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ECE-1466 Modern Optics Course Notes Part 2 Prof. Charles A. DiMarzio Northeastern University Spring 2002 March 02002 Chuck DiMarzio, Northeastern University 10100-2-1 Lens Equation as Mapping f = 10 cm. 50 March 02002 30 20 s', Image Dist., cm. • 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 40 10 0 -10 -20 -30 -40 -50 -60 -40 L4’ Chuck DiMarzio, Northeastern University -20 0 20 s, Object Dist., cm. L1 L2 L3 40 60 L4 10100-2-2 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,s) – to object space (x’,y’,s’) March 02002 B Chuck DiMarzio, Northeastern University H V V’ H’ B’ 10100-2-3 An Example; 10X Objective F F’ F’ F A’ A • s= 16 mm • s’=160 mm (A common standard) March 02002 Chuck DiMarzio, Northeastern University 10100-2-4 The Simple Magnifier F A’ March 02002 A F’ Chuck DiMarzio, Northeastern University 10100-2-5 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 ? March 02002 Chuck DiMarzio, Northeastern University 10100-2-6 Where Are We Going? • Geometric Optics – Reflection – Refraction • The Thin Lens – Multiple Surfaces – (From Matrix Optics) • Principal Planes • Effective Thin Lens – Stops • Field • Aperture – Aberrations March 02002 Ending with a word about ray tracing and optical design. Chuck DiMarzio, Northeastern University 10100-2-7 Microscope F’ F F’ F A’ A • Two-Step Magnification – Objective Makes a Real Image – Eyepiece Used as a Simple Magnifier March 02002 Chuck DiMarzio, Northeastern University 10100-2-8 Microscope Objective F F’ F’ F A’ A March 02002 Chuck DiMarzio, Northeastern University 10100-2-9 Microscope Eyepiece F F’ A2 A A2’ March 02002 F’ F Chuck DiMarzio, Northeastern University 10100-2-10 Microscope Effective Lens H H’ 192 mm Barrel Length = 160 mm FA f2=16mm f1=16mm D 19.2 mm Effective Lens: f = -1.6 mm H’ H A F’ D’ 19.2 mm F’ F March 02002 Chuck DiMarzio, Northeastern University 10100-2-11 Microscope Effective Lens March 02002 Chuck DiMarzio, Northeastern University 10100-2-12 Where Are We Going? • Geometric Optics – Reflection – Refraction • The Thin Lens – Multiple Surfaces – (From Matrix Optics) • Principal Planes • Effective Thin Lens – Stops • Field • Aperture – Aberrations March 02002 Ending with a word about ray tracing and optical design. Chuck DiMarzio, Northeastern University 10100-2-13 Stops, Pupils, and Windows (1) • Intuitive Description – Pupil Limits Amount of Light Collected – Window Limits What Can Be Seen Window March 02002 Chuck DiMarzio, Northeastern University Pupil 10100-2-14 Stops, Pupils and Windows (2) Images in Object Space Entrance Pupil Limits Cone of Rays from Object Entrance Window Limits Cone of Rays From Entrance Pupil March 02002 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 Chuck DiMarzio, Northeastern University Images in Image Space Exit Pupil Limits Cone of Rays from Image Exit Window Limits Cone of Rays From Exit Pupil 10100-2-15 Finding the Entrance Pupil • Find all apertures in object space L4’ is L4 seen through L1-L3 L1 L2 L3 L4 • Entrance Pupil Subtends Smallest Angle from Object L3’ L4’ L1 L2’ L3’ is L3 seen through L1-L2 March 02002 Chuck DiMarzio, Northeastern University 10100-2-16 Finding the Entrance Window • Entrance Window Subtends Smallest Angle from Entrance Pupil L3’ L4’ March 02002 L1 L2’ • 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 Chuck DiMarzio, Northeastern University 10100-2-17 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 March 02002 Chuck DiMarzio, Northeastern University 10100-2-18 Microscope Field Stop F F’ Entrance Window Field Stop = Exit Window March 02002 Chuck DiMarzio, Northeastern University 10100-2-19 f-Number & Numerical Aperture Numerical Aperture f-Number f q A F’ A’ F D is Lens Diameter 5 f#, f-number 4 3 2 1 0 0 0.2 0.4 0.6 NA, Numerical Aperture March 02002 0.8 1 Chuck DiMarzio, Northeastern University 10100-2-20 Importance of Aperture • ``Fast’’ System – – – – Low f-number, High NA (NA1, 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 March 02002 Chuck DiMarzio, Northeastern University 10100-2-21 Field of View Film= Exit Window March 02002 Chuck DiMarzio, Northeastern University 10100-2-22 Chief Ray Aperture Stop Exit Pupil Field Stop • Chief Ray passes through the center of every pupil March 02002 Chuck DiMarzio, Northeastern University 10100-2-23 Hints on Designing A Scanner • Place the mirrors at pupils March 02002 Chuck DiMarzio, Northeastern University Put Mirrors Here 10100-2-24 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 March 02002 Chuck DiMarzio, Northeastern University 10100-2-25 Examples of Aberrations (1) 1 Paraxial Imaging 0.5 0 -0.5 -1 -10 m4061_3 March 02002 -5 0 5 10 Chuck DiMarzio, Northeastern University 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). 10100-2-26 Example of Aberrations (2) 0.2 D z(h=1.0) Longitudinal Aberration = D z D z(h=0.6) 0.15 0.1 0.05 Transverse Aberration =D x 0 -0.05 Where Exactly is the image? -0.1 -0.15 2D x(h=1.0) m4061_3 -0.2 8.5 March 02002 9 9.5 10 10.5 Chuck DiMarzio, Northeastern University What is its diameter? 10100-2-27 Spherical Aberrations Beam Size, m -2 5 q, Shape Factor q R2 + R1 R2 R1 s=1m, s’=4cm 10 n=1.5 0 -5 -1 10 s ' s p s '+ s -0.5 0 p, Position Factor March 02002 n=2.4 n=4 0.5 10 10 -3 n=2.4 -4 -5 1 -6 10 -5 n=1.5 n=4 DL at 10 mm DL at 1.06 mm 500 nm Chuck DiMarzio, Northeastern University 0 5 q, Shape Factor 10100-2-28 Ray Tracing Fundamentals March 02002 Chuck DiMarzio, Northeastern University 10100-2-29 Ray Tracing (1) March 02002 Chuck DiMarzio, Northeastern University 10100-2-30 Ray Tracing (2) March 02002 Chuck DiMarzio, Northeastern University 10100-2-31 If One Element Doesn’t Work... “Let George Do It” Add Another Lens Different Index? Smaller angles with higher index. Thus germanium is better than ZnSe in IR. Not much hope in the visible. March 02002 Aspherics Chuck DiMarzio, Northeastern University 10100-2-32 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 March 02002 Chuck DiMarzio, Northeastern University 10100-2-33