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

Prof. Jose SasianOPTI 518

Introduction to aberrations

OPTI 518Lecture 14


Topics

• Structural aberration coefficients• Examples


Structural coefficients

Ж

Requires a focal system


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


Field curves


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


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


Shape X

X=-1

X=0

X=-1.7

X=-3.5X=3.5

X=1.7

X=1

X=0


Shape

X=0

X=0

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

X=1X=2X=3


Shape or bending factor

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

thickness the lens aspect ratio changes


2K


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


Field curves

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


Application of CoddingtonEquations


Thin lensSpherical aberration and coma

I II

Fourth-order


Spherical aberration of a F/4 lens

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


Thin lens spherical aberration

n=1.517

I

Y

X


Thin lens coma aberration

n=1.517

II

X

Y


This lensAplanatic solutions

X=4

Y=5n=1.5

' 1' 1

mYm


Thin lensSpherical and coma @ Y=0

III

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

Strong index dependence


Thin lens special casesstop at lens


Thin lens special cases stop at lens


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


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


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.


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.


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.


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


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


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.


Crown in front: BK7 and F8


Flint in front: BK7 and F8


Cemented achromatic doublet


Cemented doublet solutions

Crown in front

Flint in front


Two mirror afocal system


Merssene afocal systemAnastigmatic

Confocal paraboloids


Paul-Baker systemAnastigmatic-Flat field

AnastigmaticParabolic primarySpherical secondary and tertiaryCurved fieldTertiary CC at secondary

Anastigmatic, Flat fieldParabolic primaryElliptical secondary Spherical tertiaryTertiary CC at secondary


Meinel’s two stage optics concept (1985)

Large DeployableReflector

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

exit pupil.


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.


Lister objective


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

11100

A

A

IA

IB

Жyu


Lister objective

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

111

B

A B

B

yy


Lister objective


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


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


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:


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


Petzval objectiveFlattening of the tangential field curve


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


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


Diffractive opticshigh-index model

1/d


Ray diffractive law (1D)


Diffractive lens (n very large)

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

23 1I Y

2II Y 1III

0IV

0V 1

Ldiffractive

0T


MIRRORS


Spherical Mirror


Aspheric mirrors


Spherical mirror stop at mirror


Spherical mirror with stop shift


Stop shifting

'

2 1 2 1 ' 2 'P Py y s sSЖ Y s n Y s n


Spherical MirrorObject at infinity Y=1


Aspheric mirror


With stop shift


Paraboloid with object at infinity


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


Special aplanatic cases


Wright and Schmidt systems


Summary

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

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

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