Visual Optics

1. Visual Optics Chapter 3 Retinal Image Quality

2. The Net Monochromatic Wavefront Aberration and its Components Page 3.34

3. Photorefractive Keratectomy (PRK) Page 3.34 • PRK for myopia flattens the central cornea • Patients becomes emmetropic, but some have problems When? Why? Figure 3.28 – Shape of a myopic patient’s cornea before (dashed line) and after photorefractive keratectomy (PRK). Note the abrupt change in anterior corneal surface contour at the edge of the “ablated” zone.

4. LASIK Procedure Page 3.37 Figure 3.31 • For LASIK, a flap of anterior cornea is first cut and folded back • Underlying stroma ablated, then the flap is folded back into place • Success rate higher, but some patients still have problems When? At nightLarger pupil Why? Aberrations; due to rapid change in corneal contour at edge of ablation zone

5. Measuring the Eye’s Wavefront Aberration Page 3.35

6. Shack-Hartmann Aberrometer: Object Grid Page 3.35 Light from the object grid refracts into the eye, reflects from the retina, and re-refracts out of the eye (double pass) The emergent wavefront represents a “double sampling” of intrinsic ocular aberrations and diffraction Figure 3.29 – Shack-Hartmann object array consists of a rectangular grid pattern of point sources

7. Based on Page 3.35 Aberrometer: measures the eye’s aberrations IN (first pass) OUT (second pass) ideal system To detector

8. Based on Page 3.35 Aberrometer: measures the eye’s aberrations IN (first pass) OUT (second pass) aberrated system To detector

10. Aberrometry on PRK Patients Page 3.34 • Aberrometer detects large wavefront aberration at edge of ablation zone • Translates to significant problems with glare and halos at night • Similar findings in LASIK patients Figure 3.28 – Shape of a myopic patient’s cornea before (dashed line) and after photorefractive keratectomy (PRK). Note the abrupt change in anterior corneal surface contour at the edge of the “ablated” zone.

11. Adaptive Optics – Smoothing the Aberrated Wavefront Pp 3.36 & 3.38 • Aberrometers measure the eye’s wavefront aberration • Can we change the aberrated wavefront to an ideal one? • Yes. By using an optical device to “compensate” • The optical device is a deformable (active) mirror that continually “adapts” to a changing wavefront based on computer feedback

12. Page 3.38 Deformable Mirror: Adaptive Optics “Response” Deformable mirror resides on the input side of an aberrometer Contains a series of actuators to change local shape across mirror surface Based on computer analysis of the unmodified exiting wavefront, the mirror “deforms” into a shape that produces minimal output aberration Figure 3.32 – Basis of a deformable mirror. The mirror surface consists of multiple segments, each independently controlled by one or more underlying actuator(s).

13. Adaptive Optics in Imaging Systems based on Page 3.39 • Early applications of deformable mirrors in astronomy to overcome atmospheric “turbulence” Jupiter’s moon Europa, AO off; resolution 0.5 seconds arc Europa with AO on; resolution 0.007 seconds arc

14. Identical Principle used in Ophthalmic Imaging Page 3.39 Scanning Laser Ophthalmoscope Mirror changes shape Figure 3.34 - Schematic of high-resolution ophthalmic imaging system: the micro-deformable mirror (µDM) compensates for aberrations in the eye.

15. SLO Page 3.39

16. Wavefront-Guided Refractive Surgery Pp. 3.38-39 • Same principles can be applied to refractive surgery procedures • Can change refractive surgery from an aberration-inducing “liability” to a procedure that corrects ocular aberrations • Requirements of the “adaptive optics” system: • Real-time detection of the eye’s wavefront aberration during surgery (extremely high response rates) • Real-time compensation for the wavefront aberration: active (deformable) mirror (extremely high response rates) • What would limit visual acuity in an aberration-corrected eye? 1. Pupil size 2. Photoreceptor mosaic (anatomical limit of resolution)

