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Chapter 6 Astigmatism and Subjective Refraction 2007

VIEWS: 5 PAGES: 194

									Visual Optics 2006/2007

            Chapter 6
Astigmatism & Subjective Refraction
        Image produced by +/+ Spherocylinder
                                                                         Page 6.1
  Astigmatism = 3 D




                                                               Dioptric
                                                             separation
                                                            of FLs = 3 D




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 .
                           Page 6.2




Spherical Equivalents to
   Spherocylinders
                                                                   Fig 6.1,
                                                                   Page 6.1
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 6.1
Page 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
The Astigmatic Eye and
  Equivalent Spheres
                                                                   Page 6.3

    The Astigmatic Eye and Equivalent Spheres
• The equivalent sphere to the full astigmatic correction places the
  COLC 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
    Page 6.3     Fig 5.24
                Page 5.45



Take the eyes from
Chapter 5 that we used
to define the five clinical
types of astigmatism and
find the BVS for each
    Fig 5.24
   Page 5.45




Full ametropic correction
    Fig 5.24
   Page 5.45




                 FS = +4 D
                             In terms of COLC position:




                                                 BVS = +4 D
Full ametropic correction
    Page 6.3     Fig 5.24
                Page 5.45



Take the eyes from
Chapter 5 that we used
to define the five clinical
types of astigmatism and
find the BVS for each
    Fig 5.24
   Page 5.45




Full ametropic correction
    Page 6.3     Fig 5.24
                Page 5.45



Take the eyes from
Chapter 5 that we used
to define the five clinical
types of astigmatism and
find the BVS for each
    Fig 5.24
   Page 5.45




Full ametropic correction
    Page 6.3     Fig 5.24
                Page 5.45



Take the eyes from
Chapter 5 that we used
to define the five clinical
types of astigmatism and
find the BVS for each
    Fig 5.24
   Page 5.45




Full ametropic correction
    Page 6.3     Fig 5.24
                Page 5.45



Take the eyes from
Chapter 5 that we used
to define the five clinical
types of astigmatism and
find the BVS for each
   Fig 5.24
  Page 5.45




Full ametropic correction
Page 6.4




           Examples of Equivalent Spheres
             using ocular power and image
                      vergences
 Example 6.1: Uncorrected Simple Hyperopic Astigmatism

                              Femm = +60 D                               Page 6.4
        Full
  +3 correction                                                  Equivalent
                                                                 sphere?
          0
                                                                  +1.50 DS

                                                            LCOLC = +58.5 D




Fig. 6.2 - Reduced eye example of simple hyperopic astigmatism. Focal line
positions correspond to the uncorrected eye
Example 6.2: Uncorrected Compound Myopic Astigmatism
                     Femm = +60 D                  Fig 6.3
6      Full                                       Page 6.5
     correction
                                             Equivalent
     2                                      sphere?

                                             4.00 DS

                            LCOLC = +64 D
  Example 6.2: Compound Myopic Astigmat with BVS

                                                                        Page 6.6




                                                              2D     2D



                                       BVS produces
                                        symmetrical
                                           Mixed
                                        Astigmatism


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 .
Example 6.2: Fully Corrected Compound Myopic Astigmat
                                                    Page 6.6




                                           Full correction
                                            produces a
                                           point focus at
                                             the retina
                                        Page 6.7




Use of the BVS in Clinical Refraction
    Sphere-only Refraction (Donder’s Method)                            Page 6.7


  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.

• 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
                         Vision with BVS                            Page 6.7




• 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)
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                          2.003.00                       high
______________________________________________________________________________
   * Vision for  4 mm pupil and serif letters (for smaller pupil vision better for a given level
      of 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
  Uncorrected
                                                Page 5.48
spherical myope

                                    Vision in the uncorrected
                                    2D myope is “identical” to
                                    that of the 4 D astigmat
                                    with COLC on the retina
                                    COLC size is the basis
                                    for predicting magnitude
                                    of astigmatism
                                    Move the COLC to the
 Uncorrected                        retina with sphere.
 astigmat with                      Worse vision correlates
COLC on retina                      with higher astigmatism
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                          2.003.00                       high
______________________________________________________________________________
   * Vision for  4 mm pupil and serif letters (for smaller pupil vision better for a given level
      of 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).
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 level
      of 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).
                                       Page 6.8




