Prof. Jose Sasian

AstigmatismField Curvature

Distortion

Lens Design OPTI 517

Prof. Jose Sasian

Earliest through focus images

1.T. Young, “On the mechanism of the eye,”2.Phil Trans Royal Soc Lond 1801; 91: 23–88 and plates.

Prof. Jose Sasian

Astigmatism through focus

Prof. Jose Sasian

AstigmatismW H W H W W HW W H W H W H W H W H( , ) cos( )

cos( ) cos ( ) cos( )

111 020

2200

2

0404

1313

2222 2 2

2202 2

3113

4004

Prof. Jose Sasian

Anastigmatic

• Aplanatic: free from spherical aberration and coma.

• Stigmatic ~ pointy• Astigmatism: No pointy• Anastigmatic: No-No pointy = pointy• Anastigmatic: free from spherical aberration,

coma, and astigmatism• Aplanatic: coined by John Herschel• Astigmatism: coined by George Airy

Prof. Jose Sasian

2222

12

uW A yn

Cases of zero astigmatism

Prof. Jose Sasian

Field behavior22

220222

222 )(cos),( HWHWHW

2222

12

uW A yn

2 2220

1 14 2

uW A y Ж Pn

Prof. Jose Sasian

Review of aberrations coefficients040

131

222

220

311

020

111

18121214

12

12

I

II

III

P IV

V

L

T

W S

W S

W S

W S

W S

W C

W C

Prof. Jose Sasian

Structural coefficients

Prof. Jose Sasian

Seidel sum for thin lens(stop at lens)

DCYBXYAXySI 2234

41

2 212IIS Жy EX FY

2IIIS Ж

2 1IVS Ж

n

0VS

2 1LC y

0TC

212

nnnA

22

1nnD

1

14

nnnB

11

nnnE

nnC 23

nnF 12

12

12

21

21

rrrr

cccc

X

uuuu

mmY

''

11

))(1( 1 xccncn

Prof. Jose Sasian

Thin lens astigmatism2

IIIS Ж When the stop is a the thin lens astigmatism is fixed.

Shifting the stop in the presence of spherical aberration or coma Allows changing astigmatism

* 22III III II IS S

Prof. Jose Sasian

Controlling astigmatism

Prof. Jose Sasian

1) Stop position: singlet lens

Coma and astigmatism are zero!

* 22III III II IS S SS S S 1

2

0

0

un

A

Prof. Jose Sasian

2) Canceling/balancing negative and positive astigmatism

Prof. Jose Sasian

• In this case one adds a lens which contributes the opposite amount of astigmatism.

• The spherical aberration and coma of the new lens are corrected by the system that has the degrees of freedom for such.

• New lens hopefully contributes little comaand spherical aberration.

3-a) Adding a degree of freedom

Prof. Jose Sasian

3-b) Adding a degree of freedomRitchey-Chretien I

At best surface (Sagittal field surface)

1.7 waves of astigmatism @ f.3.3

Prof. Jose Sasian

3-c) Adding a degree of freedomRitchey-Chretien II

0.0 waves of astigmatism @ f/1.9 after conic tweak

Prof. Jose Sasian

4) Shells near the image plane (or aspheric plate)

Prof. Jose Sasian

Offner unit magnification relay

•Offner relay system:•Three spherical mirrors•Negative unit magnification•No primary aberrations•Ring field concept•Improvement of field with shell

Prof. Jose Sasian

However; beware of ghosts

Prof. Jose Sasian

Field curvature2 2

22014

uW Ж P A yn

P Cn

1

1 1

1 1n nn nn nrk k' '''

1

'k n

Petzval sum:

For a system of thin lenses:

Prof. Jose Sasian

Field curvature interpretation• Assume same glass and consider sag

of Petzval surface at a height y:

• If the Petzval sum is zero then the lens has constant thickness across the aperture or across the field.

• Compare with the image displacement S caused by a plano parallel plate:

• The conclusion is that Petzval field curvature arises because the overall lens thickness variation across the aperture (in the general case the index of refraction enters as a weight).

2 2'2 ' 2k

y n n yn r

Snnt

1

Prof. Jose Sasian

Thickness variation in atelecentric lens

Prof. Jose Sasian

Four classical ways• 1) A thick meniscus lens can contribute optical power but no field

curvature if both surfaces have the same radius. Consider doubleGasuss lens. Note the correction for color.

• 2) Separated thin lenses: Bulges and constrictionsConsider the Cooke triplet and lenses for microlithography.

• 3) A field flattener: Fully contributes to Petzval but not to spherical, coma, or astigmatism. Also there is little contribution to optical power.Consider Petzval lens with a field flattener.

• 4) New achromat: use to advantage new glass types.

1

'k n

Prof. Jose Sasian

Four classical ways

Use of a thick meniscus lens Use of a field flattener lens

Prof. Jose Sasian

Four classical ways

Creating beam bulges and constrictions

Prof. Jose Sasian

Four classical ways: Use of glass

BK7-F2P=-139 mm

BK7P=-152 mm

V-number for flint increasesV-number for crown decreases

N for crown increasesN for flint decreases

babbaa Fff

SSKN5-LF5P=-219 mm

F=100 mm

1

'k n

Prof. Jose Sasian

DistortionW H W H W W HW W H W H W H W H W H( , ) cos( )

cos( ) cos ( ) cos( )

111 020

2200

2

0404

1313

2222 2 2

2202 2

3113

4004

W311 H3cos()W511 H5cos()

DistortionH hh

100

With respect to chief ray, geometrical or physical centroid

Prof. Jose Sasian

Distortion

Top row, (barrel) distortion:0%, 2.5%, 5% and 10%. Bottom row, (pincushion) distortion 0%, 2.5%, 5% and 10%.

Prof. Jose Sasian

1) By Symmetry about the stop or phantom stop

Distortion is an odd aberration: It can be cancelled by symmetryAbout the stop

Prof. Jose Sasian

2) Aspheric plate or bending a field flattener

Prof. Jose Sasian

Exercise: Galilean telescope

A plano-convex lens objective with a focal length of about 750-1000 mm.A plano-concave lens for the eyepiece (ocular) with a focal length of about 50 mm. The objective lens was stopped downto an aperture of 12.5 to 25 mm. The field of view is about 15 arc-minutes. The instrument's magnifying power is 15-20.