ECEG105/ECEU646 Optics for Engineers Course Notes Part 4: Apertures, Aberrations Prof. Charles A. DiMarzio Northeastern University Fall 2008

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1 ECEG105/ECEU646 Optics for Engineers Course Notes Part 4: Apertures, Aberrations Prof. Charles A. DiMarzio Northeastern University Fall 2008 July Chuck DiMarzio, Northeastern University Aug 2007 Sept 2008

2 Advanced Geometric Optics Introduction Stops, Pupils, and Windows f-number Examples Magnifier Microscope Aberrations Design Process From Concept through Ray Tracing Finalizing the Design Fabrication and Alignment July Chuck DiMarzio, Northeastern University

3 Some Assumptions We Made All lenses are infinite in diameter Every ray from every part of the object reaches the image Angles are Small: sin(θ)=tan(θ)=θ cos(θ)=1 July Chuck DiMarzio, Northeastern University

4 What We Have Developed Description of an Optical System in terms of Principal Planes, Focal Length, and Indices of Refraction These equations describe a mapping from object space (x,y,z) to image space (x,y,z ) s, s are z coordinates B H V V H B July Chuck DiMarzio, Northeastern University Sept 2007 Sept 2008

5 Lens Equation as Mapping The mapping can be applied to all ranges of z. (not just on the appropriate side of the lens) We can consider the whole system or any part. The object can be another lens s', Image Dist., cm s, Object Dist., cm. L 4 f = 10 cm. L 1 L 2 L 3 L 4 July Chuck DiMarzio, Northeastern University Sept 2008

6 Stops, Pupils, and Windows (1) Intuitive Description Pupil Limits Amount of Light Collected Window Limits What Can Be Seen Window Pupil July Chuck DiMarzio, Northeastern University

7 Stops, Pupils and Images in Object Space Entrance Pupil Limits Cone of Rays from Object Entrance Window Limits Cone of Rays From Entrance Pupil Windows (2) Physical Components Aperture Stop Limits Cone of Rays from Object which Can Pass Through the System Field Stop Limits Locations of Points in Object which Can Pass Through System Images in Image Space Exit Pupil Limits Cone of Rays from Image Exit Window Limits Cone of Rays From Exit Pupil July Chuck DiMarzio, Northeastern University Sept 2008

8 Finding the Entrance Pupil Find all apertures in object space L 4 is L 4 seen through L 1 -L 3 L 1 L 2 L 3 L 4 Entrance Pupil Subtends Smallest Angle from Object L 3 L 4 L 1 L 2 L 3 is L 3 seen through L 1 -L 2 July Chuck DiMarzio, Northeastern University

9 Finding the Entrance Window Entrance Window Subtends Smallest Angle from Entrance Pupil L 3 L 4 L 1 L 2 Aperture Stop is the physical object conjugate to the entrance pupil Field Stop is the physical object conjugate to the entrance window All other apertures are irrelevant July Chuck DiMarzio, Northeastern University Sept 2008

10 f=28 mm Field of View f=55 mm f=200 mm Film= Exit Window July Chuck DiMarzio, Northeastern University

11 Example: The Telescope Aperture Stop Field Stop July Chuck DiMarzio, Northeastern University

12 The Telescope in Object Secondary Space Primary Secondary Entrance Window Entrance Pupil July Chuck DiMarzio, Northeastern University

13 The Telescope in Image Space Primary Primary Secondary Exit Pupil Exit Window July Chuck DiMarzio, Northeastern University Stopped 26 Sep 03

14 f-number & Numerical f-number Aperture Numerical Aperture f θ F A A 5 F D is Lens Diameter 4 f#, f-number NA, Numerical Aperture July Chuck DiMarzio, Northeastern University

15 Importance of Aperture ``Fast System Low f-number, High NA (NA 1, f# 1) Good Light Collection (can use short exposure) Small Diffraction Limit (λ/d) Propensity for Aberrations (sin θ θ) Corrections may require multiple elements Big Diameter Big Thickness Weight, Cost Tight Tolerance over Large Area July Chuck DiMarzio, Northeastern University Sept 2008

16 The Simple Magnifier A F A F July Chuck DiMarzio, Northeastern University

17 The Simple Magnifier (2) Image Size on Retina Determined by x /s No Reason to go beyond s = 250 mm Magnification Defined as No Reason to go beyond D=10 mm f# 1 Means f=10 mm Maximum M m =25 For the Interested Student: What if s>f? July Chuck DiMarzio, Northeastern University Sept 2008

18 Microscope F F F F A A Two-Step Magnification Objective Makes a Real Image Eyepiece Used as a Simple Magnifier July Chuck DiMarzio, Northeastern University

19 Microscope Objective F F F F A A July Chuck DiMarzio, Northeastern University

20 Microscope Eyepiece F F F F A A 2 A 2 July Chuck DiMarzio, Northeastern University

21 Microscope Effective Lens H H 192 mm Barrel Length = 160 mm FA f f 1 =16mm 2 =16mm F Effective Lens: D f = -1.6 mm D 19.2 mm H H 19.2 mm F A F July Chuck DiMarzio, Northeastern University