Control of COLC Position during Refraction
Control of COLC Position during Refraction
                                                                    Page 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 clinician
adds 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
    How much sphere is needed to return the COLC to the retina?
                                                                   Page 6.9

                                            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 Retina
                                                                  Page 6.10
Use the CMA considered earlier to demonstrate the proof




                                                           BVS
                                                          4 DS




   Fig 6.3,
   Page 6.5
 Proof that Sphere = ½ Cylinder Maintains COLC at Retina
BVS puts COLC                                       Fig. 6.4
 on the retina
  Proof that Sphere = ½ Cylinder Maintains COLC at Retina
Now add 2 DC axis 180 to the BVS; COLC moves behind retina   Fig. 6.5,
                                                              page 6.10
   Proof that Sphere = ½ Cylinder Maintains COLC at Retina
                                                                       Page 6.11


                                                                         Fig. 6.5,
                                                                         page 6.10
    L=0




                                                   PROOF: THE HARD WAY


L90 = L + F90 + FBVS + FCyl (90) = 0 + 66  4  2 = +60 D = focused at retina
L180 = 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
                                 Page 6.12




Clinical Subjective Refraction
     (Astigmatic Patient)
Fig. 6.6                                                               Page 6.12




  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
 Fig. 6.6                                                               Page 6.12




Finding BVS fills in the first piece of the puzzle. The clinician knows that the
COLC 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 state
Note that BVS power gives no information about magnitude of astigmatism
Fig. 6.6                                                            Page 6.12




Vision with BVS is a guide to amount of astigmatism, but gives NO
information about focal line orientation




Vision with BVS is the clinician’s guide to predicting amount of astigmatism
A larger COLC means more astigmatism (constant y)
Page 6.12




?


?



?
Example 6.4 - Clinical Subjective Refraction
   Example 6.4 - First step: BVS
                                                                 Page 6.13
• Start with large power increments (minimize number of steps)
• Refine with progressively smaller power increments
 Fig. 6.7
 Page 6.14




Vision worse


V much better


V better again


V better again


V unchanged ?
   Example 6.4 - Start with BVS
                                                                 Page 6.13
• Start with large power increments (minimize number of steps)
• Refine with progressively smaller power increments
• Refine with progressively smaller power increments

            Vision unchanged



            Vision unchanged



            Vision worse



            Vision better



          Marginal improvement
       • Refine with progressively smaller power increments

                    Vision DS is the BVS
• Step 9 indicates that 4 unchanged
• Now add +1 DS to BVS to deliberately “fog” patient. This should
  reduce acuity ~4 lines and helps relax accommodation
                   Vision unchanged



                    Vision worse



                    Vision better



                  Marginal improvement
             Verifying BVS: Fog-Defog   Page 6.15




The patient is now fogged
+1 D over tentative BVS
Vision 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 D
gives no improvement on
the VA chart
This procedure controls
accommodation
    Other Ways to Verify BVS
The Bichromatic (Duochrome) Test
Bichromatic Test assumes                         Fig. 6.9
that the visual system     Bichromatic Test      Page 6.16
prefers to focus yellow
(570 nm) on the retina




              Longitudinal spread of red and
              green in the eye is about 0.50 D
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 Green on retina
                                      0.25 DS
                                    focuses green
                                       on retina
                                                                Page 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
                                                                  Page 6.17
              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




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)
                                                                   Page 6.17
             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
Subjective Refraction using the
Jackson Cross Cylinder (JCC)
                                                                                Page 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 vision
  with 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




                          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 actual
                          powers in actual “meridians”

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 6.20




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
                   Assume retinoscopy was “off” for cyl giving 3 DC axis 160
   6        Full
          correction      Full correction in SC notation: 2 4 DC axis 180
              2
                                                                  Page 6.20




   Fig 6.3
   Page 6.5
                                                                          Page 6.20

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)
                                                                           Page 6.20

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




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, because
  the resultant cylinder axis will be correct (rotated 90 from the
  resultant power meridian)
Refining Cylinder Axis using Obliquely Crossed Cylinders
                                                  Page 6.20


