Prof. Jose Sasian

Summary of formulasSummary of optical systems

Lens Design OPTI 517

Prof. Jose Sasian

Imaging: central projection

X a X b Y c Z da X b Y c Z d

'

1 1 1 1

0 0 0 0

Y a X b Y c Z da X b Y c Z d

'

2 2 2 2

0 0 0 0

Z a X b Y c Z da X b Y c Z d

'

3 3 3 3

0 0 0 0

mZ f

11 \

Zf m 1 1

Zf

m'' 1

m Zf

1 ''

fZ

fZ

'' 1

.

Collinear transformationNewtonian equationsGaussian equationsCardinal points

Prof. Jose Sasian

Optical system conceptual model

Prof. Jose Sasian

Wave aberration function

2 2000 111 020 200

4 3 2 2 2040 131 222

2 2 3 4220 311 400

( , ) cos( )

cos( ) cos ( )

cos( )

W H W W H W W H

W W H W H

W H W H W H

Prof. Jose Sasian

Prof. Jose Sasian

Chromatic coefficients

0201

1 /2

j

j j ji

W A n n y

1111

/j

j j ji

W A n n y

For a system of j surfaces

1111

j

i i

W yy

2020

1

12

j

i i

W y

For a system of thin lenses in air

Prof. Jose Sasian

Aspheric contributions

aW81

040 0LC

ayyW

21

131

ayyW

3

311 21

0TC

ayyW

2

222 21

nyca 432

nyAa 448

2

22014yW ay

Prof. Jose Sasian

Stop Shifting0IS

III SyyS

IIIIII SyyS

yyS

2

2

0IVS

IIIIIIIVV SyyS

yySS

yyS

32

33

0LC

LT CyyC

Prof. Jose Sasian

Structural coefficients

Prof. Jose Sasian

Structural coefficients: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

2

2

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

Miscellaneous

1 1

1 1n nn nn nrk k' '''

1

'k n

Petzval sum:

For a system of thin lenses in air:

DistortionH hh

100

Prof. Jose Sasian

Miscellaneous

ns

ns

n I n IRs

''

' cos ' cos

n It

n It

n I n IRt

' cos ''

cos 'cos ' cos2 2

Coddington equations

uu

UU'

sinsin '

Sine condition

Prof. Jose Sasian

Some angular quantitiesThe mnemonic 12345

• Index of air ~1.0003• One arc-minute ~0.0003• One arc second ~0.000005 • 15 degrees ~1/4• One arc minute ~healthy eye resolution• Half degree ~Sun, Moon angular subtend• +/- 23.4 degrees FOV of 35 mm camera

with 50 mm lens.

Prof. Jose Sasian

Mangin mirrorInvented in 1876 by Alphonse Mangin in France

Actually described by Newton in his description about makingthe mirrors for his celebrated telescope

Mirror surface

A Mangin mirror uses a lens with one surface coated to be a mirror.

Mangin mirrors are used to reflect light from the light sources in lighthouses without the problem of tarnishing due to the salty

environment.Mangin mirrors are variable aberration generators for a given

optical power. They have very useful aberration correcting properties. Both mono-chromatic and chromatic.

Prof. Jose Sasian

Telescopes Objectives

• Achromatic and aplanatic doublet • Apochromatic and aplanatic

doublet/triplet• Schupmann medial single glass

objective

Prof. Jose Sasian

Review of telescopes

• Cassegrain• Mersenne• Schmidt camera• Maksutov• Houghton

• Paul-Baker• Offner relay• Meinel’s two

stage optics

Prof. Jose Sasian

Cassegrain type

•True Cassegrain•Ritchey-Chretien: aplanatic•Dall-Kirkham: spherical secondary•Pressman-Carmichel; spherical primary•Olivier Guyon (no diffraction rings)

Prof. Jose Sasian

Camera Schmidt

Aspheric plate at mirror center of curvature A-bar=0Stop aperture at aspheric plateNote symmetry about mirror CCNo spherical aberrationNo comaNo astigmatism.Anastigmatic over a wide field of view!Satisfies Conrady’s D-d sum

Prof. Jose Sasian

Maksutov: Meniscus lens

•Strong meniscus shape corrects spherical aberration•Coma by the position of the stop and meniscus lens•Chromatic change of focus by the meniscus lens thickness•Single glass achromat

2020

1

12

j

i i

W y

Prof. Jose Sasian

Houghton: nearly afocal doublet

Same glass doubletSeveral solutionsCorrection for spherical aberration, coma, and chromatic aberrationsCorrection for astigmatismAll spherical surfaces

Prof. Jose Sasian

Merssene afocal systemAnastigmatic

Confocal paraboloids

Prof. Jose Sasian

Image and Pupil Aberration relationships

Prof. Jose Sasian

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 Sasian

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 Sasian

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.