Upload
others
View
38
Download
7
Embed Size (px)
Citation preview
1Prof. Jose SasianOPTI 518
Introduction to aberrations OPTI518
Lecture 6
Chromatic aberrations
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
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
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
5Prof. Jose SasianOPTI 518
Change of image location with λ (Chromatic change of focus)
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
7Prof. Jose SasianOPTI 518
Chromatic change of magnification
8Prof. Jose SasianOPTI 518
With stop at CC
With stop at surface
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
10Prof. Jose SasianOPTI 518
Description at other stop location
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
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
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
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
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
16Prof. Jose SasianOPTI 518
For a system of thin lenses
17Prof. Jose SasianOPTI 518
1 2A A
18Prof. Jose SasianOPTI 518
020W
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
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
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
22Prof. Jose SasianOPTI 518
Change of Magnification 111W H
•
Change of magnification depends linearly withthe field of view.
H
23Prof. Jose SasianOPTI 518
Change of magnification'Iy H
1111'' 'Iy H W
n u
24Prof. Jose SasianOPTI 518
Clear terminology
•
Chromatic change of magnification (older: lateral, transverse color)
•
Chromatic change of focus (older: axial, longitudinal color)
Optical axis
25Prof. Jose SasianOPTI 518
Chromatic change of focus
Exit pupil
Marginal rays
Image locationdepends onwavelength
26Prof. Jose SasianOPTI 518
Chromatic change of magnification
Chief rays
Exit pupil
Image sizedepends on wavelength
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
28Prof. Jose SasianOPTI 518
2 2000 200 111 020, cosW H W W H W H W
Summary I
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
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
31Prof. Jose SasianOPTI 518
Achromatic doublet
a b
a b
aa
a b
bb
a b
a b
32Prof. Jose SasianOPTI 518
Chromatic coordinates
Sellmeier
Buchdahl
33Prof. Jose SasianOPTI 518
Adaptive formula
BK7
34Prof. Jose SasianOPTI 518
Index fit
Schott glass catalogue
35Prof. Jose SasianOPTI 518
Chromatic change of focus
36Prof. Jose SasianOPTI 518
Example
37Prof. Jose SasianOPTI 518
Chromatic focal shift: singlet, achromat, apochromat, superapochromat
38Prof. Jose SasianOPTI 518