March Chuck DiMarzio, Northeastern University ECE-1466 Modern Optics Course Notes Part 2 Prof. Charles A. DiMarzio Northeastern University Spring 2002

March 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 L1L1 L2L2 L3L3 L4L4 L4’L4’

March 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,s) –to object space (x’,y’,s’) H H’ VV’ B B’

March Chuck DiMarzio, Northeastern University An Example; 10X Objective s= 16 mm s’=160 mm (A common standard) F’ F A’ A F’ F

March Chuck DiMarzio, Northeastern University The Simple Magnifier F F’ AA’

March 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#  Means f=10 mm Maximum M m =25 For the Interested Student: What if s>f ?

March Chuck DiMarzio, Northeastern University 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 Ending with a word about ray tracing and optical design.

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

March Chuck DiMarzio, Northeastern University Microscope Objective F’ F A’ A F’ F

March Chuck DiMarzio, Northeastern University Microscope Eyepiece F’ F A2A2 A F A2’A2’

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

March Chuck DiMarzio, Northeastern University Microscope Effective Lens

March Chuck DiMarzio, Northeastern University 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 Ending with a word about ray tracing and optical design.

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

March Chuck DiMarzio, Northeastern University Stops, Pupils and Windows (2) 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 Physical Components Images in Object Space Entrance Pupil Limits Cone of Rays from Object Entrance Window Limits Cone of Rays From Entrance Pupil Images in Image Space Exit Pupil Limits Cone of Rays from Image Exit Window Limits Cone of Rays From Exit Pupil

March Chuck DiMarzio, Northeastern University Finding the Entrance Pupil Find all apertures in object space L1L1 L2L2 L3L3 L4L4 L 4 ’ is L 4 seen through L 1 -L 3 L 3 ’ is L 3 seen through L 1 -L 2 Entrance Pupil Subtends Smallest Angle from Object L1L1 L2’L2’ L4’L4’L3’L3’

March 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 L1L1 L2’L2’ L4’L4’L3’L3’

March Chuck DiMarzio, Northeastern University Microscope Aperture Stop F’ F Aperture Stop =Entrance Pupil Exit 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 Image Analysis in Image Space

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

March Chuck DiMarzio, Northeastern University f-Number & Numerical Aperture F’ F A A’ f D is Lens Diameter  NA, Numerical Aperture f#, f-number f-Number Numerical Aperture

March 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 ( /D) –Propensity for Aberrations (sin  Corrections may require multiple elements –Big Diameter  Big Thickness  Weight, Cost Tight Tolerance over Large Area

March Chuck DiMarzio, Northeastern University Field of View Film= Exit Window

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

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

March Chuck DiMarzio, Northeastern University Aberrations Failure of Paraxial Optics Assumptions –Ray Optics Based On sin(  )=tan(  )=  –Spherical Waves  =  0 +2  x 2 /  Next Level of Complexity –Ray Approach: sin(  )=    –Wave Approach:  =  0 +2  x 2 /  c    A Further Level of Complexity –Ray Tracing

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

March Chuck DiMarzio, Northeastern University Example of Aberrations (2) m4061_3  z(h=0.6)  z(h=1.0) Longitudinal Aberration =  z Transverse Aberration =  x  x(h=1.0) Where Exactly is the image? What is its diameter?

March Chuck DiMarzio, Northeastern University Spherical Aberrations Beam Size, m q, Shape Factor s=1m, s’=4cm DL at 10  m n=2.4n=1.5 n=4 DL at 1.06  m 500 nm p, Position Factor q, Shape Factor n=4 n=2.4 n=1.5

March Chuck DiMarzio, Northeastern University Ray Tracing Fundamentals

March Chuck DiMarzio, Northeastern University Ray Tracing (1)

March Chuck DiMarzio, Northeastern University Ray Tracing (2)

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

March 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