Visual Optics

1. Page 3.34 Visual Optics Chapter 3 Retinal Image Quality

2. The Monochromatic Wavefront Aberration:Key Points so Far • Corneal refractive surgery can increase (conventional) or decrease (wavefront-guided) ocular aberrations • Aberrometers measure the eye’s wavefront aberration • Adaptive Optics systems compensate for the eye’s wavefront aberration: • feedback about aberrated wavefront drives deformable mirror shape change to compensate • Used in ophthalmic imaging systems (e.g. SLO) • Used to demonstrate potential acuity by smoothing the eye’s aberrated image (e.g. keratoconus) • Zernike function (polynomial expansion) breaks net wavefront aberration into a series of components • Each component describes a feature of the overall wavefront

3. This becomes This

4. Q1. The purpose of the deformable mirror in an ocular AO (adaptive optics) system is to: • Compensate for the eye’s wavefront aberration • Remove diffraction from the eye’s PSF • Sculpt the patient’s cornea using high energy excimer photons • Measure the eye’s wavefront aberration

5. 555 nm Mono- Light; 6 mm Pupil Outer Functions produce LESS acuity loss

6. Seidel (Third Order, Monochromatic) Aberrations Page 3.40 • Seidel approach more manageable • Produces less terms (5 only) • Covers central Zernike terms (SA, coma, secondary astigmatism); the ones producing greatest image degradation

7. 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.

8. 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.

9. 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

10.  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 (): in exit pupil (measured CC-wise from horizontal) 3. Off-axis position (): must cover both on- and off-axis object points

11. 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 longitudinal distance (W) from the exit pupil plane at aperture height () and meridian ()

12. 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 ?

13. y   x Ideal Wavefront Shape in Exit Pupil Page 3.40 W Paraxial image plane W z Object plane Exit Pupil The ideal longitudinal distance (W) from the exit pupil plane for all apertures () and meridians () would match that of a spherical wavefront centered on the corresponding paraxial image point

14. Ideal Wavefront (Spherical) Actual Wavefront – Seidel Aberrations (third order) Ideal vs Aberrated Wavefront Page 3.41 Generate monochromatic aberration by replacing paraxial simplification of Snell’s Law: ni = n i with true form: n sin i = n sin i

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

16. Seidel Aberrations: Aperture (), Angular () and Object Height (0) dependence Page 3.41 Define the off-axis aberrations:

17. Q2. Identify the “off-axis” aberrations (most complete, correct answer) • SA, coma & distortion • Coma, OA astigmatism & distortion • Coma, OA astigmatism, field curvature & distortion • SA, coma, OA astigmatism, field curvature & distortion

18. 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).

19. 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

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

21. Spherical Aberration

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

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

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

25. Marginal Focus Marginal Focus Marginal Focus LSA Figure 3.37 – LSA for (a) small, (b) medium, and (c) large pupil Page 3.45 NOTE: figures assume a spherical reduced surface

26. Q3. How does the assumption of spherical reduced surface curvature affect the estimate of longitudinal spherical aberration (compared to a typical real eye)? • Underestimated • Accurately estimated • Unrelated • Overestimated

27. Calibration Sphere on Nidek OPD-Scan: corneal analogy to spherical reduced surface

28. Calibration Sphere on Nidek OPD-Scan: corneal analogy to spherical reduced surface

29. Calibration Sphere:“Power” vs. Incident Height Myopic Real Cornea: “Power” vs. Incident Height 54.00 D  46.91 D = 7.09 D 50.75 D  44.71 D = 5.04 D