OPTI518 Lecture 6 Chromatic aberrations

1Prof. Jose SasianOPTI 518

Introduction to aberrationsOPTI518Lecture 6

Chromatic aberrations


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


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


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


Change of image location with λ(Chromatic change of focus)


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


Chromatic change of magnification


With stop at CC

With stop at surface


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


Description at other stop location


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


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


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


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


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


For a system of thin lenses


1 2A A


020W


Chromatic change of magnificationcoefficient meaning

111nW A yn

1d F C

d d

n n n nn V n n

111W

Exit pupil

Optical axis


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


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


Change of Magnification 111W H

• Change of magnification depends linearly withthe field of view.

H


Change of magnification'Iy H

1111'' 'Iy H Wn u


Clear terminology

• Chromatic change of magnification (older: lateral, transverse color)

• Chromatic change of focus (older: axial, longitudinal color)

Optical axis


Chromatic change of focus

Exit pupil

Marginal rays

Image locationdepends onwavelength


Chromatic change of magnification

Chief rays

Exit pupil

Image sizedepends on wavelength


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


2 2000 200 111 020, cosW H W W H W H W

Summary I


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


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

Rule of 2s 1111'' 'Iy H Wn u

Rule of 1s


Achromatic doublet

a b

a b

aa

a b

bb

a b

a b


Chromatic coordinates

Sellmeier

Buchdahl


Adaptive formula

BK7


Index fit

Schott glass catalogue


Chromatic change of focus


Example


Chromatic focal shift: singlet, achromat, apochromat, superapochromat

OPTI518 Lecture 6 Chromatic aberrations

Documents

Transcript of OPTI518 Lecture 6 Chromatic aberrations