optics for residents astigmatic lenses amy nau, od
TRANSCRIPT
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Optics for Residents
Astigmatic Lenses
Amy Nau, OD
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Astigmatic Lenses
Spherical lenses form a point image for each object point Stigmatic = point-like
Toroidal are not-point-likeAstigmatic!This is a second order aberration
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Toroidal Surfaces
Have two radii of curvature
r1
r2
r3
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Toroidal Surfaces
The surface is created by two radii of unequal length, Each in a plane at right angle to the other
Vertical plane
Horizontal
plane
1 2
r1=r2 P=n1-n2/r
For any object vergence, a toricSurface creates two separateimages.
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The astigmatic image- plano cyl
r1
r2
r1r1
Looks like a stack of thin plus lenses, eachOf the same refracting power
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The astigmatic lens- plano cyl
Say each lens has P=5D. Then if we put anObject 50cm in front of them, EACH lens formsA point image 33cm away.
The final composite image will be a series of Points oriented in a straight vertical line
x
r1 X’
X’
X’
HORIZONTAL LENS FORMS VERTICAL LINE IMAGE
Cylinder axis
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Astigmatic Lenses-plano cyl
x
Horizontal line image
X’
X’
X’
X’
VERTICAL LENS FORMS HORIZONTAL LINE IMAGE
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Astigmatic Lens- plano cyl
Vertical plane
Horizontal
plane
1 2
r1 is shorter than r2, so the power of r1 will be greater than r2.
F=n1-n2/r
Therefore, the VERGENCE of the twoPowers will be different
Recall do+di=1/f and F=1/f
So, if F1>F2, then di2 is farther from The lens than di1
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Astigmatic Lens- plano cyl
All toroidal surfaces have two major meridians- the one with the maxpower and the one with minimal power 90 degrees away. Eachwill form a line image, so what happens in the plano (no power)meridian?
Each horizontal sliceHas parallel faces w/oCurvature and thus noRefractive power. SameAlignment as axis.Vertical lens
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Problem type
Find the powers of a plano cyl lens using radius information.Determine image position using radius information.
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Maddox Rod
This is used to test EOM imbalances.
X
Real horizontal line image
Position of virtual, vertical line image, same position as X
THE MADDOX ROD IS A STACKOF THESE LENSES ALL TOGETHER.
point source
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Maddox Rod
This vertical line image is virtual Cannot be focused on a screen CAN be seen when looked at
through the lens towards X.
X
Since the eye is very close to the lens, the horizontal line is not seen.The eye then sees the virtual, VERTICAL image line that appears to be Located at the object point (where the light is).
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Maddox Rod
Eye sees VIRTUAL horizontal image
Eye sees VIRTUALvertical image
Remember the eye behind the red lens (OD) deviates in the direction OPPOSITE to that of the virtual red line.
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Problem Type
Know generally how Maddox rod works.Know what occurs clinically!
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The Cross Diagram
Take the example some power, P x 180This has a maximum power is located in the vertical meridian.
{An equivalent expression would be P@90- this is how K’s are expressed.}
+1.00 = +2.00 x 180
+1.00
+1.00 pl
+2.00 +3.00
+1.00
=
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Transpositon
+3.00
+1.00
=
+3.00
+3.00
pl
-2.00
+3.00 = -2.00 x 090
Combined cyl
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Transposition
+3.00 = -2.00 x 090is same as +1.00= +2.00 X180
+1.00
+1.00 pl
+2.00+3.00
+1.00
=
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Problem Types
Be able to convert an Rx into a cross diagram
Be able to convert a cross diagram into an Rx
Know how to transform between plus and minus cyl
Draw cross diagrams in plus and minus form
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The Circle of Least Confusion
x
+5.00 x 090
+3.00 x 180 X’v
X’h
20cm33cm
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The Circle of Least Confusion
X’v
X’h
x
Interval of Sturm - distance between the two line images
CLC
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CLC
Vergence at the clc is the average emergent vergence leaving the lens.
Lc=L1+L2/2 The location of the clc is the reciprocal of
Lc
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The Circle of Least Confusion
x8
8
2
pl
10
8
Object is placed 1 m in front of this lens.
