Distortion

1
Distortion
2
Distortion
Page 3.67
Strongly dependent on paraxial image height
Aperture-dependent (? does not match the ideal
wavefront) Distortion depends on aperture
position in the optical system
Simple meridional variation
Figure 62 Distortion 3D wavefront profile in
the (exit) pupil plane produced by distortion of
an object.
3
Stops in Optical Instruments

• Apertures and stops determine total amount of
  light passing through system
• Aperture stop - most restrictive aperture
• Chief ray - most important ray
• Chief ray for any given object point
• passes through center of aperture stop
• defines center of ray bundle through system
• Nodal ray ray through optical center of lens or
  lens system ? defines undeviated ray path and
  optical centration

Pp 3.68 3.69
4
Stops in Optical Instruments

• Apertures and stops determine total amount of
  light passing through system
• Aperture stop - most restrictive aperture
• Chief ray - most important ray
• Chief ray for any given object point
• passes through center of aperture stop
• defines center of ray bundle through system
• Dealing with coma and OA, the lens was also the
  aperture stop (toisolate each aberration) ?
  nodal ray ? chief ray. NOT the case here

Pp 3.68 3.69
5
Apertures Distortion
Pp 3.68 3.69

• Distortion demonstrates relationship between
• optical centration (nodal ray), and
• aperture centration (chief ray) in an optical
  system

6
Apertures Distortion
Pp 3.68 3.69

• Distortion ? no image blur
• Due to presence and position of aperture stop in
  system
• Distortion ? variation in lateral magnification
  for off-axis points with distance from the axis

7
Types of Distortion

• Pincushion Distortion image magnification
  increases with distance from the optic axis
• Barrel Distortion image magnification decreases
  with distance from the optic axis

Pp 3.68 3.69
8
Distortion
Fig 63 Page 67
IMAGE
IMAGE
D
D
Object
Pincushion Distortion
Barrel Distortion
9
Distortion

• Dependent on aperture presence position because
  both affect chief ray path

10
Distortion

• Isolated thin lens, or thin lens at the aperture
  stop is distortion-free
• Moving aperture stop away from lens alters chief
  ray path ? distortion

11
Distortion - Aperture Stop at Lens
F()
F'
OC
F
Fig 64 Page 68
12
Pincushion Distortion
F()
OC
F
D
Fig 65 Page 69
F'
13
Barrel Distortion
Fig 66 Page 70
F()
F'
OC
D
F
14
Distortion

• Consider distortion in terms of lateral (linear)
  magnification (m) along chief ray path
  (non-paraxial application of m)

15
Pincushion Distortion
Chief ray (passes outside optical center of lens)
Fig 65 Page 69
F()
OC
F
D
F'
Image side chief ray path longer than nodal ray
path
D ? (h?)3
If aperture placement increases chief ray path in
image space ? pincushion distortion
16
Barrel Distortion
Fig 66 Page 70
D ? (h?)3
If aperture placement increases chief ray path in
object space ? barrel distortion
17
Distortion Positive vs. Negative Lenses

• Positive Lens
• object-side aperture ? barrel distortionimage-sid
  e aperture ? pincushion distortion
• Negative Lens
• object-side aperture ? pincushion
  distortionimage-side aperture ? barrel distortion

18
Summary Distortion

• Transverse origin
• Quantifying

h? paraxial image height

• Due to presence and position of stop
• Stop that increases image space CR path increases
  magnification with image height (3) ? pincushion
  D.
• Stop that increases object space CR path
  decreases magnification with image height (3) ?
  barrel D.
• Systems affected system with asymmetric stop
  eye with high-power spectacle lens
• Correcting/reducing distortion orthoscopic
  (distortion-free) lens aspheric spectacle lens

19
Dispersion
Page 71
20
Dispersion

• Based on inverse relationship between refractive
  index and wavelength of light
• In any given medium, blue has a higher index than
  red ? blue is refracted more strongly than red

21
Dispersion
Fig 67 Page 71
normal
a
normal
22
Dispersion
normal
a
23
Dispersion

• For thin prisms, angle of deviation (d) depends
  only on prism index and apical angle
• For a given prism (given a), d is a simple
  function of index
• This is the basis of prism dispersion, since
  index varies with wavelength

24
Fig 68 Page 72
Higher index for lower ?? greater angle of
deviation for lower ?
25
Dispersion
Fig 69 Page 73
white
26
Dispersion

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

27
Prism Dispersion Neutralized by a 2nd Prism
Fig 70 Page 73
glass
?
?
glass
28
Prism-Dispersed Colors recombined by a Lens
Fig 71 Page 74
?
white
glass
29
Quantifying Dispersion
Page 74

• Angle of deviation varies with index and index
  varies with wavelength
• Therefore angle of deviation varies with
  wavelength
• Choose three, well-defined wavelengths to
  quantify dispersion
• Red 656.3 nm (hydrogen C line)
• Yellow-green 587.6 nm (Helium d line)
• Blue 486.1 nm (hydrogen F line)