17. Deformable Mirrors in LASIK Systems Page 3.39

18. Deformable Mirrors in LASIK Systems Page 3.39 • The VISX Wavescan system incorporates an active mirror measuring 8.0 mm  9.6 mm across with: • 48,000 separate mirror elements (each 40 m  40 m) • each element has four independently operated actuators • each element can readjust 250 times per second Mirrors based on micro-electro-mechanical system (MEM) technology are compact, with drive electronics fabricated directly onto the mirror substrate

19. Defining and Quantifying Monochromatic Wavefront Aberrations of the Eye: Page 3.39

20. Perfect refracted wavefront Lenses and the eye do not produce perfect wavefronts Ideal Lens Spherical Wavefront Spherical Wavefront How do we quantify the aberrated wavefront? Typically use a polynomial function based on a circular aperture Examples: Zernike polynomial, Seidel function PointImage PointObject PARAXIAL IMAGE PLANE EXIT PUPIL PLANE

21. Making Sense of a Complex Wavefront Shape Zernike Approach: describe wavefront as a polynomial function with 0, 1st, 2nd, 3rd…..nth order terms First five orders include 21 separate terms

22. The First Five Zernike Orders Zernike polynomials from zero to fifth order. The zero order (piston), and first order (tilt), also called “prism” have no bearing on image quality. Fifth order aberrations (bottom row) are pentafoil (far right and far left), secondary trefoil (second from left and right), and secondary coma (third from left and right).

23. Seidel (Third Order, Monochromatic) Aberrations Page 3.40

24. Seidel Approach: Wavefront Shape in Exit Pupil & Image Plane • Paraxial Optics predicts that an axial point object produces an axial point image r Page 3.40 Figure 31 – Relationship between wavefront coordinates in the (exit) pupil plane (x, y, z) and image plane (x0, y0, z0). r = wavefront radius of curvature.

25. Seidel Approach: Wavefront Shape in Exit Pupil & Image Plane For the ideal wavefront, all locations in the exit pupil would converge to (x0 y0 z0 ) at the paraxial image point r Page 3.40 Figure 31 – Relationship between wavefront coordinates in the (exit) pupil plane (x, y, z) and image plane (x0, y0, z0). r = wavefront radius of curvature.

26. An aberrated wavefront does not converge to x0 y0 z0 (paraxial image point). Different parts of the wavefront converge to different locations in image space

27.  x  x0 Defining Wavefront Shape in Exit Pupil Plane Based on page 3.40 Exit Pupil Paraxial image plane Object plane Most important wavefront attributes to quantify mono-chromaticaberrations: 1. Aperture (): distance from center of ExP 2. Meridian (): orientation in exit pupil 3. Off-axis position ()

28. y   x Coordinates in Exit Pupil: Wave at Oblique Angle Page 3.40 Paraxial image plane W z Object plane Exit Pupil Defining wavefront position as a distance (W) from the exit pupil plane at aperture height () and meridian ()

29. y x  x0  x Coordinates in Exit Pupil (and displacement in image plane): Off-axis Object Point Page 3.40 Paraxial image plane Object plane Exit Pupil For an off-axis object point, how does the image point vary from the paraxial prediction, x0 ?

30. Ideal Wavefront (Spherical) Actual Wavefront – Seidel Aberrations Ideal vs Aberrated Wavefront Page 3.41

31. Seidel Aberrations: Aperture (), Angular () and Object Height (0) dependence Page 3.41 Which aberrations are aperture-dependent? Spherical aberration and Coma (aperture dependence > 2)

32. Seidel Aberrations: Aperture (), Angular () and Object Height (0) dependence Page 3.41 Define the off-axis aberrations: Coma, off-axis astigmatism, field curvature and distortion (all have an 0 term).

