introduction to aberrations...opti 518 introduction to aberrations opti 518 lecture 14 prof. jose...

Prof. Jose SasianOPTI 518

Introduction to aberrations

OPTI 518Lecture 14

Prof. Jose SasianOPTI 518

Topics

• Structural aberration coefficients• Examples

Prof. Jose SasianOPTI 518

Structural coefficients

Ж

Requires a focal system

Prof. Jose SasianOPTI 518

Prof. Jose SasianOPTI 518

Prof. Jose SasianOPTI 518

Structural stop shifting parameter

s’ is the distance from the rear principal plane to exit pupil

s is the distance from the front principal plane to entrance pupil

2

2 2P P Py y yS SЖ Ж

'

2 1 2 1 ' 2 'P Py y s sSЖ Y s n Y s n

1 / 2nu Y y

Using ω on we can express:

2P Py ySЖ

Prof. Jose SasianOPTI 518

Field curves

Prof. Jose SasianOPTI 518

Prof. Jose SasianOPTI 518

Review of concepts

• Thin lens as the thickness tends to zero

• Shape of a lens and shape factor• Conjugate factor to quantify how the lens

is used. Related to transverse magnification

• Must know well first-order optics

1 2 1 2tn

Prof. Jose SasianOPTI 518

Shape and Conjugate factors

nu ' 1' 1

mYm

1 2 1 2

1 2 1 2

c c R RXc c R R

Lens bending concept

Prof. Jose SasianOPTI 518

Shape X

X=-1

X=0

X=-1.7

X=-3.5X=3.5

X=1.7

X=1

X=0

Prof. Jose SasianOPTI 518

Shape

X=0

X=0

X=-1X=-2X=-3

X=1X=2X=3

Prof. Jose SasianOPTI 518

Shape or bending factor

• Maintains optical power of thin lens• For a given shape factor and lens

thickness the lens aspect ratio changes

Prof. Jose SasianOPTI 518

Prof. Jose SasianOPTI 518

Prof. Jose SasianOPTI 518

2K

Prof. Jose SasianOPTI 518

Prof. Jose SasianOPTI 518

Prof. Jose SasianOPTI 518

Prof. Jose SasianOPTI 518

Spherical MirrorA spherical mirror can be treated as a thin lens with n=-1

If a dummy plane unfolding surface is added

2

1

11

000

I

II

III

IV

V

L

T

XYY

14

011401

A

BC

D

EF

n=-1

Prof. Jose SasianOPTI 518

Field curves

Rt~f/3.66Rm~f/2.66Rs~f/1.66Rp~f/0.66

Prof. Jose SasianOPTI 518

Application of CoddingtonEquations

Prof. Jose SasianOPTI 518

Application of CoddingtonEquations

Prof. Jose SasianOPTI 518

Thin lensSpherical aberration and coma

I II

Fourth-order

Prof. Jose SasianOPTI 518

Spherical aberration of a F/4 lens

•Asymmetry•For high index 4th order predicts well the aberration

Prof. Jose SasianOPTI 518

Thin lens spherical aberration

n=1.517

I

Y

X

Prof. Jose SasianOPTI 518

Thin lens coma aberration

n=1.517

II

X

Y

Prof. Jose SasianOPTI 518

This lensAplanatic solutions

X=4

Y=5n=1.5

' 1' 1

mYm

Prof. Jose SasianOPTI 518

Thin lensSpherical and coma @ Y=0

III

N=1.5N=2N=2.5N=3N=3.5N=4

Strong index dependence

Prof. Jose SasianOPTI 518

Thin lens special casesstop at lens

Prof. Jose SasianOPTI 518

Thin lens special cases stop at lens

Prof. Jose SasianOPTI 518

Thin lens special cases stop at lens

Prof. Jose SasianOPTI 518

Thin lens special cases stop at lens

Prof. Jose SasianOPTI 518

Thin lens special cases stop at lens

Prof. Jose SasianOPTI 518

Achromatic doubletTwo thin lenses in contactThe stop is at the doublet

1 2

1 2

11

22

y y

1 2

21

1

12

2

1

YY

YY

Prof. Jose SasianOPTI 518

Achromatic doubletCorrection for chromatic change of focus

1 2

1 2

11 2

1 2

22 1

1 2

1

1

L

L

L

0L

For an achromatic doublet:

