Astigmatism and Subjective Refraction

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Visual Optics 2006/2007

Chapter 6

Astigmatism & Subjective Refraction



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



Spherical Equivalents to

Spherocylinders

Page 6.2



• 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



• 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



The Astigmatic Eye and

Equivalent Spheres



• 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



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



Fig 5.24

Page 5.45

Full ametropic correction



Fig 5.24

Page 5.45


In terms of COLC position:

BVS = +4 D

FS = +4 D



Page 6.3





Fig 5.24

Page 5.45



Fig 5.24

Page 5.45




Page 6.3





Fig 5.24

Page 5.45



Fig 5.24

Page 5.45




Page 6.3





Fig 5.24

Page 5.45



Fig 5.24

Page 5.45




Page 6.3





Fig 5.24

Page 5.45



Fig 5.24

Page 5.45




Examples of Equivalent Spheresusing ocular power and image

vergences

Page 6.4



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



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



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



Example 6.2: Fully Corrected Compound Myopic Astigmat

Page 6.6

Full correction

produces apoint focus at

the retina



Use of the BVS in Clinical Refraction

Page 6.7



• 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.



• 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



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).



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




Page 6.8



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

______________________________________________________________________________








Page 6.8



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

______________________________________________________________________________







Control of COLC Position during Refraction

Page 6.8



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.



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?



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



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



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



Proof that Sphere = ½ Cylinder Maintains COLC at Retina

Fig. 6.4BVS puts COLC

on the retina




Fig. 6.5,

page 6.10

Now add 2 DC axis 180 to the BVS; COLC moves behind 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



Clinical Subjective Refraction

(Astigmatic Patient)

Page 6.12

Page 6.12Fig 6 6



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



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



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



?

?

?



Example 6.4 - Clinical Subjective Refraction

E l 6 4 Fi t t BVS



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



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



Example 6.4 - Start with BVS

• Start with large power increments (minimize number of steps)


Page 6.13




Vision unchanged

Vision unchanged

Vision worse

Vision better

Marginal improvement




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



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



Other Ways to Verify BVS

The Bichromatic (Duochrome) Test

Fig. 6.9

Bi h ti T tBichromatic Test assumes



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



Bichromatic Test: Emmetrope tries to focus yellow on retina

Adding +0 25 D to Emmetrope focuses Red on retina



+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



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



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





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)





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



Subjective Refraction using the

Jackson Cross Cylinder (JCC)

JCC ft Obj ti S bj ti R f tiPage 6.17



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

Page 6 19



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”

Page 6 20



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



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




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)


Page 6.20




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



Refining Cylinder Axis using

Obliquely Crossed Cylinders

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)





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





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)



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



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



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



JCC:

Refining Cylinder Axis

g

Page 6.22

Fig. 6.13



JCC:


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



JCC:


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





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



Refining Cylinder Power using the

Jackson Cross Cylinder

Page 6.23Refining Cylinder Power using the JCC



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



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



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



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



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



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



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



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



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



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



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



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



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



g

Flip

1st 2nd

BVS ONLY in Phoropter

Page 6.28Initial axis Determination – Axis Search Method



Flip

2nd 1st

1st 2nd

Initial axis Determination – Axis Search Method



Page 6.29

1st 2nd 2nd 1st

Starting TCA

1st 2nd

Initial axis Determination – Axis Search Method



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



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




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




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




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



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



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



g

Axis refinement

with TCA 90

Axis Shift for JCC with Handle Parallel to Trial Cylinder Axis



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



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



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



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



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



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)



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



Smaller IOS means smaller

COLC means clearer

vision for the patient

Larger IOS means larger

COLC means worse


Patient wants MORE minus cyl

Fig 6.23 (bottom)

Page 6.36



Smaller IOS means smaller

COLC means clearer


Larger IOS means larger

COLC means worse



Fig 6.23 (top)

P 6 36



Page 6.36

Minus on

minus Plus on

minus


be 5.00 DC axis 110

Fig 6.24 (top)

P 6 38



Page 6.38

Minus on

minus


be 5.00 DC axis 110

Plus on

minus

Fig 6.24 (bottom)

Page 6.38



Reducing a 0.50 D IOS to

zero means a point focus

1.0 D IOS means a “1 D”

COLC which means worse



Fig 6.25 (top)

Page 6 39



Page 6.39

Minus on

minus


be 5.00 DC axis 110

Plus on

minus?????