30
Quantifying Dispersion
Page 74

• Because the standard paraxial wavelength is 587.6
  nm, the d value for nglass implies deviation of
  587.6 nm and implies the index for 587.6 nm

• Therefore, we can also define

31
Quantifying Dispersion
Fig 72, Page 75
angle of dispersion
?
? 656.3 nm
glass
? 486.1 nm
Angle of dispersion (a) is defined as the spread
of the F and C lines
32
Quantifying Dispersion
Fig 72, Page 75
angle of dispersion
?
? 656.3 nm
glass
? 486.1 nm
Angle of dispersion also defines chromatic
aberration
33
Quantifying Dispersion
Fig 72, Page 75
?
glass
? 587.6 nm
Define Mean deviation (dd) as the angle of
deviation for the d-line
34
Quantifying Dispersion
Page 76

• Combining the equations for angle of dispersion
  and mean deviation, gives the Abbe Number
  (V-number)

• The Abbe number is a measure of the ability of a
  prism to deviate light (587.6 nm), relative to
  the amount of chromatic aberration (dispersion of
  red and blue) induced in the process

35
Quantifying Dispersion
Page 76

• The ideal lens material would have high
  refractivity and low dispersion ? would strongly
  refract light without inducing significant
  chromatic aberration (dispersion)

36
Fig 72, Page 75
angle of dispersion
?
? 656.3 nm
glass
? 486.1 nm
?
glass
? 587.6 nm
37
Specifying Ophthalmic Materials
Manufacturers use a six digit number to describe
the mean refractive index and dispersive power of
any lens material
Example 617363 or
519604
nd 1.519
Vd 60.4
nd 1.617
Vd 36.3
38
Abbe Numbers of Typical Lens Materials
Type Material Abbe Number Flint SF11 25.7
6 Flint LaSFN9 32.17 Flint
F2 36.37 Crown BaK1 57.55 Crown BK7 6
4.17
39
Practice Problem 19
A variant of polycarbonate is specified by the
manufacturer as 586300. Determine the mean
dispersion (chromatic aberration) for this
material.
nd 1.586 Vd 30.0
?

• 0.0195
• 0.0257
• 0.0296
• 0.0308

40
Aberrations

• Spherical Aberration
• Coma
• Oblique (Radial) Astigmatism
• Curvature of Field
• Distortion

Chromatic Aberration
41
CA explains Dispersion
Fig 69 Page 73
white
42
Chromatic Aberration

• Based on

43
Paraxial Focus
LCA vs. Pupil Diameter
Reduced Surface
LCA
Fig 74, 75 Pp 78-9
44
Defining Longitudinal CA (Dioptric)
Page 79

• Chromatic aberration is a property of light
• LCA is a measure of the longitudinal spread of
  chromatic foci (from blue to red)
• LCA is independent of aperture diameter

45
Paraxial Focus
LCA Plus Lens
Fig 76, Page 80
Reduced Surface
LCA
46
Paraxial Focus
LCA Reduced Eye
Reduced Surface
486.1 nm
656.3 nm
Linear Definition
LCA f ?C ? f ?F
47
Paraxial Focus
LCA Reduced Eye
Reduced Surface
486.1 nm
656.3 nm
Dioptric Definition
LCA FF ? FC
LCA
48
Transverse CA
Page 79

• Transverse Chromatic aberration is the lateral
  image spread perpendicular to the optic axis
• When CA is captured on a screen, it is TCA that
  is visualized
• TCA is also measured at the two extremes of the
  LCA distribution ? the 486.1 nm focus and the
  656.3 nm focus

49
Transverse CA
Page 79

• Different ways to quantify TCA
• Chromatic difference of magnification
  difference in image height for 486.1 nm vs. 656.3
  nm (for a given object)

50
Chromatic Difference of Magnification
Page 79
Positive Lens
h?C
h?F
Usually expressed at either red or blue image
plane
51
Transverse CA
Page 79

• Different ways to quantify TCA
• Chromatic difference of magnification
  difference in image height for 486.1 nm vs. 656.3
  nm (for a given object)

• To evaluate the effect of pupil diameter on TCA
  of the eye, look at the size of the red blur
  patch at the blue focus and vice versa

52
TCA Medium Pupil
Fig 76 Page 80
Paraxial Focus
Reduced Surface
Iris
53
TCA Large Pupil
Fig 76 Page 80
Iris
Paraxial Focus
Reduced Surface
54
Aperture dependence of CA
LCA is a property of light ? unaffected by
aperture diameter TCA bears the same relationship
to LCA as TSA to LSA LSA ? y2 TSA ? y3
(differ by factor of y) LCA independent of y TCA
? y (differ by factor of y)
55
Controlling CA in Optical Systems
56
Prism Achromatic Doublet
Page 82

• The key to an achromatic doublet is to combine a
  low dispersion prism (crown) with a high
  dispersion prism (flint)
• A larger angle crown prism (1) provides excess
  deviation with low dispersion (CA)
• Meantime, a smaller angle flint prism (2) can
  provide equal and opposite dispersion with
  minimal (opposing) deviation

