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 Have two radii of curvature r1 r2 r3

4. 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.

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

6. 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 LENS FORMS VERTICAL LINE IMAGE Cylinder axis

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

8. 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

9. 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 Refractive power. Same Alignment as axis. Vertical lens

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

11. 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 STACK OF THESE LENSES ALL TOGETHER. point source

12. 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).

13. 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.

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

15. 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 =

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

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

18. 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

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

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

21. 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

22. 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

23. 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

24. 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

25. Images of Extended Objects E Vertical meridian focus Horiz meridian focus Circle focus

26. 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 45Axis 135

27. Differential Motion of Image Lines It is possible to move only ONE part of a toric image P1 X 090 combined with P2 X 180 You can place a new cyl lens in front of the above, P3 x 180 p1p1 PL p2p2 + p3p3 The result is (p2 + p3) x 180. P1 is unaffected! If p3 is +, pulls the horizontal line image closer to the lens itself If p3 is -,the vergence is decreased and the image is pushed away THIS IS HOW THE JCC LENS WORKS…………………

28. Differential Motion of Line Images You can move both the horizontal and vertical images simultaneously pl p1p1 p2p2 + p3p3 p3p3 (p1+p3)x180 combined with (p2+p3) x 090 Changes the vergence in both meridians equally If it is of the proper strength, the concoid of Sturm Can be collapsed, thus eliminating the astigmatism

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

30. Differential Motion of Line Images Note that the image moves equally, but only in the dioptric sense—the linear distance moved by the more distant line must be greater that that moved by the closer line. This is due to proximity to the lens (vertex) 10112526 A 1cm linear distance between 10 and 11 cm corresponds To a dioptric change of 0.9D A 1 cm linear distance between 25 and 26 cm corresponds To a dioptric change of.15D =.9D =.15D

31. 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

32. 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 )

33. Meridional power of cyl lenses 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.

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

35. 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! - - - -

36. JCC for power refinement + axis at 090 - Axis at 180 Both focal lines will move away from each other And the astigmatism will increase (CLC increases in size) + axis at 180 - Axis at 090 Both focal lines will move towards each other And the astigmatism will decrease (CLC decreases In size) Note the position of the clc is stationary

37. 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.

38. 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.

39. 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

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

42. Is it moving and shimmering? Buy a poster! Look at this illusion for a while and it will appear to be shimmering and moving. Also: Follow the outermost groove and watch it change from a groove to a hump as you go around the wheel. Buy a poster!