ECEG105 & ECEU646 Optics for Engineers Course Notes Part 4: Apertures, Aberrations Prof. Charles A. DiMarzio Northeastern University Fall 2003 July 2003 Chuck DiMarzio, Northeastern University

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 2003 Chuck DiMarzio, Northeastern University

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(q)=tan(q)=q cos(q)=1 July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University 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 image space (x,y,z) to object space (x’,y’,z’) s, s’ are z coordinates H H’ V V’ B B’ July 2003 Chuck DiMarzio, Northeastern University

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 L1 L2 L3 L4 L4’ July 2003 Chuck DiMarzio, Northeastern University

Stops, Pupils, and Windows (1) Intuitive Description Pupil Limits Amount of Light Collected Window Limits What Can Be Seen Window Pupil July 2003 Chuck DiMarzio, Northeastern University

Stops, Pupils and Windows (2) Physical Components Images in Object Space Images in Image Space Aperture Stop Limits Cone of Rays from Object which Can Pass Through the System Entrance Pupil Limits Cone of Rays from Object Exit Pupil Limits Cone of Rays from Image Entrance Window Limits Cone of Rays From Entrance Pupil Field Stop Limits Locations of Points in Object which Can Pass Through System Exit Window Limits Cone of Rays From Exit Pupil July 2003 Chuck DiMarzio, Northeastern University

Finding the Entrance Pupil Find all apertures in object space Entrance Pupil Subtends Smallest Angle from Object L4’ is L4 seen through L1-L3 L1 L2 L3 L4 L1 L2’ L3’ L4’ L3’ is L3 seen through L1-L2 July 2003 Chuck DiMarzio, Northeastern University

Finding the Entrance Window Entrance Window Subtends Smallest Angle from Entrance Pupil 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 L1 L2’ L3’ L4’ July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Field of View f=28 mm f=55 mm Film= Exit Window f=200 mm July 2003 Chuck DiMarzio, Northeastern University

Example: The Telescope Aperture Stop Field Stop July 2003 Chuck DiMarzio, Northeastern University

The Telescope in Object Space Secondary’ Primary Secondary Entrance Pupil Entrance Window July 2003 Chuck DiMarzio, Northeastern University

The Telescope in Image Space Primary Primary’’ Secondary Exit Pupil Exit Window July 2003 Chuck DiMarzio, Northeastern University Stopped 26 Sep 03

Chuck DiMarzio, Northeastern University Chief Ray Aperture Stop Exit Pupil Field Stop Chief Ray passes through the center of every pupil July 2003 Chuck DiMarzio, Northeastern University

Hints on Designing A Scanner Place the mirrors at pupils Put Mirrors Here July 2003 Chuck DiMarzio, Northeastern University

f-Number & Numerical Aperture q F’ A’ A F D is Lens Diameter 5 4 3 f#, f-number 2 1 0.2 0.4 0.6 0.8 1 NA, Numerical Aperture July 2003 Chuck DiMarzio, Northeastern University

Importance of Aperture ``Fast’’ System Low f-number, High NA (NA1, f# 1) Good Light Collection (can use short exposure) Small Diffraction Limit (l/D) Propensity for Aberrations (sin q  q) Corrections may require multiple elements Big Diameter  Big Thickness  Weight, Cost Tight Tolerance over Large Area July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University The Simple Magnifier F F’ A’ A July 2003 Chuck DiMarzio, Northeastern University

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 Mm=25 For the Interested Student: What if s>f ? July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Microscope F’ F’ F F A’ A Two-Step Magnification Objective Makes a Real Image Eyepiece Used as a Simple Magnifier July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Microscope Objective F’ F’ F F A’ A July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Microscope Eyepiece F’ F’ F F A2 A A2’ July 2003 Chuck DiMarzio, Northeastern University

Microscope Effective Lens H H’ 192 mm Barrel Length = 160 mm A f2=16mm F f1=16mm F’ Effective Lens: f = -1.6 mm D D’ 19.2 mm 19.2 mm H H’ A F’ F July 2003 Chuck DiMarzio, Northeastern University