Fig 6.25 (bottom)

Page 6 39



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



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



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



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



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:



Negative JCC Axis



Positive JCC Axis

If we are refining

TCA



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



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



g

cyl power, where

is the TCA?

(a) 90 or 180

(b) 45 or 135

TCA

OR

If TCA is 180 and the



patient prefers this

view, what do we do

next?

(a) cyl power 0.5 D

(b) cyl power 0.5 D



TCA

TCA

If TCA is 90 and the



patient prefers this

view, what do we do

next?

(a) cyl power 0.5 D

(b) cyl power 0.5 D



Rationale of “Power Search” (Full Subjective JCC) Pp 6 29 30 Lab step 4 p 5



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



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



“Power Search”

accept with TCA

set at 90, IF thepatient prefers

this view

This would be a



“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



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



Clinical Subjective Refraction:

Focal Line Approach

Clinical Subjective

Refraction Focal



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)



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



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



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



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


Fig. 6.30



Page 6.46

Step 1: BVS (b)

Step 2: vision with BVS. Should get ~20/60Therefore we predict 2 D astigmatism


Fig. 6.30



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


Fig. 6.30



With the posterior FL on the retina, we now direct the patient to view

the Fan Chart

Page 6.46


Fig. 6.30



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



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



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



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



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



Maddox V

The "Fan and

Block" Chart



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


Page 6.49

Both sides equally blurry




(22.5 away from 90)


Page 6.49



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:



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


Page 6.49

Right side clearer rotate



toward 90 again


Page 6.49




q y y



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



Corrector “Block”



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



The Fanand Block

Procedure

Page 6.51



Example 6.8

Fan and Block Procedure - a more Clinical Approach

Fan and Block ProcedurePage 6.51



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



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



+2 DS Fog

over BVS

Fig 6.34 (c), Page 6.52

2 5 DS

Fig. 6.36

Page 6.54



Fig 6.34 (d), Page 6.52

+2.5 DS

Fog over BVS

Fig. 6.37

Page 6.55



+3 DS Fog

over BVS

Fig 6.34 (e), Page 6.52

Further Refining Cylinder Axis – Maddox VPage 6.56



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).




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




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



0 DC

Page 6.59

2 DC

Page 6.59

4 DC

Page 6.60

Fig 6.34 (e), Page 6.52


Fig. 6.41

Page 6 59

Fig. 6.42

Page 6.59

Fig. 6.43

Page 6 60



0 DC

Page 6.59

2 DC

Page 6.59

4 DC

Page 6.60

Fig 6.34 (f), Page 6.52


Fig. 6.41

Page 6.59

Fig. 6.42

Page 6.59

Fig. 6.43

Page 6.60



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



Fig 6.34 (h), Page 6.52

Full cylinder correction

5 DC

Fig. 6.45

Page 6.61



Excess

cylinder

5.5 DC

Fig 6.34 (i ), Page 6.52



Vision in Astigmatism (ŵ BVS) vs. Spherical

AmetropiaFig. 5.25

Uncorrected



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



Blur Circle

Diameter

Airy Disc

Diameter

Compare Blur Circle & Airy Disc Diameter for 1 D Myope with 2.8 mm Pupil



Blur Circle

Diameter

Airy Disc

Diameter

Spreads over ~ 23 foveal cones

Spreads over ~ 4 foveal cones

Airy Disc



Blur Circle

Visual Angle vs. Actual Height of 20/20 Letter 20/20 letter subtends 5 (1/12) from 20 feet



= 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



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



x

h A

:Line125




x

h A

:Line100




x

h A

:Line80




x

h A

:Line63




x

h A

:Line50




x

h A

:Line40




x

h A

COLC Diameter for 4 mm pupil and 0.5 D and 1.0 D Residual Astigmatism



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



20/120 letter

20 foveolar receptors = 40 µM20/100 letter height = 120 µM



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




20/120 letter




FIRST




SECOND


Astigmatism and Subjective Refraction

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Transcript of Astigmatism and Subjective Refraction