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Introduction• Past Homework solutions

• Glass Properties

• Chromatic aberrations

• Stop Shift theory

• Thin lenses and aberrations

• Achromatization

• Introduction to Zemax

• Homework

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HOMEWORKSurface (Radius=R1)

concentric to STOP( B=0)

STOP

Aplanatic surface (Radius=R2)

Δ(u/n)=0

Specifications

EFL=150 mm

F/#=5.6

WL=0.55

Find.

1. Refractive index of lens

2. Radii of lens –use Lens Maker formula

3. Determine which aberrations are present for each surface

R2=R1

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Solution to Homework - 1For the first surface where s1=∞, n=1, n’=μ

Rnn

sn

sn −

+='

''

11

1'1 −=μμRs

For the second surface 11

'12 −=−

−=−=

μμμ RRRRss

Since the second surface is aplanatic then 11'

2 −=

+=

+= μμ

μ RRRn

nns

012 =−− μμ From where we get μ=1.618034

⎥⎦

⎤⎢⎣

⎡ −+−−=

2121

)1(11)1(1RR

dRRf μ

μμ R1=R2=d with f=150 mm we get R=35.4102

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Solution to Homework - 2

(SI)1

0

0

(SIV)1=X

0

0

0

0

(SV)2

Surface1 Surface2

(SIV)2=-X

TOTAL

(SI)1

0

0

0

(SV)2

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Glass Properties

Abbe number

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Glass Properties

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Glass Chart

CROWNS

FLINTS

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Chromatic Aberrations

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Chromatic Aberrations

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Chromatic Aberrations

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Stop Shift Theory

STOP STOP

Figure above shows a lens near a STOP, and the same lens with a remote STOP. In the second case the STOP diameter has been adjusted to keep the size of the ray pencil unchanged.

This type of movement and diameter adjustment is a stop shift within the context of the stop-shift formulae.

The Seidel eccentricity ratio E is the parameter used to denote the stop position. It is defined as

hhE =

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Stop Shift TheoryA stop shift corresponds to a change in E of δE

And as result we find that B changes by

The stop shift formulae are valid not only for the calculation of non-central thin-lens aberrations, but also for the calculation of the change in aberrations for a general thick-lens system as a result of the stop movement

A complex thick system with a stop in some position and total primary aberrations given by SI, SII, SIII, SIV, SV, CL, CT; now the stop is moved so that for every surface E is changed by δE (it can be proved that δE is the same for all the surfaces) and the total aberrations become starred.

hhE δδ =

EAB δδ =

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Stop Shift FormulaeII SS =*

IIIII ESSS δ+=*

IIIIIIIII SEESSS 2* 2 δδ ++=

IVIV SS =*

IIIIVIIIVV SESESSESS 32* 3)3( δδδ ++++=

LL CC =*

LTT ECCC δ+=*

These powerful formulae enable us to calculate the effect of a stop shift on the aberrations of any system.

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In summaryThird Order Aberration Theory applies to:

1. Rotationally symmetric systems

2. It is valid for system with small apertures

3. It is valid for small fields of view

4. The wavefront aberration is a smooth function without discontinuities

As a result of the theory

1. Stopping down a lens will not improve distortion, or lateral color.

2. Symmetrical systems have zero lateral color and distortion. Theyalso have reduced coma.

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Aberrations using Thin LensesShape Parameter X

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Aberrations using Thin Lenses

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Spherical Aberration for a thin lens

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Thin Lenses approximation

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Thin Lenses approximation

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Achromatization

Contents

Definition of Achromatic, Apochromatic and Superachromatic lenses

Examples

Designing an achromat

Designing an apochromat

Designing a superachromat

References

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DefinitionsACHROMAT: Two Wavelengths at the same focus

APOCHROMAT: Three wavelengths at the same focus

SUPERACHROMAT: Four wavelengths at the same focus

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EXAMPLES

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Designing an Achromat

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Introduction to Zemax

An Achromatic Doublet. The Paths of the rays are much exaggerated.

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Introduction to Zemax

Partial Dispersion

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Partial Dispersion versus V-number

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Introduction to Zemax

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Designing a Superachromat

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References

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Introduction to ZemaxTo start any optical design you may need the following: The boldrepresent the must have parameters.

Object Distance

Image Distance

F/# or NA

Full Field of View

Focal Length

Image Format

Magnification

Transmittance

Spectral Range

Image Quality – MTF, RMS WFE, Encircled Energy, Distortion

Mechanical and packaging requirements – Diameter, Weight, etc

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Introduction to Zemax

Example of a Single Lens Parameters

•Focal ratio f/5.6

•Glass is N-BK7

•Focal Length is 100mm

•Field of view is 8 degrees

•Central Lens thickness 2mm to 12mm

•Wavelength 632.8nm (HeNe)

•Edge thickness minimum 2mm

•Lens should be optimized for smallest RMS

•Object is at infinity

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Surface Type

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Introduction to Zemax

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General button

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Field of View Button

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Spectral Range Button

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Glass Specifications

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Solves

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Performance Evaluation

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Optimization

In our for the single lens the variables of optimization could be

Radii, thickness of lens, back focal distance and/or Refractive index

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HomeWorkDesign a single lens using Zemax and show performance using Spot Diagrams

•Focal ratio f/5.6

•Glass is N-BK7

•Focal Length is 100mm

•Field of view is 8 degrees

•Central Lens thickness 2mm to 12mm

•Wavelength 632.8nm (HeNe)

•Edge thickness minimum 2mm

•Lens should be optimized for smallest RMS

•Object is at infinity