L’=F+L L’=10-1=9D and l’=11.11cmL’’=F+LL’’=8-1=7D and l’’=14.28cmLocation of clc = reciprocal of average verg.L’c=L’+L’’/2 = (9+7)/2 = 8D; and l’c=1/L’c so,l’c=1/8 =12.5cm
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Spherical equivalent
Take ½ the cyl and add to sphere
-4.00+1.00x180 becomes-3.50D
Good for patients who can’t tolerate cyl in spectacles
Good for contact lenses
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Problem types
Understand the terminology
Know how to calculate the length of the conoid of Sturm
Know how to find the spherical equivalent in an Rx
Know how to locate the CLC
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Images of Extended Objects
E
Verticalmeridianfocus
Horizmeridianfocus
Circlefocus
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Images of Extended Objects
If the astigmatism is such that the two cyl axes are not Oriented vertically and horizontally but at some other position, Each image line is still parallel to the corresponding axis
Axis 45 Axis 135
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Differential Motion of Image Lines
It is possible to move only ONE part of a toric image
P1 X 090 combined with P2 X 180You can place a new cyl lens in front of the above, P3 x 180
p1
PL p2
PL + PL
p3
The result is (p2 + p3) x 180. P1 is unaffected!
If p3 is +, pulls the horizontal line image closer to the lens itselfIf p3 is - ,the vergence is decreased and the image is pushed away
THIS IS HOW THE JCC LENS WORKS…………………
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Differential Motion of Line Images
You can move both the horizontal and vertical images simultaneously
pl
plp1
p2
+
p3
p3
(p1+p3)x180 combined with (p2+p3) x 090
Changes the vergence in both meridians equallyIf it is of the proper strength, the concoid of SturmCan be collapsed, thus eliminating the astigmatism
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Differential Motion of Line Images
P1 @ 090P2 @ 180
-p3 @ 180
+3D sph
P1P2
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Differential Motion of Line Images
Note that the image moves equally, but only in the dioptricsense—the linear distance moved by the more distant linemust be greater that that moved by the closer line. This is due to proximity to the lens (vertex)
10 11 25 26
A 1cm linear distance between 10 and 11 cm correspondsTo a dioptric change of 0.9DA 1 cm linear distance between 25 and 26 cm correspondsTo a dioptric change of .15D
= .9D =.15D
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Cyl orientation (convention)
The 0-180 axis (horizontal)0 begins at the patients LEFT ear and rotates counterclockwise when you are facing the patient. This is true for both eyes.
Left reference ear
30 deg120 deg
0180
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Meridional Powers of Cyl Lenses
What about the powers between the major meridians???
The power gradation from max to min is NOT a straight linechange; the power gain moving from the axis meridian (min)to the maximum increases by the sin 2 of the angle away from the axis.
60
In this 3D cyl, the power in the meridian 60 to the axis is 3(sin260) = 3(.866)2 = 3(.75) = +2.25D
F(sin2)
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Meridional power of cyl lenses
FactoidFor any spherocylinder lens, the power in
the meridian 45 degrees to the axis (that is, halfway between the max and min meridional powers) is always the spherical equivalent of that lens.
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Problem type
Be able to calculate an off axis power
What is the power at 45 degrees?-1.00-2.00x180? A. -2.00D
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Jackson Cross Cylinder
A toric lens that is composed of a + cyl and – cyl of equalpowers ground on to one lens, with their axes at right anglesTo each other.
The strength of the cyl is always two times, and of opposite sign to the power of the sphere +1.00 = -2.00 x 180 or -0.25 + 0.50 x 090
ALL CROSS CYL LENSES HAVE AN EQUIVALENT POWER OF ZEROTHUS, THE CLC WILL NOT BE MOVED!
+
+
+ +Plus axis at 90Plus axis at 180
The meridians marked are the axes!
- -
-
-
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JCC for power refinement
+ axis at 090- Axis at 180
Both focal lines will move away from each otherAnd the astigmatism will increase (CLC increases in size)
+ axis at 180- Axis at 090
Both focal lines will move towards each otherAnd the astigmatism will decrease (CLC decreasesIn size)
Note the position of the clc is stationary
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JCC for power refinement
Clinically, the CLC is placed as Close to the retina as possibleUsing the sphere powers (usually the spherical equivalent). ThenThe patient can determine if the size of the blur circle increases or decreases
As soon as the patient can no longer tell the difference, then the Interval of sturm is collapsed, and there is “no more” astigmatism.
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Problem type
Be able to recognize a JCC in Rx formBe able to write JCC in Rx formatUnderstand how it works in general terms.
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Learning Goals
Nature of toricsMaddox rod opticsCross diagramsTranspositionCLCImages formed by
torics
Manipulation of image position
Meridional (off axis) powers
Optics of the JCC
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Free Optics Textbook online
http://www.lightandmatter.com/bk5a.pdf
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Is it moving and shimmering?
Buy a poster!
Look at this illusion for a while and it willappear to be shimmering and moving.
Also: Follow the outermost groove and watch itchange from a groove to a hump as you go around the wheel.