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Page 3.34. Visual Optics. Chapter 3 Retinal Image Quality. Q1. The origins of spherical aberration (SA), coma and off-axis astigmatism (OAA) respectively are: . (a) all three are longitudinal (b) SA longitudinal, coma transverse, OAA longitudinal

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visual optics

Page 3.34

Visual Optics

Chapter 3

Retinal Image Quality

q1 the origins of spherical aberration sa coma and off axis astigmatism oaa respectively are
Q1. The origins of spherical aberration (SA), coma and off-axis astigmatism (OAA) respectively are:

(a) all three are longitudinal

(b) SA longitudinal, coma transverse, OAA longitudinal

(c) SA longitudinal, coma transverse, OAA transverse

(d) SA transverse, coma transverse, OAA longitudinal


Q2. Decentered ablation is one of the more common causes of visual problems in post-LASIK or PRK patients. One reason for the problems is:

(a) Longitudinal Spherical Aberration

(b) Transverse Spherical Aberration

(c) Coma

(d) Off-Axis Astigmatism

quantifying astigmatic error



Quantifying Astigmatic Error

Page 3.66

For an equiconvex spherical lens, distant object (and angles of obliquity up to 25):

For a near object (as in figure):

+5.0 D spherical lens,  = 25

Astigmatic error varies with the square of the angle of obliquity of the chief ray (tan2)



Ocular OA

Page 3.78

Figure 3.68 – The human eye has significant intrinsic oblique astigmatism for larger retinal eccentricities.


Ocular OA

Page 3.78

  • Oblique rays travel to more peripheral retinal locations
  • Resolving power decreases rapidly with retinal eccentricity
  • Rapid increase in ocular OA with eccentricity not a problem because peripheral retina has low resolution potential
  • Exception: patients with central retinal disease and VA loss

Curvature of Field

Page 3.68

  • Removing SA, coma and OA: mono- point object  point image
  • Plane objects do not necessarily form plane images
  • Common example of curvature of field seen with 35 mm projector image (parts of image clear; parts blurred)

Figure *.** – Curvature of field: 3D wavefront profile in the (exit) pupil plane produced by curvature of field for a plane object


Origin of Curvature of Field

Page 3.68

Figure 3.57 – refracting surface (devoid of spherical aberration, coma, or oblique astigmatism) with focal length, f, images parallel on-axis light rays at its second focus (F’). Oblique incident rays also refract at the curved surface and focus the same distance away.


Origin of Curvature of Field

Page 3.68

  • Parallel incident rays focus at F′ (distance f′ from surface)
  • Oblique parallel incident rays also focus a distance f ′ from surface
  • Oblique direction of f ′ places the focal point short of the axial position of F′ (error “p”)
  • Resulting image surface “Petzval’s Surface”

Curvature of Field & Petzval’s Surface

Page 3.69

Positive meniscus lens produces a concave image of a plane object

Figure 3.58 - The image of a plane object produced by an ophthalmic lens is curved. Here a positive lens produces negative (concave) image curvature for the plane object.


Spherical refracting surface:

Origin of Curvature of Field

Page 3.68


Origin of Curvature of Field

Page 3.68

  • Radius of curvature of Petzval’s surface varies with focal length and index of lens (or image space medium of spherical refracting surface)
  • This limits design options to reduce curvature of field in any optical system

Eliminating Curvature of Field

Page 3.68

Petzval Condition for lens system:

  • To produce a flat-field image with a camera lens system or microscope, the Petzval condition must be met
  • Anastigmatic camera lenses have zero OA and also satisfy the Petzval condition (flat image)

OA and Curvature of Field in Lens Design

Page 3.66

Spread of T and S foci increases exponentially with 

Equiconvex lens produces maximum OA (equal positive power distribution between front and back surfaces)

Equiconvex lens also produces curvature of field

1.09 D

0.25 D

Figure 3.55 – oblique astigmatism produced by an equiconvex positive lens for angles of obliquity  and 2 . In dioptric terms, the “astigmatic error” is the difference in image vergence between tangential and sagittal focus. Note that the astigmatic error increases exponentially between  and 2.

