Introduction
• Past Homework solutions
• Glass Properties
• Chromatic aberrations
• Stop Shift theory
• Thin lenses and aberrations
• Achromatization
• Introduction to Zemax
• Homework
ECE 4616
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ECE 4616
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HOMEWORK
Find.
Surface (Radius=R1) concentric to STOP( B=0)
1.
Refractive index of lens
2.
Radii of lens –use Lens Maker formula
3.
Determine which aberrations are present for each surface
STOP
R2=R1
Aplanatic surface (Radius=R2)
Δ
(u/n)=0
Specifications
EFL=150 mm
F/#=5.6
WL=0.55
2

Solution to Homework - 1 n ' s
1
'
= n s
1
+ n '
− n
For the first surface where s
1
R
=
∞
, n=1, n’=
μ
For the second surface s
1
'
=
μ
μ
R
−
1 s
2
= s
1
'
−
R
=
μ
μ
R
−
1
−
R
=
μ
R
−
1
Since the second surface is aplanatic then s
2
= n
+ n n '
R
=
1
+
μ
μ
R
=
μ
R
−
1
μ
2 − μ −
1
=
0 From where we get
μ
=1.618034
1 f
=
(
μ −
1 )
⎡
⎢
1
R
1
−
1
R
2
+ d (
μ
μ
R
1
−
R
2
1 )
⎤
⎥ R1=R2=d with f=150 mm we get R=35.4102
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ECE 4616
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Solution to Homework - 2
Surface2 TOTAL Surface1
(S
I
)
1
0
0
(S
IV
)
1
=X
0
0
0
0
(S
IV
)
2
=-X
(S
V
)
2
(S
I
)
1
0
0
0
(S
V
)
2
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Glass Properties
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Abbe number
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CROWNS
FLINTS
7

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STOP
Stop Shift Theory
STOP
Figure above shows a lens near a STOP, and the same lens with a remote
STOP. In the second case the STOP diameter has been adjusted to keep the size of the ray pencil unchanged.
This type of movement and diameter adjustment is a stop shift within the context of the stop-shift formulae.
The Seidel eccentricity ratio E is the parameter used to denote the stop position. It is defined as
E
= h h
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Stop Shift Theory
A stop shift corresponds to a change in E of
δ
E
δ
E
=
δ h h
And as result we find that B changes by
δ
B
=
A
δ
E
The stop shift formulae are valid not only for the calculation of non-central thinlens aberrations, but also for the calculation of the change in aberrations for a general thick-lens system as a result of the stop movement
A complex thick system with a stop in some position and total primary aberrations given by S
I
, S
II
, S
III
, S
IV
, S
V
, C
L
, C
T
; now the stop is moved so that for every surface E is changed by
δ
E (it can be proved that
δ
E is the same for all the surfaces) and the total aberrations become starred .
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Stop Shift Formulae
S
I
* =
S
I
S
II
* =
S
II
+ δ
ES
I
*
S
III
=
S
III
+
2
δ
ES
II
+ δ
E
2
S
I
S
*
IV
=
S
IV
S
V
* =
S
V
+ δ
E ( 3 S
III
+
S
IV
)
+
3
δ
E
2
S
II
+ δ
E
3
S
I
C
*
L
=
C
L
C
T
* =
C
T
+ δ
EC
L
These powerful formulae enable us to calculate the effect of a stop shift on the aberrations of any system.
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In summary
Third Order Aberration Theory applies to:
1. Rotationally symmetric systems
2. It is valid for system with small apertures
3. It is valid for small fields of view
4. The wavefront aberration is a smooth function without discontinuities
As a result of the theory
1. Stopping down a lens will not improve distortion, or lateral color.
2. Symmetrical systems have zero lateral color and distortion. They also have reduced coma.
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Aberrations using Thin Lenses
Shape Parameter X
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Aberrations using Thin Lenses
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Spherical Aberration for a thin lens
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Thin Lenses approximation
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Thin Lenses approximation
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Achromatization
Contents
Definition of Achromatic, Apochromatic and
Superachromatic lenses
Examples
Designing an achromat
Designing an apochromat
Designing a superachromat
References
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ACHROMAT:
APOCHROMAT:
Definitions
Two Wavelengths at the same focus
Three wavelengths at the same focus
SUPERACHROMAT: Four wavelengths at the same focus
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EXAMPLES
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Designing an Achromat
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Introduction to Zemax
An Achromatic Doublet. The Paths of the rays are much exaggerated.
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Introduction to Zemax
Partial Dispersion
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Partial Dispersion versus V-number
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Introduction to Zemax
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Designing a Superachromat
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References
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Introduction to Zemax
To start any optical design you may need the following: The bold represent the must have parameters.
Object Distance
Image Distance
F/# or NA
Full Field of View
Focal Length
Image Format
Magnification
Transmittance
Spectral Range
Image Quality – MTF, RMS WFE, Encircled Energy, Distortion
Mechanical and packaging requirements – Diameter, Weight, etc
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Introduction to Zemax
Example of a Single Lens Parameters
•Focal ratio f/5.6
•Glass is N-BK7
•Focal Length is 100mm
•Field of view is 8 degrees
•Central Lens thickness 2mm to 12mm
•Wavelength 632.8nm (HeNe)
•Edge thickness minimum 2mm
•Lens should be optimized for smallest RMS
•Object is at infinity
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Surface Type
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Introduction to Zemax
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General button
34

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Field of View Button
35

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Spectral Range Button
36

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Glass Specifications
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Solves
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Performance Evaluation
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Optimization
In our for the single lens the variables of optimization could be
Radii, thickness of lens, back focal distance and/or Refractive index
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ECE 4616
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HomeWork
Design a single lens using Zemax and show performance using Spot Diagrams
•Focal ratio f/5.6
•Glass is N-BK7
•Focal Length is 100mm
•Field of view is 8 degrees
•Central Lens thickness 2mm to 12mm
•Wavelength 632.8nm (HeNe)
•Edge thickness minimum 2mm
•Lens should be optimized for smallest RMS
•Object is at infinity
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