   Obliquely crossed
   cylinders of the same sign
   will produce a resultant
   cylinder with an axis
   between the two
   Like an airplane’s path
   through the air with wind
   direction at an acute angle




                   NO WIND
Refining Cylinder Axis using Obliquely Crossed Cylinders
                                                  Page 6.20


   Obliquely crossed
   cylinders of the same sign
   will produce a resultant
   cylinder with an axis
   between the two                 resultant
                                   direction
   Like an airplane’s path
   through the air with wind
   direction at an acute angle
            Obliquely Crossed Cylinders (same sign)
                                                                  Page 6.21

                                 Resultant cylinder axis between two
                                 obliquely crossed cylinder axes
                                 Resultant axis will be closer to the
                                 axis of the higher power cyl




Fig 6.12 - Two negative cylinders with axes crossed at an oblique angle
produce a resultant negative cylinder with an intermediate axis.
                         Trial cyl axis (TCA) 90
  Resultant axis                                                 Page 6.19




For JCC axis
refinement, we place
the handle parallel to                              Obliquely crossed
the TCA                                             negative cylinders with
                                                    axes 45 apart
This produces
obliquely crossed
negative cylinders
The resultant axis is
in between, and
closer to the higher
power cyl (axis)
                                                                   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
   Page 6.22




JCC:
Refining Cylinder Axis
    Fig. 6.13
   Page 6.22




JCC:
Refining Cylinder Axis
First and second views are
equivalent to rotating the
TCA clockwise then
counterclockwise from 160
The advantage of the JCC is
that the patient sees instant
comparisons, not a gradual
change in axis
The axis “rotation” is also
identical between first and
second
    Fig. 6.13
    Page 6.22




JCC:
Refining Cylinder Axis
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
                                                                        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
           Refining 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 lines
  relative to the retina
                        JCC: Refining Cylinder Power                         Page 6.23


                                                             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 6.14 - 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
Fig. 6.15   Refining Cylinder Power – JCC Power Meridians Shown
Page 6.24
            JCC axes parallel and perpendicular to TCA for power refinement




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
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   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 preferred
Clinician 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 20/60
Defog in negative 0.25 DS steps
Expected vision:
    1.00 DS (+1.00 D fog) 20/60
    1.25 DS (+0.75 D fog) 20/40
    1.50 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
                                                     Page 6.26




                       Example 6.5

Jackson Cross Cylinder Procedure as “Seen” by the Clinician
 Patient for Full Subjective Refraction; BVS/JCC: ax = 23.39 mm
                                                                          Page 6.26




Fig. 6.16 - Application of the ametropia equation in lens cross format to show the
patient’s required ametropic correction for Example 6.5.
                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
                   Vision with BVS                      Page 6.27


     3.5 DS




    Vision        Astigmatism
                                  Dioptric separation
                   with BVS
                                     of FLs = 5 D
    20/20            Small
    20/30            1.00       Assume that the patient has
    20/40            1.50       smaller pupils and gets 20/120;
    20/60            2.00       so 4 D astigmatism is predicted

    20/80            3.00
    20/120           4.00
                                Based on table 6.1, page 6.8
20/160 – 20/200      5.00
      Initial Cylinder Axis Determination                  Fig 6.17, Page 6.27




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 Determination                     Page 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)
Initial axis Determination – Axis Search Method   Page 6.28



   1st               2nd




           Flip



                  BVS ONLY in Phoropter
Initial axis Determination – Axis Search Method   Page 6.28



      1st               2nd




        Flip
Initial axis Determination – Axis Search Method
                                     1st          2nd
  1st           2nd




                  Starting TCA


                                                  Page 6.29
    Initial axis Determination – Axis Search Method
                                                 1st             2nd
        1st             2nd




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?”


                                                                 Page 6.29
   Initial axis Determination – Power Search Method               Page 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?”


