1. Optics for Residents Astigmatic Lenses Amy Nau, OD

2. Astigmatic Lenses Spherical lenses form a point image for each object point  Stigmatic = point-like Toroidal are not-point-like  Astigmatic!  This is a second order aberration

3. 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=r2P=n 1 -n 2 /r For any object vergence, a toric Surface creates two separate images.

4. The astigmatic image- plano cyl r1 r2 r1 Looks like a stack of thin plus lenses, each Of the same refracting power

5. The astigmatic lens- plano cyl Say each lens has P=5D. Then if we put an Object 50cm in front of them, EACH lens forms A point image 33cm away. The final composite image will be a series of Points oriented in a straight vertical line x r1 X’ HORIZONTAL plano-cyl LENS FORMS VERTICAL LINE IMAGE Cylinder axis

6. Astigmatic Lenses-plano cyl Horizontal line image x X’ VERTICAL plano cyl LENS FORMS HORIZONTAL LINE IMAGE

7. 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=n 1 -n 2 /r Therefore, the VERGENCE of the two Powers will be different Recall d o +d i =1/f and F=1/f So, if F1>F2, then d i2 is farther from The lens than d i1

8. Astigmatic Lens- plano cyl All toroidal surfaces have two major meridians- the one with the max power and the one with minimal power 90 degrees away. Each will form a line image, so what happens in the plano (no power) meridian? Each horizontal slice Has parallel faces w/o Curvature and thus no power. Same Alignment as axis. Vertical lens

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

10. Maddox Rod X Real horizontal line image Behind the eye Position of virtual, vertical line image, same position as X This is what the patient sees THE MADDOX ROD IS A STACK OF THESE LENSES ALL TOGETHER. point source Horizontal line image x X’

11. 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).

12. Maddox Rod Eye sees VIRTUAL horizontal image Eye sees VIRTUAL vertical image Remember the eye behind the red lens (OD) deviates in the direction OPPOSITE to that of the virtual red line.

13. Problem Type Know generally how Maddox rod works. Know what occurs clinically!

14. The Cross Diagram Take the example some power, P x 180 This 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 pl +2.00+3.00 +1.00 =

15. Transpositon +3.00 +1.00 = +3.00 pl -2.00 +3.00 = -2.00 x 090 Combined cyl

16. Transposition +3.00 = -2.00 x 090 is same as +1.00= +2.00 X180 +1.00 pl +2.00 +3.00 +1.00 =

17. 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

18. The Circle of Least Confusion x +5.00 x 090 +3.00 x 180 X’v X’h 20cm 33cm

19. The Circle of Least Confusion X’v X’h x Interval of Sturm - distance between the two line images CLC

20. 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

21. The Circle of Least Confusion  x  8 8 2 pl 10 8 Object is placed 1 m in front of this lens. L’=F+L L’=10-1=9D and l’=11.11cm L’’=F+L L’’=8-1=7D and l’’=14.28cm Location 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

22. 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

23. 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

24. Meridional Powers of Cyl Lenses What about the powers between the major meridians??? The power gradation from max to min is NOT a straight line change; 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(sin 2 60) = 3(.866) 2 = 3(.75) = +2.25D F(sin 2 )

25. Meridional power of cyl lenses Important OKAP Factoid For 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.

26. Problem type Be able to calculate an off axis power What is the power at 45 degrees? -1.00-2.00x180? A. -1.50D

27. Differential Motion of Line Images P1 @ 090 P2 @ 180 -p3 @ 180 +3D sph P1 P2

28. Jackson Cross Cylinder A toric lens that is composed of a + cyl and – cyl of equal powers ground on to one lens, with their axes at right angles To 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 ZERO THUS, THE CLC WILL NOT BE MOVED! + + ++ Plus axis at 90 Plus axis at 180 The meridians marked are the axes! - - - -

29. JCC for power refinement Clinically, the CLC is placed as Close to the retina as possible Using the sphere powers (usually the spherical equivalent). Then The 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.

30. 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 deg 120 deg 0 180

31. Problem type Be able to recognize a JCC in Rx form Be able to write JCC in Rx format Understand how it works in general terms.

32. Free Optics Textbook online http://www.lightandmatter.com/bk5a.pdf

33. Learning Goals Nature of torics Maddox rod optics Cross diagrams Transposition CLC Images formed by torics Manipulation of image position Meridional (off axis) powers Optics of the JCC