Introduction to aberrations OPTI518 Lecture 6 · Lecture 6 Chromatic aberrations. Prof. Jose Sasian...
Transcript of Introduction to aberrations OPTI518 Lecture 6 · Lecture 6 Chromatic aberrations. Prof. Jose Sasian...
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1Prof. Jose SasianOPTI 518
Introduction to aberrations OPTI518
Lecture 6
Chromatic aberrations
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2Prof. Jose SasianOPTI 518
Chromatic aberrations
•
Consider up to second order terms•
Change of image location with λ
(axial or
longitudinal chromatic aberration)•
Change of magnification with λ
(transverse
or lateral chromatic aberration)•
We start with a single surface
2 2000 200 111 020, cosW H W W H W H W
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3Prof. Jose SasianOPTI 518
Second-order: single surface
2
020' '0,
2 'y n n n nW W
r s s
1 1 1 1' ''
A n y A n yr s r s
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4Prof. Jose SasianOPTI 518
Chromatic change of focus: single surface
2
0201 1 1 1'
2 '' 1
2 ' 2
yW n nr s r s
y n n nA A yn n n
''
n n nn n n
F Cn n n
486.1F nm
656.3C nm
587.6d nm
dn n
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5Prof. Jose SasianOPTI 518
Change of image location with λ (Chromatic change of focus)
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6Prof. Jose SasianOPTI 518
Chromatic coefficient meaning
02012
nW A yn
1d F C
d d
n n n nn V n n
In air case
020W
Exit pupil
Optical axis
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7Prof. Jose SasianOPTI 518
Chromatic change of magnification
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8Prof. Jose SasianOPTI 518
With stop at CC
With stop at surface
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9Prof. Jose SasianOPTI 518
With stop at cc chief rays is not refracted and therefore there is no change of magnification
with
λ
111 0W
000 020,W H W W
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10Prof. Jose SasianOPTI 518
Description at other stop location
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11Prof. Jose SasianOPTI 518
Stop shifting
Ey
Ey
Old stop plane at CCNew stop
Marginal ray height at old pupil
New chiefray
Hyyy EEshiftE
HAAH
yy
E
Eshift
New chief ray height at old pupil
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12Prof. Jose SasianOPTI 518
Perform stop shifting
000 020 0001,2
nW H W W W A yn
SH
000 020,W H W W
000
2000
2
000
1, ,2
1 12 2
1 12 2
nW H W H W A yn
n n nW A y AS y H A yS H Hn n n
n n n AW A y A y H A y H Hn n n A
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13Prof. Jose SasianOPTI 518
Chromatic changes
000
2
,
1 12 2
W H W
n n n AA y A y H A y H Hn n n A
Chromatic change of focusChromatic change of magnificationChromatic change of piston
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14Prof. Jose SasianOPTI 518
For a system of j surfaces
•
Optical paths add•
Aberration coefficients add
•
Though there might be other very small terms, called extrinsic, that are missing.
2
2001
1 /2
jj
j ji j
AW n n y
A
0201
1 /2
j
j j ji
W A n n y
1111
/j
j j ji
W A n n y
0000
' 'j
i F Ci i
W t n n
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15Prof. Jose SasianOPTI 518
Thin lens concept
•
Has no thickness•
Properties are found by setting t=0 in pertinent equations
•
For example y is the same for both surfaces
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16Prof. Jose SasianOPTI 518
For a system of thin lenses
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17Prof. Jose SasianOPTI 518
1 2A A
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18Prof. Jose SasianOPTI 518
020W
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19Prof. Jose SasianOPTI 518
Chromatic change of magnification coefficient meaning
111nW A yn
1d F C
d d
n n n nn V n n
111W
Exit pupil
Optical axis
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20Prof. Jose SasianOPTI 518
Thin lens: stop at lens
Any ray at any wavelength through the center of the thin lens is un-deviated as it sees a
parallel plate of thickness zero. Thus,
111 0W
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21Prof. Jose SasianOPTI 518
Aberration function for thin lens with stop at the lens and with stop
shifting
2000 020 000
2 2 2 2000
22 2
000
1,2
,
1 12 2
/
1 12 2
W H W W W y
W H
nW y y S y H y S H Hn
S y y
yW y yy H y H Hy
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22Prof. Jose SasianOPTI 518
Change of Magnification 111W H
•
Change of magnification depends linearly withthe field of view.
H
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23Prof. Jose SasianOPTI 518
Change of magnification'Iy H
1111'' 'Iy H W
n u
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24Prof. Jose SasianOPTI 518
Clear terminology
•
Chromatic change of magnification (older: lateral, transverse color)
•
Chromatic change of focus (older: axial, longitudinal color)
Optical axis
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25Prof. Jose SasianOPTI 518
Chromatic change of focus
Exit pupil
Marginal rays
Image locationdepends onwavelength
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26Prof. Jose SasianOPTI 518
Chromatic change of magnification
Chief rays
Exit pupil
Image sizedepends on wavelength
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27Prof. Jose SasianOPTI 518
Equation summary
0201
1 /2
j
j j ji
W A n n y
1111
/j
j j ji
W A n n y
2
2001
1 /2
jj
j ji j
AW n n y
A
For a system of j surfaces
0000
' 'j
i F Ci i
W t n n
2200
1
12
j
i i
W y
1111
j
i i
W yy
2020
1
12
j
i i
W y
For a system of thin lenses
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28Prof. Jose SasianOPTI 518
2 2000 200 111 020, cosW H W W H W H W
Summary I
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29Prof. Jose SasianOPTI 518
Summary II
0201
1 /2
j
j j ji
W A n n y
1111
/j
j j ji
W A n n y
1111
j
i i
W yy
2020
1
12
j
i i
W y
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30Prof. Jose SasianOPTI 518
Summary III
0202
2020
2020
1' 2' '
' 8 / #'
' / #4
0.0005
Wsn uWs fn
s f in micrometers for W
mm
2c
NA
Cut-off spatial frequency for a LSIS with incoherent illumination
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31Prof. Jose SasianOPTI 518
Achromatic doublet
a b
a b
aa
a b
bb
a b
a b
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32Prof. Jose SasianOPTI 518
Chromatic coordinates
Sellmeier
Buchdahl
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33Prof. Jose SasianOPTI 518
Adaptive formula
BK7
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34Prof. Jose SasianOPTI 518
Index fit
Schott glass catalogue
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35Prof. Jose SasianOPTI 518
Chromatic change of focus
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36Prof. Jose SasianOPTI 518
Example
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37Prof. Jose SasianOPTI 518
Chromatic focal shift: singlet, achromat, apochromat, superapochromat
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38Prof. Jose SasianOPTI 518