                          1st             2nd

   Trial cylinder                                       Trial cylinder
0.50 DC axis 180                                    0.50 DC axis 180
   Initial axis Determination – Power Search Method                    Page 6.28

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


                            1st               2nd

   Trial cylinder                                           Trial cylinder
0.50 DC axis 180                                        0.50 DC axis 180
   Initial axis Determination – Power Search Method                 Page 6.28

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)




                           1st              2nd

   Trial cylinder                                         Trial cylinder
0.50 DC axis 180                                      0.50 DC axis 180
   Initial axis Determination – Power Search Method                     Page 6.28

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)
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

                            1st              2nd          Trial cylinder
                                                        0.50 DC axis 45




     Trial cylinder
   0.50 DC axis 45
     Power Search for Predicted Astigmatism > 1 D                   Page 6.30


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
Axis refinement is used after “axis” or “power” search, or
following objective refraction (retinoscopy)
                  Resultant cylinder axis   Figure 6.20
                                            Page 6.31




Axis refinement
with TCA 90
Axis Shift for JCC with Handle Parallel to Trial Cylinder Axis

                                                          Table 6.2

                             Axis Shift                   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                13.5
             2.50                  5.5                11
             3.00                  4.5                 9
             4.00                  3.5                 7
             5.00                   3                 5.5
             6.00                  2.5                4.5
           3.5 from
           90 = 86.5   Resultant cylinder axis
           Axis error
            = 23.5                                +3.5 from
                                                    90 = 93.5
                                                    Axis error
                                                     = 16.5



Axis refinement
with TCA 90

                                                  Outcome: rotate
                                                   TCA counter-
                                                   clockwise. We
                                                    will rotate to
                                                  112.5 (midpoint
 Figure 6.20                                       of 90 and 135)
 Page 6.31
                                                                       Page 6.33




                                                           We are now only
                                                           2.5 away from the
                                                           required correcting
                                                           cylinder axis




Fig. 6.21 - TCA and correcting cylinder axis orientation for the second stage of
axis refinement
                                                   Fig 6.22
                                                   Page 6.33



                                         6 axis
  1 axis                                 error
   error




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




                          3.5 axis
3.5 axis
                            error
  error




Continue refining until
“equal” blur response
with TCA at CCA (110)
                   JCC Power Refinement                        Page 6.35


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’s
           full cylinder correction will
             be 5.00 DC axis 110
Fig 6.23 (bottom)
   Page 6.36




               Patient wants MORE minus cyl

Smaller IOS means smaller
                                              Larger IOS means larger
  COLC means clearer
                                                COLC means worse
  vision for the patient
                                                vision for the patient
Fig 6.23 (bottom)
   Page 6.36




               Patient wants MORE minus cyl

Smaller IOS means smaller
                                              Larger IOS means larger
  COLC means clearer
                                                COLC means worse
  vision for the patient
                                                vision for the patient
                              Fig 6.23 (top)
                                Page 6.36

Minus on
 minus
                      Plus on
                      minus




           Remember: the patient’s
           full cylinder correction will
             be 5.00 DC axis 110
                            Fig 6.24 (top)
                             Page 6.38

Minus on
 minus



                              Plus on
                              minus




           Remember: the patient’s
           full cylinder correction will
             be 5.00 DC axis 110
Fig 6.24 (bottom)
   Page 6.38




               Patient wants MORE minus cyl


  Reducing a 0.50 D IOS to                     1.0 D IOS means a “1 D”
  zero means a point focus                    COLC which means worse
                                                 vision for the patient
                              Fig 6.25 (top)
                                Page 6.39

 Minus on
  minus



                               Plus on
?????                          minus




            Remember: the patient’s
            full cylinder correction will
              be 5.00 DC axis 110
Fig 6.25 (bottom)
   Page 6.39




          Patient likes 5.00 D cyl

  The JCC changes a point              The JCC changes a point
 focus to a 0.50 D IOS with           focus to a 0.50 D IOS with
 anterior FL oriented at 20          anterior FL oriented at 110
    Fine-tuning 0.25 DC steps around 5.00 DC              Fig 6.26
                                                          Page 6.40




       Patient wants more minus cyl

The JCC changes anterior              The JCC increases the IOS to
and posterior FL orientation                    0.75 D
 but retains a 0.25 D IOS
                                                       Fig 6.27
                                                      Page 6.41




