12 aberration theory part iibecee.colorado.edu/~ecen5616/webmaterial/12 aberration...2. it is valid...
TRANSCRIPT
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Introduction• Past Homework solutions
• Glass Properties
• Chromatic aberrations
• Stop Shift theory
• Thin lenses and aberrations
• Achromatization
• Introduction to Zemax
• Homework
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HOMEWORKSurface (Radius=R1)
concentric to STOP( B=0)
STOP
Aplanatic surface (Radius=R2)
Δ(u/n)=0
Specifications
EFL=150 mm
F/#=5.6
WL=0.55
Find.
1. Refractive index of lens
2. Radii of lens –use Lens Maker formula
3. Determine which aberrations are present for each surface
R2=R1
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Solution to Homework - 1For the first surface where s1=∞, n=1, n’=μ
Rnn
sn
sn −
+='
''
11
1'1 −=μμRs
For the second surface 11
'12 −=−
−=−=
μμμ RRRRss
Since the second surface is aplanatic then 11'
2 −=
+=
+= μμ
μ RRRn
nns
012 =−− μμ From where we get μ=1.618034
⎥⎦
⎤⎢⎣
⎡ −+−−=
2121
)1(11)1(1RR
dRRf μ
μμ R1=R2=d with f=150 mm we get R=35.4102
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Solution to Homework - 2
(SI)1
0
0
(SIV)1=X
0
0
0
0
(SV)2
Surface1 Surface2
(SIV)2=-X
TOTAL
(SI)1
0
0
0
(SV)2
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Glass Properties
Abbe number
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Glass Properties
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Glass Chart
CROWNS
FLINTS
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Chromatic Aberrations
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Chromatic Aberrations
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Chromatic Aberrations
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Stop Shift Theory
STOP 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
hhE =
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Stop Shift TheoryA stop shift corresponds to a change in E of δE
And as result we find that B changes by
The stop shift formulae are valid not only for the calculation of non-central thin-lens 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 SI, SII, SIII, SIV, SV, CL, CT; now the stop is moved so that for every surface E is changed by δE (it can be proved that δE is the same for all the surfaces) and the total aberrations become starred.
hhE δδ =
EAB δδ =
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Stop Shift FormulaeII SS =*
IIIII ESSS δ+=*
IIIIIIIII SEESSS 2* 2 δδ ++=
IVIV SS =*
IIIIVIIIVV SESESSESS 32* 3)3( δδδ ++++=
LL CC =*
LTT ECCC δ+=*
These powerful formulae enable us to calculate the effect of a stop shift on the aberrations of any system.
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In summaryThird 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. Theyalso have reduced coma.
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Aberrations using Thin LensesShape 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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DefinitionsACHROMAT: Two Wavelengths at the same focus
APOCHROMAT: 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 ZemaxTo start any optical design you may need the following: The boldrepresent 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
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Field of View Button
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Spectral Range Button
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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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HomeWorkDesign 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