Visual Optics

1
Visual Optics
Page 3.34

• Chapter 3
• Retinal Image Quality

2
The Monochromatic Wavefront AberrationKey
Points so Far

• Corneal refractive surgery can increase
  (conventional) or decrease (wavefront-guided)
  ocular aberrations
• Aberrometers measure the eyes wavefront
  aberration
• Adaptive Optics systems compensate for the eyes
  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 eyes 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 eyes wavefront aberration
• Remove diffraction from the eyes PSF
• Sculpt the patients cornea using high energy
  excimer photons
• Measure the eyes 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
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-chromatic aberrations
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
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
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
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 vs Aberrated Wavefront
Page 3.41
Generate monochromatic aberration by replacing
paraxial simplification of Snells 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 gt ?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
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
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 SpherePower vs. Incident Height
Myopic Real Cornea Power vs. Incident Height
50.75 D ? 44.71 D 5.04 D
54.00 D ? 46.91 D 7.09 D