     Patient wants less minus cyl

                                    The JCC changes anterior
The JCC increases the IOS to
                                    and posterior FL orientation
          0.75 D
                                     but retains a 0.25 D IOS
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
                                                             Page 6.42
 Equivalent 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
         FCyl        1.50
  FS                       0.75 DS
          2            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

 Equivalent sphere to             5.25  2.75
 partial correction:        FS                  4.00 DS
                                       2
                    Negative JCC Axis




Positive JCC Axis
                     TCA
If we are refining
axis, where is the
TCA?
(a) 180
(b) 90
(c) 45
(d) 135
                               Resultant of obliquely crossed TCA and JCC
                         TCA   negative 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
                     TCA
If we are refining
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
(c) change TCA to 125
(d) change TCA to 145
                        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
(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

• 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

  •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
• 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
                    TCA
This would be a
“Power Search”
accept with TCA
set at 90, IF the
patient prefers
this view
This would be a
“Power Search”
reject with TCA
set at 180, IF the
patient prefers
this view



            TCA
  Rationale of “Power Search” (Full Subjective JCC)
                                                     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
  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




                                                Plus sphere

  To maintain control of patient accommodation, the posterior focal
  line is moved to the retina with sphere before starting the
  astigmatic correction
                   The Astigmatic Fan Chart

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
    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
Example 6.7 - The "Fan and Block" Method of Refraction
    Fig. 6.30
    Page 6.46




   Step 1: BVS (b)

   Step 2: vision with BVS. Should get ~20/60
   Therefore we predict 2 D astigmatism
Example 6.7 - The "Fan and Block" Method of Refraction
  Fig. 6.30
  Page 6.46




  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
Example 6.7 - The "Fan and Block" Method of Refraction
  Fig. 6.30
  Page 6.46




 With the posterior FL on the retina, we now direct the patient to view
 the Fan Chart
Example 6.7 - The "Fan and Block" Method of Refraction
  Fig. 6.30
  Page 6.46




  With the posterior FL on the retina, we now direct the patient to view
  the Fan Chart
Verification Example (extreme case): BVS Initially 2 D too Low    FLs REVERSED
                                                                     Fig. 6.31
                                                                     Page 6.48


   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




   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
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
Because the horizontal FL can no longer be focused, and less
accommodation is now required to focus the vertical line, the patient may
report 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
  handout
              COLC 2 D behind
              retina w “low” BVS

Vision with “low BVS” 20/60
(with accom.)  predict 2 D
astigmatism, so fog +1 D

 With extra +1 D over initial
 fog, 180 line more
 blurred, but 90 line
 perfectly clear with a little
 accommodation

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
Returning to the Current Example, with Posterior FL 0.50 D in front of Retina
  Fig. 6.30
  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
Fig. 6.32   The "Fan and Block" Chart
Page 6.49
                                    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
Fig. 6.32   The "Fan and Block" Chart
Page 6.49
                            Both sides equally blurry
                            (22.5 away from 90)
   Fig. 6.32           The "Fan and Block" Chart
   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
The key to axis refinement:
                                       to 90)  rotate in opposite
    rotate the ‘V’ in the
                                       direction to clearer leg
  opposite direction to its
 clearer leg until both legs
are equally blurry. Just like
 JCC, the endpoint will be
 an “equal blur” response
Fig. 6.32   The "Fan and Block" Chart
Page 6.49
                             Right side clearer  rotate
                             toward 90 again
Fig. 6.32   The "Fan and Block" Chart
Page 6.49
                            Both sides equally blurry
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 FL
backward. Note that cyl axis is parallel to the anterior focal line
Fig. 6.32
            Initially the horizontal “blocks” will be very blurred
Page 6.49   As we add minus cyl axis 180, the horizontal blocks gradually
            become clearer. Endpoint = H and V blocks equally clear

Corrector
 “Block”
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)

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
   Fig. 6.34
  Page 6.52



The Fan
and Block
Procedure
                                               Page 6.51




                   Example 6.8

Fan and Block Procedure - a more Clinical Approach
    Page 6.51           Fan and Block Procedure




                 5 D astigmatism




                                                   Fig 6.34 (a), Page 6.52


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).
    Page 6.51           Fan and Block Procedure