2,

,0

kP kk

L L ki P

yy

Prof. Jose SasianOPTI 518

Achromatic doubletCorrection for spherical aberration

3 2 2 3 2 21 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2I A X B X Y CY D A X B X Y C Y D

43,

,0

kP kk

I I ki P

yy

For a given conjugate factor Y, spherical aberration is a functionOf the shape factors X1 and X2 . For a constant value of spherical

aberration we obtain a hyperbola as a function of X1 and X2.

Prof. Jose SasianOPTI 518

Achromatic doubletCorrection for coma aberration

22

,, ,

0

kP kk

II II k k I ki P

yS

y

2 21 1 1 1 1 2 2 2 2 2II E X FY E X F Y

For a given conjugate factor Y and a constant amount of coma the graph of X1 and X2 is a straight line.

Prof. Jose SasianOPTI 518

Achromatic doubletAstigmatism aberration

2, , ,

0

2k

kIII III k k II k k I k

i

S S

1 21 1III

Astigmatism is independent of the relative lens powers, shape factors,or conjugate factors.

Prof. Jose SasianOPTI 518

Achromatic doublet

1 2

1 2IV n n

2 1

2 1

n n

Field curvature aberration

,0

kk

IV IV ki

0IV For an achromatic doublet there is no field curvature if

Prof. Jose SasianOPTI 518

Achromatic doubletDistortion and chromatic change of magnification

, ,0

k

T T k k L ki

S

2

2 3, , , , ,

0 ,

3 3k

PV V k k IV k III k k II k k I k

i P k

y S S Sy

00

V

T

Prof. Jose SasianOPTI 518

Cemented achromatic doublet

1 1 2 212 21

1 2

1 1 2 2

1 2

2 1

1 12 1 2 1

1 11 1

1 1

X Xc c

n n

X Xn n

X X

2 1

1 2

2 1

1 2

11

11

nn

nn

For achromat

For a cemented achromatic lens the graph of X1 and X2 is a straight line.

Prof. Jose SasianOPTI 518

Crown in front: BK7 and F8

Prof. Jose SasianOPTI 518

Flint in front: BK7 and F8

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Cemented achromatic doublet

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Cemented doublet solutions

Crown in front

Flint in front

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Two mirror afocal system

Prof. Jose SasianOPTI 518

Prof. Jose SasianOPTI 518

Prof. Jose SasianOPTI 518

Prof. Jose SasianOPTI 518

Merssene afocal systemAnastigmatic

Confocal paraboloids

Prof. Jose SasianOPTI 518

Paul-Baker systemAnastigmatic-Flat field

AnastigmaticParabolic primarySpherical secondary and tertiaryCurved fieldTertiary CC at secondary

Anastigmatic, Flat fieldParabolic primaryElliptical secondary Spherical tertiaryTertiary CC at secondary

Prof. Jose SasianOPTI 518

Meinel’s two stage optics concept (1985)

Large DeployableReflector

Second stage correctsfor errors of first stage;fourth mirror is at the

exit pupil.

Prof. Jose SasianOPTI 518

Aplanatic, Anastigmatic, Flat-field, Orthoscopic (free from distortion, rectilinear, JS 1987)

Spherical primary telescope.The quaternary mirror is near the exit pupil. Spherical aberration and

Coma are then corrected with a single aspheric surface. The Petzval sum is zero.If more aspheric surfaces are allowed then more aberrations

can be corrected.

