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

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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

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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

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Adaptive formula

BK7

34Prof. Jose SasianOPTI 518

Index fit

Schott glass catalogue

35Prof. Jose SasianOPTI 518

Chromatic change of focus

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Example

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Chromatic focal shift: singlet, achromat, apochromat, superapochromat

38Prof. Jose SasianOPTI 518