4 d hyperope matching petzval s surface to the fps
+4 D Hyperope: Matching Petzval’s Surface to the FPS

Far Point Sphere (FPS) = surface of Far Point loci traced out as the eye rotates

Page 3.65

Figure 3.59

Petzval’s surface is flatter (longer radius) than the FPS with a +4.0 D spectacle correction. “Needing” more plus in the periphery to maintain the image on the FPS, the eye becomes “undercorrected.”

oa in spectacle lenses
OA in Spectacle Lenses

Page 3.69

As the eye rotates off-axis, the amount of induced off-axis astigmatism increases. This can be corrected by “Corrected Curve” Lenses. However, these lenses cannot correct both OA and curvature of field. Punktal Lenses fully correct OA but undercorrect curvature of field

Figure 3.63 – Left: +4.0 D Punktal lens corrects oblique astigmatism but not curvature of field. The eye becomes undercorrected as it rotates away from the primary position. FPS = Far Point Sphere; PS = Petzval’s surface. Right: Lens Field diagram: power error versus angle of gaze. At 35 the 0.21 D undercorrection could be compensated by accommodation.

q3 the aberration curvature of field
Q3. The aberration, curvature of field:

(a) produces no image blur

(b) blurs plane objects

(c) blurs point objects

(d) produces transverse displacement of the image


Page 3.79




Page 3.79

Strongly dependent on paraxial image height

Depends on aperture position in the optical system

Distortion produces NO image blur

Figure 3.69 – Distortion: 3D wavefront profile in the (exit) pupil plane produced by distortion of an object.


Types of Distortion

Page 3.79


Pincushion distortion

Barrel distortion

Take grid-shaped object and image through a plus lens-aperture stop combination. Resulting image:

No distortion

With aperture AT the plus lens:

Pincushion distortion

With aperture to right of plus lens:

Barrel distortion

With aperture to left of plus lens:




With aperture AT the plus lens: chief ray and nodal ray “equivalent”

Page 3.80


Figure 3.71

Could correctly define lateral magnification (m = /) using either  and  measured along the optic axis, or along the nodal ray (or chief ray) path


Quantifying Distortion

Page 3.54

D  (h)3

  • D measured relative to paraxial image point
  • Negative lens distortion effects opposite to plus lens
  • Negative lens and aperture to right:
  • Negative lens and aperture to left:
  • Systems affected: system with asymmetric stop; eye with high-power spectacle lens
  • Correcting/reducing distortion: orthoscopic (distortion-free) lens; aspheric spectacle lens
q4 high plus spectacle lenses in front of a patient s eye will produce
Q4. High plus spectacle lenses in front of a patient’s eye will produce:

(a) pincushion distortion

(b) barrel distortion

(c) no image distortion

(d) transverse displacement of the image



Page 3.83



Explain the wavelength-dependence of refractive index

Use this information to describe prism dispersion of white light

Describe and quantify chromatic aberration (LCA and TCA)

Define “Abbe Number” and explain its significance

Explain the principle and function of an achromatic doublet


Prism Deviation: mono- Light

Page 3.83



Why does a prism deviate incident light toward its base?


Prism Dispersion: poly- Light

Page 3.85

Angle of deviation vs :


Prism Deviation

Page 3.83

 fixed for a given prism, so what determines angle of deviation, d ?


Chromatic Aberration

Page 3.84

Prism Dispersion is just one example of chromatic aberration

  • The angle of deviation of white light incident at a prism decreases with increasing wavelength





Prism Dispersion “Neutralized” by a 2nd Prism

Page 3.85







Prism-Dispersed Colors recombined by a + Lens

Fig 3.78 Page 3.86



quantifying dispersion

Quantifying Dispersion

Page 3.86

  • Purpose of a prism is to deviate light
  • For most applications, a uniform deviation of all wavelengths is the ideal
  • Prism dispersion is therefore an unwanted by-product in most applications/instruments that require deviation of light