Prof. Jose SasianOPTI 518

Lister objective

Prof. Jose SasianOPTI 518

Lister objective• Two achromatic doublets that are spaced• Telecentric in image space• Normalized system

11100

A

A

IA

IB

Жyu

Prof. Jose SasianOPTI 518

Lister objective

The aperture stop is at the first lens.The system is telecentric

111

B

A B

B

yy

Prof. Jose SasianOPTI 518

Lister objective

Prof. Jose SasianOPTI 518

Condition for zero coma

22,

, ,0

2 2 2 2

2 2

2

2

0

1 0

1

kP kk

II II k k I ki P

II A A IIA B B IIB

IB

II B IIA B IIB

BIIA IIB

B

yS

y

y y

y y

yy

Prof. Jose SasianOPTI 518

Condition for zero astigmatism

2, , ,

0

2

2

1 0

1 1 0

2 02

12

2

1

kk

III III k k II k k I ki

III A B B IIB

III B B IIB

B B IIB

BIIB

BIIB

B

B BIIA

B

S S

y

y y

y y

y

yy

y y

y

, ,

2k P k P k

k

y yS

Ж

Prof. Jose SasianOPTI 518

Lister Objective

2

2 2

2 2

221

1

1 212123

3

IIB IIA

B BB

B B

B B

B B B

B

A

IIA

IIB

y yyy y

y y

y y y

y

Choose:

Prof. Jose SasianOPTI 518

Petzval objective

R +52.9 -41.4 +436.2 +104.8 +36.8 45.5 -149.5N-crown=1.517; N-flint=1.576

T 5.8 1.5 23.3/23.3 2.2 0.7 3.6F=100 mm

Prof. Jose SasianOPTI 518

Petzval objectiveFlattening of the tangential field curve

Prof. Jose SasianOPTI 518

Variance criterion

2 22 2 3

020 040 220 222 111 131 311

2 22 2040 131 222

1 1 1 212 2 4 3

1 1 1180 72 24

W W W W W H W W H W H

W W H W H

220 222

222 220

122

W W

W W

Zero sagittal field curvature

Prof. Jose SasianOPTI 518

Zero tangential field curve curvature

,0

2

2

1

1 1

3

1 1 23

2 13

23

1

2 12 3 23

2

1

1

kk

IV IV k B IVA IVBi

III B B IIB

IV III

IVB B IIB B B IIB

IVB IIB

IV

BIIB

IVIV B

B BIIB

B B

B BIIA

B

IIA IIB

B

y

y y

y y y y

y

y

yy yy y

y y

yq

y

2 13 2

IV

BB

qyy

Prof. Jose SasianOPTI 518

Diffractive opticshigh-index model

1/d

Prof. Jose SasianOPTI 518

Diffractive opticshigh-index model

1/d

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Ray diffractive law (1D)

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Diffractive lens (n very large)

A=0B=0C=3D=1E=0F=2

23 1I Y

2II Y 1III

0IV

0V 1

Ldiffractive

0T

Prof. Jose SasianOPTI 518

MIRRORS

Prof. Jose SasianOPTI 518

Spherical Mirror

Prof. Jose SasianOPTI 518

Aspheric mirrors

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Aspheric mirrors

Prof. Jose SasianOPTI 518

Spherical mirror stop at mirror

Prof. Jose SasianOPTI 518

Spherical mirror with stop shift

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Stop shifting

'

2 1 2 1 ' 2 'P Py y s sSЖ Y s n Y s n

Prof. Jose SasianOPTI 518

Spherical MirrorObject at infinity Y=1

Prof. Jose SasianOPTI 518

Aspheric mirror

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With stop shift

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Paraboloid with object at infinity

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Aspheric mirror with corrector plateShift stop from mirror and insert corrector at stop

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Special aplanatic cases

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Wright and Schmidt systems

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Wright and Schmidt systems

Prof. Jose SasianOPTI 518

Summary

• Structural coefficients• Basic treatment• There is more to it• Use of Y-Ybar diagram• Analysis of simple systems• See R. Shack notes