33. Seidel Aberrations: Aperture (), Angular () and Object Height (0) dependence Page 3.41 Which are the meridionally-dependent aberrations? Coma, OAA ( cos2; greatest meridional variation) and distortion Significance of no meridional dependence of SA and field curvature? Symmetrical image

34. Off-axis Astigmatism Coma Point-spread functions: Which are the meridionally-dependent aberrations? Spherical aberration Ideal wavefront Airy disc pattern

35. Spherical Aberration

36. Spherical Aberration: Ray Diagram Page 3.43 Figure 3.36 – Spherical aberration

37. Quantifying Spherical Aberration Page 3.44 • Longitudinal Spherical Aberration (LSA) • Transverse Spherical Aberration (TSA)

38. Longitudinal Spherical Aberration (LSA) Page 3.44 Note: in Geometrical Optics, the symbol “y” is often used for aperture diameter instead of 

39. Marginal Focus Marginal Focus Marginal Focus LSA Figure 3.37 – LSA for (a) small, (b) medium, and (c) large pupil Page 3.45

40. Spherical Aberration: Longitudinal (LSA) and Transverse (TSA) Page 3.46 Figure 3.38 – LSA and TSA for a reduced eye (spherical reduced surface) with large pupil diameter. Object is a distant axial point source. The waist of least aberration (WOLA) is well to the left of the paraxial focus. Spherical aberration greatly exaggerated.

41. LSA and TSA Page 3.47 Figure 3.39 – (a) Relationship between LSA and TSA. fm = marginal focal length; fp = paraxial focal length. Appearance of screen image at the paraxial focus also shown. (b) Using similar triangles to relate LSA to TSA in terms of pupil diameter (y);  = angle subtended by marginal ray (at optical axis).

42. SA and Real Eyes Page 3.48 • Real eyes do not have spherical corneas or crystalline lenses • Experimental results show positive corneal SA and negative lenticular SA • Positive corneal SA < predicted for spherical cornea • SA also differs between myopes and hyperopes Why would hyperopes have higher corneal SA? Less aspheric corneas (less peripheral flattening). Reason? Unknown

43. Page 3.49 Figure 3.38 – (a) Spherical cornea (b) Aspheric cornea (c) Aspheric rays (_______) vs spherical rays (- - - - - - - -)

44. Ocular SA and Refractive Surgery Page 3.50 If pupil diameter exceeds ablation zone diameter  SA Larger ablation zone means deeper ablation LASIK produces similar problems at the edge of the ablated zone Replacing a non-ablated flap over the reshaped stroma is also a problem, often introducing higher order aberrations Figure 3.41 – Light ray traveling through the center of the pupil and two rays either side are shown refracting through the flattened (ablated) corneal zone. Another ray immediately either side of the ablated zone refracts at a significantly sharper angle through the now steepest corneal curvature. This causes considerable positive spherical aberration

45. Coma Page 3.52

46. Coma Page 3.52 Comatic image ofa point Most complex monochromatic aberration “Off-axis” version of spherical aberration Asymmetric, comet-shaped, image very detrimental to overall image quality

47. Coma Page 3.52 Greater wavefront curvature above axis: converges marginal image rays below the paraxial image point Lower wavefront curvature below axis: leaves too little convergence for marginal rays to reach the paraxial image point Figure 3.42 (bottom) – Seidel positive coma ray pattern for a spherical refracting surface

48.   Reference Planes for Asymmetric Aberrations Page 3.53 x0 x Tangential Plane: plane passing through optic axis in direction of OA point contains chief ray (pupil ray) from OA point and optic axis perpendicular to tangential plane; also passing through optic axis Sagittal Plane:

49. Coma: Tangential & Sagittal Planes Page 3.54 Greatest wavefront asymmetry in tangential plane Object presents the most asymmetric profile in this plane Least wavefront asymmetry in sagittal plane All sagittal rays focus in the tangential plane Figure 3.44 – Coma produced by a spherical refracting surface (e.g. the cornea) for a below-axis object point in the tangential plane (top) and sagittal plane (bottom).

50. Coma: 45 Oblique Planes Page 3.55 45 oblique planes focus right and left of the tangential plane Stronger refraction above axis; weaker below-axis Figure 3.45 – Coma produced by a spherical refracting surface for a below-axis object point in oblique incident planes, 45 from vertical (top); +45 from vertical (bottom).