22 Microscope Aperture Stop Analysis in Image Space F F Image Exit Pupil Aperture Stop =Entrance Pupil Put the Entrance Pupil of your eye at the Exit Pupil of the System, Not at the Eyepiece, because 1) It tickles (and more if it s a rifle scope) 2) The Pupil begins to act like a window July Chuck DiMarzio, Northeastern University Sept 2008 Stopped here 30 Sep 03

23 Microscope Field Stop F F Entrance Window Field Stop = Exit Window July Chuck DiMarzio, Northeastern University

24 Microscope Effective Lens July Chuck DiMarzio, Northeastern University

25 Apertures Summary Object and Image Space Locating All the Elements Finding the Pupil Computing the Pupil Size and NA or f# Finding the Window Computing the Field of View July Chuck DiMarzio, Northeastern University Dec 2004

26 Aberrations Failure of Paraxial Optics Assumptions Ray Optics Based On sin(θ)=tan(θ)=θ Spherical Waves φ=φ 0 +2πx 2 /ρλ Next Level of Complexity Ray Approach: sin(θ)=θ+θ 3 /3! Wave Approach: φ=φ 0 +2πx 2 /ρλ+cρ A Further Level of Complexity Ray Tracing July Chuck DiMarzio, Northeastern University

27 Examples of Aberrations 1 (1) Paraxial Imaging R = 2, n=1.00, n =1.50 s=10, s = m4061_ In this example for a ray having height h at the surface, s (h)<s (0). July Chuck DiMarzio, Northeastern University

28 Example of Aberrations z(h=1.0) z(h=0.6) (2) Longitudinal Aberration = z Transverse Aberration = x Where Exactly is the image? x(h=1.0) m4061_ What is its diameter? July Chuck DiMarzio, Northeastern University

29 Spherical Aberration Thin Lens in Air July Chuck DiMarzio, Northeastern University

30 Transverse Spherical Aberration h s x s(0) July Chuck DiMarzio, Northeastern University

31 Evaluating Transverse SA July Chuck DiMarzio, Northeastern University

32 Coddington Shape Factors -1 p=0 +1 q= July Chuck DiMarzio, Northeastern University

33 Numerical Examples 5 Beam Size, m 10-2 s=1m, s =4cm q, Shape Factor p, Position Factor n=1.5 n=2.4 n= n=2.4 n=4 n=1.5 DL at 10 µm DL at 1.06 µm 500 nm q, Shape Factor July Chuck DiMarzio, Northeastern University

34 Phase Description of Aberrations v y Object Entrance Pupil Exit Pupil Image z Mapping from object space to image space Phase changes introduced in pupil plane Different in different parts of plane Can change mapping or blur images July Chuck DiMarzio, Northeastern University Sept 2008

35 Coordinates for Phase v y z v v Analysis phase Solid Line is phase of a spherical wave toward the image point. Dotted line is actual phase. Our goal is to find (ρ,φ,h). 2a ρa u 0<ρ<1 y h x July Chuck DiMarzio, Northeastern University

36 Aberration Terms Odd Terms involve tilt, not considered here. Δ=ρ cosφ July Chuck DiMarzio, Northeastern University

37 Second Order Image Position Terms: The spherical wave is approximated by a second-order phase term, so this error is simply a change in focal length. July Chuck DiMarzio, Northeastern University

38 Fourth Order (1) ρ 2 is focus: depends on h 2 and h 2 cosφ Spherical Aberration Astigmatism and Field Curvature Tangential Plane T S Sagittal Plane Sample Images At T At S July Chuck DiMarzio, Northeastern University Sept 2008

39 Fourth Order (2) ρ cosφ is Tilt: Depends on h 3 Coma y v Barrel Distortion Pincushion Distortion u x July Chuck DiMarzio, Northeastern University Sept 2008

40 Optical Design Process July Chuck DiMarzio, Northeastern University

41 Ray Tracing Fundamentals July Chuck DiMarzio, Northeastern University

42 If One Element Doesn t Add Another Lens Work... Let George Do It Different Index? Smaller angles with higher index. Thus germanium is better than ZnSe in IR. Not much hope in the visible. Aspherics July Chuck DiMarzio, Northeastern University

43 Aberrations Summary Origin of Aberrations On-Axis Aberrations Change of Focus Spherical Aberration Off-Axis Aberrations Additional Blurring Effects Distorting Effects July Chuck DiMarzio, Northeastern University Dec 2004

44 Summary of Concepts So Far Paraxial Optics with Thin Lenses Thick Lenses (Principal Planes) Apertures: Pupils and Windows Aberration Correction Analytical Ray Tracing What s Missing? Wave Optics July Chuck DiMarzio, Northeastern University

Lecture 4: Geometrical Optics 2. Optical Systems. Images and Pupils. Rays. Wavefronts. Aberrations. Outline

Lecture 4: Geometrical Optics 2 Outline 1 Optical Systems 2 Images and Pupils 3 Rays 4 Wavefronts 5 Aberrations Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl Lecture 4: Geometrical