 BVS = 3.50 DS
 Vision with BVS: 20/160 to 20/200  estimate around 5 D astigmatism
 Fog over BVS for 5 D predicted astigmatism would be +2.50 DS (net
 sphere 3.50 + 2.50 = 1.00 DS)




                                                   Fig 6.34 (a), Page 6.52


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. 6.35
  Page 6.53


+2 DS Fog
over BVS




              Fig 6.34 (c), Page 6.52
  Fig. 6.36
 Page 6.54


+2.5 DS
Fog over
  BVS




              Fig 6.34 (d), Page 6.52
  Fig. 6.37
  Page 6.55


+3 DS Fog
over BVS




              Fig 6.34 (e), Page 6.52
Page 6.56
            Further Refining Cylinder Axis – Maddox V




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 V
Page 6.57




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
Page 6.58
            Further Refining Cylinder Axis – Maddox V




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                  Fig. 6.42     Fig. 6.43
Page 6.59                  Page 6.59     Page 6.60




0 DC                       2 DC         4 DC




               Fig 6.34 (e), Page 6.52
            Refining Cylinder Power
Fig. 6.41                   Fig. 6.42    Fig. 6.43
Page 6.59                  Page 6.59     Page 6.60




0 DC                       2 DC         4 DC




               Fig 6.34 (f), Page 6.52
            Refining Cylinder Power
Fig. 6.41                  Fig. 6.42     Fig. 6.43
Page 6.59                  Page 6.59     Page 6.60




0 DC                       2 DC         4 DC




               Fig 6.34 (g), Page 6.52
   Fig. 6.44
   Page 6.60




Full cylinder
 correction
   5 DC




                Fig 6.34 (h), Page 6.52
   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
                       Ametropia              Fig. 5.25
Uncorrected
                                                 Page 5.48
 spherical
  myope                    L R
                      L




 Uncorrected
 astigmat with
COLC on retina
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
                     Spreads over ~ 23 foveal cones
Diameter



Airy Disc
Diameter




                        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

        h = fe tan  = 16.67 mm tan 5 = 24 m
                                             P                       R
               20/200 letter 240 m

                                                       n  1.33 3
h                                                              
                         




              = test distance                           R
       standard = 20 feet (6.096 m)
       20          Letter height 240 m, Blur circle 46 m
          Line :
      200
          The VA Chart to our 1 D myope with 2.8 mm pupil

 x

hA
       20          Letter height 192 m, Blur circle 46 m
          Line :
      160
 x

hA
       20
          Line : Letter height 150 m, Blur circle 46 m
      125
 x

hA
       20
          Line : Letter height 120 m, Blur circle 46 m
      100
 x

hA
      20          Letter height 96 m, Blur circle 46 m
         Line :
      80
 x

hA
      20          Letter height 76 m, Blur circle 46 m
         Line :
      63
 x

hA
      20          Letter height 60 m, Blur circle 46 m
         Line :
      50

 x


hA
      20          Letter height 48 m, Blur circle 46 m
         Line :
      40
 x


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




 COLC             L1  L2 
                                    0.5 D 
Diameter          L  L   4 mm   120 D   16.7 M
             x y                          
                  1      2                 
                                         1.0 D 
                                          120 D   33.3M
                                  4 mm          
                                                 

                                     2.44    2.44  587.6  10 9 m
 Airy Disc       sin  AD Diameter         
 Diameter                              d            4  10 3 m
                                  
                    AD Diameter  2.05  10     
                                                2 




                                          
  h Diameter  f e tan  ADD   16.67 tan 2.05  102
   AD                                                     
                                                          
                                                               5.98 M
20 foveolar receptors = 40 µM




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



   Airy Disc
   Diameter

                                                 Blur circle diameter for
                                                 4 mm pupil and 0.50 D
                                                 residual astigmatism =
                 Blur circle diameter for        16.67 µM
                 4 mm pupil and 1.00 D
                 residual astigmatism
                 = 33.33 µM
20 foveolar receptors = 40 µM




     20/120 letter
20 foveolar receptors = 40 µM




           FIRST
20 foveolar receptors = 40 µM




           SECOND
20 foveolar receptors = 40 µM
20 foveolar receptors = 40 µM

								
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