optics for residents astigmatic lenses amy nau, od

Optics for Residents

Astigmatic Lenses

Amy Nau, OD

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

Toroidal Surfaces

Have two radii of curvature

r1

r2

r3

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.

The astigmatic image- plano cyl

r1

r2

r1r1

Looks like a stack of thin plus lenses, eachOf the same refracting power

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

Astigmatic Lenses-plano cyl

x

Horizontal line image

X’

X’

X’

X’

VERTICAL LENS FORMS HORIZONTAL LINE IMAGE

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

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

Problem type

Find the powers of a plano cyl lens using radius information.Determine image position using radius information.

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

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).

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.

Problem Type

Know generally how Maddox rod works.Know what occurs clinically!

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

=

Transpositon

+3.00

+1.00

=

+3.00

+3.00

pl

-2.00

+3.00 = -2.00 x 090

Combined cyl

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

=

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

The Circle of Least Confusion

x

+5.00 x 090

+3.00 x 180 X’v

X’h

20cm33cm

The Circle of Least Confusion

X’v

X’h

x

Interval of Sturm - distance between the two line images

CLC

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

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

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

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

Images of Extended Objects

E

Verticalmeridianfocus

Horizmeridianfocus

Circlefocus

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

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…………………

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

Differential Motion of Line Images

P1 @ 090P2 @ 180

-p3 @ 180

+3D sph

P1P2

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

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

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)

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.

Problem type

Be able to calculate an off axis power

What is the power at 45 degrees?-1.00-2.00x180? A. -2.00D

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!

- -

-

-

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

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.

Problem type

Be able to recognize a JCC in Rx formBe able to write JCC in Rx formatUnderstand how it works in general terms.

Learning Goals

Nature of toricsMaddox rod opticsCross diagramsTranspositionCLCImages formed by

torics

Manipulation of image position

Meridional (off axis) powers

Optics of the JCC

Free Optics Textbook online

http://www.lightandmatter.com/bk5a.pdf

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.