Microscope Aperture Stop Analysis in Image Space F’ F Exit Pupil Image 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 2003 Chuck DiMarzio, Northeastern University Stopped here 30 Sep 03

Chuck DiMarzio, Northeastern University Microscope Field Stop F’ F Entrance Window Field Stop = Exit Window July 2003 Chuck DiMarzio, Northeastern University

Microscope Effective Lens July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Aberrations Failure of Paraxial Optics Assumptions Ray Optics Based On sin(q)=tan(q)=q Spherical Waves f=f0+2px2/rl Next Level of Complexity Ray Approach: sin(q)=q+q3/3! Wave Approach: f=f0+2px2/rl+cr4+... A Further Level of Complexity Ray Tracing July 2003 Chuck DiMarzio, Northeastern University

Examples of Aberrations (1) Paraxial Imaging 0.5 R = 2, n=1.00, n’=1.50 s=10, s’=10 In this example for a ray having height h at the surface, s’(h)<s’(0). -0.5 m4061_3 -1 -10 -5 5 10 July 2003 Chuck DiMarzio, Northeastern University

Example of Aberrations (2) 0.2 D z(h=1.0) Longitudinal Aberration = D z Transverse Aberration =D x 0.15 D z(h=0.6) 0.1 0.05 -0.05 Where Exactly is the image? What is its diameter? -0.1 -0.15 2D x(h=1.0) m4061_3 -0.2 8.5 9 9.5 10 10.5 July 2003 Chuck DiMarzio, Northeastern University

Spherical Aberration Thin Lens in Air July 2003 Chuck DiMarzio, Northeastern University

Transverse Spherical Aberration Ds h Dx s(0) July 2003 Chuck DiMarzio, Northeastern University

Evaluating Transverse SA July 2003 Chuck DiMarzio, Northeastern University

Coddington Shape Factors +1 -1 p=0 -1 q=0 +1 July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Numerical Examples Beam Size, m -2 5 10 s=1m, s’=4cm -3 10 n=2.4 n=1.5 n=1.5 n=4 10 -4 q, Shape Factor DL at 10 mm n=2.4 10 -5 DL at 1.06 mm n=4 500 nm 1 -5 -6 10 -1 -0.5 0.5 -5 5 p, Position Factor q, Shape Factor July 2003 Chuck DiMarzio, Northeastern University

Phase Description of Aberrations v y Image z Object Entrance Pupil Exit Pupil 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 2003 Chuck DiMarzio, Northeastern University

Coordinates for Phase Analysis v v y Solid Line is phase of a spherical wave toward the image point. Dotted line is actual phase. Our goal is to find D(r,f,h). D z phase v y 2a ra u h 0<r<1 x July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Aberration Terms Odd Terms involve tilt, not considered here. July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University 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 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Fourth Order (1) r2 is focus: depends on h2 and h2cosf Spherical Aberration Astigmatism and Field Curvature S Sagittal Plane Tangential Plane T Sample Images At T At S July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Fourth Order (2) r2cosf is Tilt: Depends on h3 Coma y Object v Pincushion Distortion Barrel Distortion x u July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Example: Mirrors By Fermat’s Principle, r1+r2 = constant v r1 r2 z Result is an Ellipse with these foci. One focus at infinity requires a parabola Foci co-located requires a sphere. July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Mirrors for Focussing v, cm. -0.1 -0.08 -0.06 -0.04 -0.02 -0.05 0.05 0.1 Ellipse Parabola Sphere s=30 cm, s’=6cm Note: These Mirrors have a very large NA to illustrate the errors. In most mirrors, the errors could not be seen on this scale. z, cm. July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Numerical Example July 2003 Chuck DiMarzio, Northeastern University

Optical Design Process July 2003 Chuck DiMarzio, Northeastern University

Ray Tracing Fundamentals July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Ray Tracing (1) July 2003 Chuck DiMarzio, Northeastern University

Chuck DiMarzio, Northeastern University Ray Tracing (2) July 2003 Chuck DiMarzio, Northeastern University

If One Element Doesn’t Work... Add Another Lens “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 2003 Chuck DiMarzio, Northeastern University

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 2003 Chuck DiMarzio, Northeastern University