (JCC axes parallel and to TCA)
Page 6.43
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Clinical Subjective Refraction:
Focal Line Approach
Clinical Subjective
Refraction Focal
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Refraction Focal
Line Approach
Fig. 6.28
Page 6.43
Take a Compound
hyperopic astigmat to
demonstrate the
method: (works for any astigmat)
Clinical Subjective Refraction Focal Line Approach (CHA)
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Fig. 6.28 (1)
Page 6.43
To maintain control of patient accommodation, the posterior focalline is moved to the retina with sphere before starting the
astigmatic correction
Plus sphere
The Astigmatic Fan Chart
Fi 6 29
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Fig. 6.29
Page 6.45
With a vertical FL on the retina, the patient should see the 90 Fan Chart Line clear. The 180 lines should be most blurred
The Astigmatic Fan Chart
Fig 6 29
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Fig. 6.29
Page 6.45
Because the anterior FL is in front of the retina, the clinician has control of
patient accommodation. The patient cannot make the horizontal lines clear
Example 6.7 - The "Fan and Block" Method of Refraction
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This is the most complete form of subjective focal line refraction.
Like JCC, it is rarely used as a fully subjective procedure
After a difficult retinoscopy, or inconsistent JCC findings, the Fan and
Block Method is a good alternative, especially to locate cylinder axis.
The Fan and Block Method is most useful for patients with large
amounts of astigmatism
Example 6.7 - The "Fan and Block" Method of Refraction
Fig. 6.30
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Page 6.46
Step 1: BVS (b)
Step 2: vision with BVS. Should get ~20/60Therefore we predict 2 D astigmatism
Example 6.7 - The "Fan and Block" Method of Refraction
Fig. 6.30
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Step 2: vision with BVS. Should get ~20/60
Therefore we predict 2 D astigmatism
Step 3: Move the posterior FL to the retina (c)
With the COLC on the retina of a 2 D astigmat (b), we add +1.00 DS
to shift the posterior FL to the retina (c).
This moves the COLC 1 D in front
Page 6.46
Example 6.7 - The "Fan and Block" Method of Refraction
Fig. 6.30
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With the posterior FL on the retina, we now direct the patient to view
the Fan Chart
Page 6.46
Example 6.7 - The "Fan and Block" Method of Refraction
Fig. 6.30
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With the posterior FL on the retina, we now direct the patient to view
the Fan Chart
Page 6.46
Verification Example (extreme case): BVS Initially 2 D too Low FLs REVERSED
Fig. 6.31
Page 6.48
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Assume we initially underestimated BVS by 2.0 DS (a). Estimate +3.0 D
With our low BVS estimate, the COLC is 2 D behind retina
Vision with “BVS” can be no better than 20/60 (with accommodation) We therefore assume 2 D astigmatism and Fog with 1 DS (b)
With the anterior FL on the retina, the 180 Fan Chart line is clearer
But, the patient can accommodate and move the COLC or posterior FL to
the retina. Fan Chart responses will be inconsistent or wrong
The figure that will be shown for this example differs from Figure 6.31
(page 6.48). The eye is identical to the one used for Example 6.7.
