opti518 lecture 7 primary aberrations...6 standard -20.4942 -10.0135 16.69285 0 sto standard...

Prof. Jose SasianOPTI 518

Introduction to aberrations

Lecture 7

Fourth-order terms

Prof. Jose SasianOPTI 518

Fourth-order terms

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2040,

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Spherical aberrationComaAstigmatism (cylindrical aberration!)Field curvatureDistortionPiston

Prof. Jose SasianOPTI 518

Primary monochromatic aberrationsFourth-order terms

Prof. Jose SasianOPTI 518

Key concept

22040 131 222

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220 311 400

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W H H W H H H W H H

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•Total wavefront deformation is the superposition (addition) of all aberration orders.

•The fourth-order group of aberrations is also know as the primary aberrations.

•For slow systems, ~F/8 or less, and for small fields of view, a few degrees, the primary aberrationsprovide a substantially accurate approximation to the wavefront deformation.

Prof. Jose SasianOPTI 518

Spherical aberration

We have a spherical surface of radius of curvature r, a ray intersecting the surface at point P, intersecting the reference sphere at B’, intersecting the

wavefront in object space at B and in image space at A’, and passing inimage space by the point Q’’ in the optical axis. The reference spherein object space is centered at Q and in image space is centered at Q’

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Prof. Jose SasianOPTI 518

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Prof. Jose SasianOPTI 518

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Spherical aberration

Prof. Jose SasianOPTI 518

Spherical aberration

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0 A

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040 81

Prof. Jose SasianOPTI 518

Surface of radius r

StopS0y

S’

s s’

Objectplane

Image plane

Petzval field curvature PW220

We locate the aperture stop at the center of curvature of the spherical surface. With being the object height, then the inverse of the distancealong the chief ray from the off-axis object point to the surface is:

Prof. Jose SasianOPTI 518

Petzval field curvature

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Prof. Jose SasianOPTI 518

Petzval field curvature

0 A

By inserting the Eqs. into the quadratic term of Eq. 8,:

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Prof. Jose SasianOPTI 518

Aberration function at CC

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SurfaceExit pupil

Chief ray

CC

Prof. Jose SasianOPTI 518

Ideal image point

Reference sphereOld exit

pupil

New exitpupil

,newW H

' ', , , ,' ' '

old old old oldold old old new

old old old

y y H y yW H W H W H H W Hy y y

Stop shifting

,oldW H

Prof. Jose SasianOPTI 518

Expansion about the new chief ray height

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yy

E

Eshift

Prof. Jose SasianOPTI 518

Graphical view

Old Pupil

New pupil

Ey

Old chief rayNew chief ray

Prof. Jose SasianOPTI 518

Quadratic term

HHAAH

AA

HAAH

AA

shiftshift

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2

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AA

HHWHHW

PP

PP

Prof. Jose SasianOPTI 518

Quartic term

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AAHH

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AA

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AA

HHAAH

AA

shiftshift

Prof. Jose SasianOPTI 518

All terms

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Piston

Prof. Jose SasianOPTI 518

Entrance and exit pupils

Prof. Jose SasianOPTI 518

Exit pupil becomes entrance pupil for next surface

Exit pupil for surface J

Entrance pupil for surface J+1

OPD’s add

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A B B

2040,B B B BW H W

A B B

Prof. Jose SasianOPTI 518

Exit pupil becomes entrance pupil for next surface

Pupil

OPD’s add

,A AW H

A B B

,B BW H

BB

B

Pupil

A B

Prof. Jose SasianOPTI 518

Extrinsic terms

Entrance pupil for surface J+1

2 2020 040 040

020

2 2040 040

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2

...

....

A B B A A B B

A B B B B

A A A A A A B B B

A B B B B B B

A B B B B B B B B B

B B B B B

W H W H W H

W H W H

W W W

W

W W

A B B

Prof. Jose SasianOPTI 518

Fourth-order contributionsFor a given system ray we add the OPD contributed by each surface.The problem is that because of pupilaberrations we do not know the pupil coordinates of the ray at previous exit pupils.However, the third-order error in the ray pupilcoordinate leads to six-order aberrations.

To fourth-order we do not haveother fourth-order terms to account for.

We are assuming we do not have second-order aberrations. Otherwise these will generateother fourth-order terms.

Prof. Jose SasianOPTI 518

RephraseThere are no second order terms in the

aberration function of each surface

Then for a system of surfaces the fourth-order coefficients are the sum of the

coefficients contributed by each surface

There are no fourth-order extrinsic termsfrom previous aberration in the system

Prof. Jose SasianOPTI 518

Prof. Jose SasianOPTI 518

Prof. Jose SasianOPTI 518

First-order chief and marginal rays

Imageplane

's

'u'uy

y

Stopaperture

Object and image space quantities

Prof. Jose SasianOPTI 518

The slope alpha αNormal line

ry

α

Spherical surface

u u’

s s’

i

/ /A ni ny s ny rnu n

From the axis/normal to theray in a counter-clock wise rotationindicates a positive slope

Prof. Jose SasianOPTI 518

Example : Cooke triplet lens

Prof. Jose SasianOPTI 518

Wave coefficients

1.0000 5.8831 16.4912 11.5569 37.9424 61.2785 -10.4705 -14.67532.0000 4.6978 -50.6336 136.4338 -0.1227 -366.9639 -6.5847 35.48543.0000 -22.3709 117.1708 -153.4247 -36.2070 295.7159 18.4586 -48.33984.0000 -9.6490 -65.3484 -110.6438 -40.4402 -324.2767 14.8117 50.15645.0000 1.6894 24.1504 86.3110 10.3704 382.5921 -4.7481 -33.93876.0000 22.0849 -42.6064 20.5492 43.9016 -52.2587 -12.3359 11.8993Totals 2.3352 -0.7760 -9.2175 15.4444 -3.9128 -0.8690 0.5872

W040 W131 W222 W220 W311 W020 W111

In waves at 0.000587 mm

Prof. Jose SasianOPTI 518

PrescriptionF/4, f=50 mm; FOV +/- 20 degrees

Stop at surface 3SURFACE DATA SUMMARY:Surf Type Radius Thickness Glass Diameter Conic CommentOBJ STANDARD Infinity Infinity 0 0 1 STANDARD 23.713 4.831 LAK9 20.26679 0 2 STANDARD 7331.288 5.86 18.17704 0 3 STANDARD -24.456 0.975 SF5 9.598584 0 4 STANDARD 21.896 4.822 9.909458 0 5 STANDARD 86.759 3.127 LAK9 16.07715 0 6 STANDARD -20.4942 -10.0135 16.69285 0

STO STANDARD Infinity 51.25 12.90717 0 IMA STANDARD Infinity 36.46158 0

Prof. Jose SasianOPTI 518

Summary

• Fourth-order terms• Derivation of the coefficients in terms of

systems parameters• Application of stop shifting• Rely on second-order structure• Example for a Cooke triplet