57
Prism Achromatic Doublet - Principle

• If the CA induced by the crown prism is equal to
  that produced by the flint prism ? net CA 0
  (base-to-apex)
• If the mean deviation (d) of the crown prism gt
  dflint ? we can produce deviation without
  dispersion
• This defines a prism achromatic doublet

58
Prism Achromatic Doublet
Flint
n2
? 1
For each prism,Chromatic Aberration
? 2
n1
Crown
59
Prism Achromatic Doublet
Flint
n2
? 1
For prisms base-to-apex
? 2
n1
Crown
60
Achromatic Doublet Lens
Page 83
Same principle as achromatic doublet prism
F2 (?) Flint
F1 () Crown
61
Cemented Achromatic Doublet Lens
Fig 78 Page 83
Red and blue focus at the same location. Other
spectral colors focus at slightly different
locations
F2 (?) Flint
F1 () Crown
62
Cemented Achromatic Doublet Lens
As for the prism doublet, we want LCA1 ?
LCA2
63
Chromatic Spherical Aberration
Effects of SA and CA on Ocular Image Formation
64
n 1
n' gt 1
400 nm
700 nm
65
Chromatic aberration causes a spread of paraxial
foci along the axis (blue to left red to right)
n 1
Paraxial Focus
n' gt 1
400 nm
700 nm
66
Spherical aberration spreads foci according to
incident height (lateral distance from axis)
Effect of SA on green light
Paraxial Focus
400 nm
700 nm
67
Summary Chromatic Aberration

• Longitudinal origin property of light
• Quantifying

• Longitudinal CA (LCA) independent of aperture

Fd paraxial power (587.6 nm) V Abbe
number, V-number

• Transverse CA TCA ? y
• Quantify as chromatic difference in
  magnification size of blue patch at red focus,
  etc.

68
Summary Chromatic Aberration

• Correcting CA Achromatic doublet
• Prism combine more powerful, lower dispersion
  prism (for deviation) with higher dispersion
  prism (to neutralize dispersion)
• () Lens combine more powerful, lower dispersion
  plus lens (for convergence) with higher
  dispersion, weaker negative lens (to neutralize
  dispersion)

Both cases LCA1 ?LCA2
Negative sign ? opposite bases for prism
opposite powers for lens doublet
69
Chromatic Aberration in Microscope Objectives
70
Chromatic Aberration in Microscope Objectives
71
Achromat Microscope Objective

• Simplest CA-compensated design. Achromatic
  doublet corrects LCA at 486 and 656 nm
• LSA corrected at 546 nm ( paraxial ?)
• Despite coincident focus of 486 and 656 nm on
  axis, TCA is evident in the periphery ? larger
  blue image than red (CDM - chromatic difference
  of magnification) creating overlapping images.
  Compensating eyepieces can reduce CDM.

72
Fluorite (Semi-Apochromatic) Objective

• Achromatic doublets and triplet correct LCA at
  486, 656 nm and the focus for 546 nm is much
  closer.
• LSA corrected for two or all three of these
  wavelengths

73
Apochromat Microscope Objective

• Most highly corrected of all microscope
  objectives
• Almost eliminates LSA and CDM
• LCA corrected at (short ? blue), 486 , 656, and
  546 nm.
• LSA corrected for three or all four wavelengths

74
CA and Microscope Objectives
http//www.olympusmicro.com/primer/java/aberration
s/chromatic/index.html
75
Practice Problem 21
An optical system has been corrected for all, but
one, monochromatic aberration. The system
consists of a positive spherical lens and an
aperture stop to the right of the lens. For a
monochromatic plane object, this system will
produce

• Curvature of field
• Pincushion distortion
• Barrel distortion
• Transverse chromatic aberration

?
Physical Optics PS Questions 35, 36
76
Practice Problem 22
An ametropic eye is spectacle-corrected for
distance vision. As the eye rotates around its
center of rotation, a surface is traced out that
corresponds to where the retina is actually
focused. This surface is
?

• the Far point sphere
• the tangential image shell
• the sagittal image shell
• Petzvals surface

Physical Optics PS Questions 30 - 32
77
Practice Problem 23
An ametropic eye is spectacle-corrected for
distance vision. As the eye rotates around its
center of rotation, a surface is traced out that
corresponds to the location of the image produced
by the spectacle lens. This surface is

• the Far point sphere
• the tangential image shell
• the sagittal image shell
• Petzvals surface

?
Physical Optics PS Questions 30 - 32
78
Practice Problem 24
A spectacle lens will fully correct image
curvature if

• the tangential and sagittal focal lines coincide
• The spectacle correction has a very high positive
  power ( 19 D)
• a Plan lens, producing a flat-field image is
  used
• Petzvals surface matches the far point sphere

?
Physical Optics PS Question 31
79
Practice Problem 25
A net positive cemented achromatic doublet lens
is to be used to eliminate chromatic aberration
in an optical system. The first element is a
positive glass lens, specified by the
manufacturer as 517642. The most appropriate
choice for the second element would be

• 487704
• 523588
• 620364
• 713538

n 1.620, V 36.4 (high dispersion)
?
80
(No Transcript)
81
Prism Achromatic Doublet