+3 DS
With the extra +0.50 D fog, the horizontal Fan Chart line first starts to blur
But, with accommodation, the patient can bring the COLC or vertical FL
to the retina
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to the retina
Because the horizontal FL can no longer be focused, and less
accommodation is now required to focus the vertical line, the patient mayreport that the vertical line is becoming clearer
This is the first indication for the clinician that BVS power was incorrect:
the opposite focal line becomes clearer AFTER adding a net plus
power that should have moved the entire IOS in front of the retina
Fig. 6.31R
handoutCOLC 2 D behind
retina w “low” BVS
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Vision with “low BVS” 20/60
(with accom.) predict 2 Dastigmatism, so fog +1 D
With extra +1 D over initial
fog, 180 line more
blurred, but 90 line
perfectly clear with a littleaccommodation
Finally, with extra +2 D over
initial fog (3 D net over BVS)
posterior FL moves to retina
An extra +2.5 D over initial
fog moves the posterior FL
in front of the retina
Fig. 6.30
Returning to the Current Example, with Posterior FL 0.50 D in front of Retina
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Page 6.46
Next step is axis refinement
This is done with a Maddox „V‟ (Locator) in the center of the full Fan
and Block Chart
The "Fan and Block" ChartFig. 6.32
Page 6.49
Maddox V
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Maddox V
The "Fan and
Block" Chart
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Fig. 6.32
Page 6.49
22.5 22.5
Each leg of the „V‟ subtends 22.5 with the direction the V is pointing
The two legs therefore correspond to Fan Chart line orientations 22.5 away from where the „V‟ is pointing
The "Fan and Block" ChartFig. 6.32
Page 6.49
Both sides equally blurry
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Both sides equally blurry
(22.5 away from 90)
The "Fan and Block" ChartFig. 6.32
Page 6.49
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When the V points at the retinal FL, both sides appear equally blurry
If the retinal FL is vertical, and the V is rotated 22.5 clockwise, the right
leg will be parallel to 90, and the left leg will be pointing at 135
The "Fan and Block" Chart
Right side clearer (parallel
t 90) t t i itThe key to axis refinement:
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to 90) rotate in opposite
direction to clearer leg
y
rotate the „V‟ in the
opposite direction to itsclearer leg until both legs
are equally blurry. Just like
JCC, the endpoint will be
an “equal blur” response
The "Fan and Block" ChartFig. 6.32
Page 6.49
Right side clearer rotate
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toward 90 again
The "Fan and Block" ChartFig. 6.32
Page 6.49
Both sides equally blurry
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q y y
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We now know the posterior FL is oriented at exactly 90 (V pointing at 90)
Next we add minus cylinder to move the anterior (horizontal) FL back
toward the retina
Negative cylinder (power meridian 90) axis 180 will move the horizontal FLbackward. Note that cyl axis is parallel to the anterior focal line
Fig. 6.32
Page 6.49
Initially the horizontal “blocks” will be very blurred
As we add minus cyl axis 180, the horizontal blocks gradually
become clearer. Endpoint = H and V blocks equally clear
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Corrector “Block”
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With posterior FL 0.50 D in front of the retina, we will add minus cyl axis
180 in 0.50 D, then 0.25 D increments (Fig 6.30 (e) – (j), Page 6.46).
Notice that no sphere adjustment is made throughout the cylinder phase
The endpoint of the cylinder phase is a point focus 0.50 D in front of the
retina.If too much cylinder is added, a new IOS is created with the horizontal FL
becoming the posterior FL.
If 0.25 D excess cyl is added, the horizontal FL will be 0.25 D in front of
the retina and the vertical remains 0.50 D in front
A reversal of “block” clarity is the cue that excess cylinder has been added
Cyl is dropped back to 2.00 DC (equal clarity of blocks)
The final stage is a sphere fog (+0.50 DS; total +1.00 DS) and defog to
optimum Visual Acuity)
Fig. 6.34
Page 6.52
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The Fanand Block
Procedure
Page 6.51
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Example 6.8
Fan and Block Procedure - a more Clinical Approach
Fan and Block ProcedurePage 6.51
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Fig. 6.33 - Application of the ametropia equation in lens cross format to show
the required ametropic correction for Example 6.8. Focal lines will appear as
in Figure 6.34 (a).
Fig 6.34 (a), Page 6.52
5 D astigmatism
Fan and Block ProcedurePage 6.51
BVS = 3 50 DS
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Fig. 6.33 - Application of the ametropia equation in lens cross format to show
the required ametropic correction for Example 6.8. Focal lines will appear as
in Figure 6.34 (a).
Fig 6.34 (a), Page 6.52
BVS = 3.50 DS
Vision with BVS: 20/160 to 20/200 estimate around 5 D astigmatismFog over BVS for 5 D predicted astigmatism would be +2.50 DS (net
sphere 3.50 + 2.50 = 1.00 DS)
Fig. 6.35
Page 6.53
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+2 DS Fog
over BVS
Fig 6.34 (c), Page 6.52
2 5 DS
Fig. 6.36
Page 6.54
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Fig 6.34 (d), Page 6.52
+2.5 DS
Fog over BVS
Fig. 6.37
Page 6.55
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+3 DS Fog
over BVS
Fig 6.34 (e), Page 6.52
Further Refining Cylinder Axis – Maddox VPage 6.56
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Fig. 6.38 - Fan and Block Chart with Maddox V (locator) pointing at the 20 line. Both arms of the V appear equally clear (blurred).
