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Introduction to Lens Design and Tools

TA : Lin Lin-Yao Yao Liao(廖?嶢) Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu, Taiwan

e-mail: finalhome.eo95g@nctu.edu.tw

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Lin-Yao Liao

Outline

? What’s Imaging? ? Gauss Optics ? Aberrations ? Classical Study

– The Optimal Design of Doublet

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What’s Imaging?

Imaging is the representation or reproduction of an object; especially a visual representation

Image Object

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Image Formed by A Lens

Object Space

Image Space p

Object Point

Image Point Lens

Optical system (the lens) is used to form a image 1 at the position where we want. 1. want 2. with an acceptable quality.

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Imaging Model We Learned Before..

Graphical Method of Finding Image

Q

M’ M F A F’’ Q’

In this model, we only know.. 1 The parallel rays pass through the focal point 1. point. 2. The rays pass through the center of lens will not be reflected.

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Gauss Optics

Gauss Optics (First-Order Optics, Paraxial Optics)

Taylor series of sine Only take the 1st order Snell’s Law :

θ1 n1 θ2 n2

Gauss Optics only takes the 1st term of sine’s Taylor series to make all the analysis linear.

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Gauss Optics

Single Surface

n M θi r A θt O n’ M’ M

s

s’

Gauss Formula: Optical Power of A Surface:

Gauss Formula describes the relation of s, s’, r, and two refractive indexes.

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Sign Conversion

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Thin Lens Formula

Thin Lens ? thickness d is zero n A1 M A2 r2 M’’ M’ r1 n’ n’’

s1

If the thickness d is zero ? S1’=S2

d

s 2’

s 1’ s2

Thin Lens Formula:

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WorkshopWorkshop -1

1. Use OSLO to simulate a thin lens with the following specifications… specifications

? ? ? ? EFL = 50mm Aperture size = 3mm Material of the lens : N-BK7 Thickness of the lens = 0 mm

2. Thicken d = 2mm. How the EFL will be changed? 3. Use the “Optimization Function” to re-fit the spec.

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Start

Start a new lens

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Surface Data

Surface #

Radius of each Surface

Distance to next surface

Material M t i l of f this space

Others..

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Parameters..

Field angle Effective focal length

The Primary Th Pi wave length we use Radius of incident beam (Entrance Pupil size, F/#)

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Key in Data

EFL = 50mm and n=1.5168 (N-BK7)? we can choose r1=-r2=51.68mm

The result almost fits our purpose

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“Solves”

Set axial ray height 0 : Make the axial ray height 0 at the next surface, it is usually y used to find the focal p plane.

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How to Know The Material Data

Glass Companies…

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Glass Map

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Layout Our Lens

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Further Drawing

Drawing g Result

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D=2mm

It doesn’t fit the thin lens result

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Optimization

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Set Variables

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Optimize

We realized a single lens with the focal length we expect.

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Combination of Two Thin Lenses

n’ A1 M A2 f2 M’’ M’

s1

f1

s 1’ s2 s 2’

t

We can use the formula above to have a quick initial design of lens combination.

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WorkshopWorkshop -2

1. Use two thin lenses to replace the optical system of Workshop 1 Workshop-1.

? ? ? ? ? ? ? Lens1: f1 < 0, Lens2 : f2 > 0 (NP) EFL = 50mm Aperture size = 3mm Field Angle = 10 ° The separation of two lenses t = 10mm Material of the lens : Lens1? Schott, N-BK7; Lens2? Schott, N-BK7 Thickness of the lenses = 0 mm

2. Thicken d = 2mm for both lenses. How the EFL will be changed? 3. Use the “Optimization Function” to re-fit the spec.

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Homework (due date : 2010/04/09)

1. Use two thin lenses to replace the optical system of Workshop 1 Workshop-1.

? ? ? ? ? ? ? Lens1: f1 > 0, Lens2 : f2 < 0 (PN) EFL = 50mm Aperture size = 5mm Field Angle = 10 ° The separation of two lenses t = 10mm Material of the lens : Lens1?Schott, N-BK7; Lens2? Schott, SF2 Thickness of the lenses = 0 mm

2. Thicken d = 2mm for both lenses. How the EFL will be changed? 3. Use the “Optimization Function” to re-fit the spec. 4. Discuss what are the difference between NP and PN case.

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Aberrations

The results which cannot fit Gauss Image are called Aberration

Reasons… 1. Diffraction 2 Tolerance 2. 3. Real ray tracing? we discuss today Gauss Optics (First-Order Optics, Paraxial Optics)

Taylor series of sine Only take the 1st order is not enough!

We have to take the higher order term into optical calculation. The analysis y will not be linear and “Aberrations” appear. pp

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LowerLower -order Aberrations

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Spherical Aberration

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Coma

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Astigmatism

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Field Curvature

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Distortion

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Qualitative Effects of Aberrations on Image Quality

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Chromatic Aberration

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The Most Important Parameters of A Lens Head

Aperture Size (F/#)

Image Size Field of View (FOV)

Effective Focal Length (EFL)

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Specifications

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MTF

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Doublet

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