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: finalho
me.eo95g@nctu.edu.tw
Advanced Display Optical Lab
1
Lin-Yao Liao
Outline
? What’s Imaging? ? Gauss Optics ? Aberrations ? Classical Study
– The Optimal Design of Doublet
Advanced Display Optical Lab
2
Lin-Yao Liao
What’s Imaging?
Imaging is the representation or reproduction of an object; especially a visual representation
Image Object
Advanced Display Optical Lab
3
Lin-Yao Liao
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.
Advanced Display Optical Lab
4
Lin-Yao Liao
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.
Advanced Display Optical Lab
5
Lin-Yao Liao
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.
Advanced Display Optical Lab
6
Lin-Yao Liao
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.
Advanced Display Optical Lab
7
Lin-Yao Liao
Sign Conversion
Advanced Display Optical Lab
8
Lin-Yao Liao
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:
Advanced Display Optical Lab
9
Lin-Yao Liao
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.
Advanced Display Optical Lab
10
Lin-Yao Liao
Start
Start a new lens
Advanced Display Optical Lab
11
Lin-Yao Liao
Surface Data
Surface #
Radius of each Surface
Distance to next surface
Material M t i l of f this space
Others..
Advanced Display Optical Lab
12
Lin-Yao Liao
Parameters..
Field angle Effective focal length
The Primary Th Pi wave length we use Radius of incident beam (Entrance Pupil size, F/#)
Advanced Display Optical Lab
13
Lin-Yao Liao
Key in Data
EFL = 50mm and n=1.5168 (N-BK7)? we can choose r1=-r2=51.68mm
The result almost fits our purpose
Advanced Display Optical Lab
14
Lin-Yao Liao
“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.
Advanced Display Optical Lab
15
Lin-Yao Liao
How to Know The Material Data
Glass Companies…
Advanced Display Optical Lab
16
Lin-Yao Liao
Glass Map
Advanced Display Optical Lab
17
Lin-Yao Liao
Layout Our Lens
Advanced Display Optical Lab
18
Lin-Yao Liao
Further Drawing
Drawing g Result
Advanced Display Optical Lab
19
Lin-Yao Liao
D=2mm
It doesn’t fit the thin lens result
Advanced Display Optical Lab
20
Lin-Yao Liao
Optimization
Advanced Display Optical Lab
21
Lin-Yao Liao
Set Variables
Advanced Display Optical Lab
22
Lin-Yao Liao
Optimize
We realized a single lens with the focal length we expect.
Advanced Display Optical Lab
23
Lin-Yao Liao
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.
Advanced Display Optical Lab
24
Lin-Yao Liao
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.
Advanced Display Optical Lab
25
Lin-Yao Liao
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.
Advanced Display Optical Lab
26
Lin-Yao Liao
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
Advanced Display Optical Lab
27
Lin-Yao Liao
LowerLower -order Aberrations
Advanced Display Optical Lab
28
Lin-Yao Liao
Spherical Aberration
Advanced Display Optical Lab
29
Lin-Yao Liao
Coma
Advanced Display Optical Lab
30
Lin-Yao Liao
Astigmatism
Advanced Display Optical Lab
31
Lin-Yao Liao
Field Curvature
Advanced Display Optical Lab
32
Lin-Yao Liao
Distortion
Advanced Display Optical Lab
33
Lin-Yao Liao
Qualitative Effects of Aberrations on Image Quality
Advanced Display Optical Lab
34
Lin-Yao Liao
Chromatic Aberration
Advanced Display Optical Lab
35
Lin-Yao Liao
The Most Important Parameters of A Lens Head
Aperture Size (F/#)
Image Size Field of View (FOV)
Effective Focal Length (EFL)
Advanced Display Optical Lab
36
Lin-Yao Liao
Specifications
Advanced Display Optical Lab
37
Lin-Yao Liao
MTF
Advanced Display Optical Lab
38
Lin-Yao Liao
Doublet
Advanced Display Optical Lab
39
Lin-Yao Liao