Further Refining Cylinder Axis – Maddox VPage 6.57
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Fig. 6.39 - Maddox V rotated clockwise to point at the 30 line. Now the upper
limb of the arrow is clearer than the lower. The clinician therefore needs to
rotate the V in the opposite direction (counterclockwise) toward 180
Further Refining Cylinder Axis – Maddox VPage 6.58
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Fig. 6.40 - Maddox V rotated counterclockwise to point at the 10 line. This
time the lower limb of the arrow is clearer. Again, the clinician needs to rotate
the V in the opposite direction (clockwise).
Refining Cylinder Power
Fig. 6.41
Page 6 59
Fig. 6.42
Page 6 59
Fig. 6.43
Page 6 60
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0 DC
Page 6.59
2 DC
Page 6.59
4 DC
Page 6.60
Fig 6.34 (e), Page 6.52
Refining Cylinder Power
Fig. 6.41
Page 6 59
Fig. 6.42
Page 6.59
Fig. 6.43
Page 6 60
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0 DC
Page 6.59
2 DC
Page 6.59
4 DC
Page 6.60
Fig 6.34 (f), Page 6.52
Refining Cylinder Power
Fig. 6.41
Page 6.59
Fig. 6.42
Page 6.59
Fig. 6.43
Page 6.60
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0 DC
Page 6.59
2 DC
Page 6.59
4 DC
Page 6.60
Fig 6.34 (g), Page 6.52
Fig. 6.44
Page 6.60
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Fig 6.34 (h), Page 6.52
Full cylinder correction
5 DC
Fig. 6.45
Page 6.61
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Excess
cylinder
5.5 DC
Fig 6.34 (i ), Page 6.52
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Vision in Astigmatism (ŵ BVS) vs. Spherical
AmetropiaFig. 5.25
Uncorrected
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Page 5.48Uncorrected
spherical
myope
Uncorrectedastigmat with
COLC on retina
L
L R
Compare Blur Circle & Airy Disc Diameter for 1 D Myope with 2.8 mm Pupil
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Blur Circle
Diameter
Airy Disc
Diameter
Compare Blur Circle & Airy Disc Diameter for 1 D Myope with 2.8 mm Pupil
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Blur Circle
Diameter
Airy Disc
Diameter
Spreads over ~ 23 foveal cones
Spreads over ~ 4 foveal cones
Airy Disc
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Blur Circle
Visual Angle vs. Actual Height of 20/20 Letter 20/20 letter subtends 5 (1/12) from 20 feet
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= test distance
standard = 20 feet (6.096 m)
R
333.1n
R P
h
h = f e
tan = 16.67 mm tan 5 = 24 m
20/200 letter 240 m
:Line200
20 Letter height 240 m, Blur circle 46 m
The VA Chart to our 1 D myope with 2 8 mm pupil
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x
h A
The VA Chart to our 1 D myope with 2.8 mm pupil
:Line160
20Letter height 192 m, Blur circle 46 m
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x
h A
:Line125
20Letter height 150 m, Blur circle 46 m
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x
h A
:Line100
20Letter height 120 m, Blur circle 46 m
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x
h A
:Line80
20Letter height 96 m, Blur circle 46 m
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x
h A
:Line63
20Letter height 76 m, Blur circle 46 m
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x
h A
:Line50
20Letter height 60 m, Blur circle 46 m
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x
h A
:Line40
20Letter height 48 m, Blur circle 46 m
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x
h A
COLC Diameter for 4 mm pupil and 0.5 D and 1.0 D Residual Astigmatism
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COLC
Diameter
Airy Disc
Diameter
21
21
L L
L L
y x M D
D
mm 7.16120
5.0
4
M D
Dmm 3.33
120
0.14
2
3
9
1005.2
104
106.58744.244.2sin
Diameter AD
Diameter AD
m
m
d
M f h ADDe Diameter AD 98.51005.2tan67.16tan 2
20 foveolar receptors = 40 µM
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20/120 letter
20 foveolar receptors = 40 µM20/100 letter height = 120 µM
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Blur circle diameter for
4 mm pupil and 0.50 D
residual astigmatism =16.67 µMBlur circle diameter for
4 mm pupil and 1.00 D
residual astigmatism
= 33.33 µM
Airy DiscDiameter
20 foveolar receptors = 40 µM
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20/120 letter
20 foveolar receptors = 40 µM
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FIRST
20 foveolar receptors = 40 µM
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SECOND
20 foveolar receptors = 40 µM
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20 foveolar receptors = 40 µM
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