1. March 02002 Chuck DiMarzio, Northeastern University 10100-2-1 ECE-1466 Modern Optics Course Notes Part 2 Prof. Charles A. DiMarzio Northeastern University Spring 2002

2. March 02002 Chuck DiMarzio, Northeastern University 10100-2-2 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’

3. March 02002 Chuck DiMarzio, Northeastern University 10100-2-3 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’

4. March 02002 Chuck DiMarzio, Northeastern University 10100-2-4 An Example; 10X Objective s= 16 mm s’=160 mm (A common standard) F’ F A’ A F’ F

5. March 02002 Chuck DiMarzio, Northeastern University 10100-2-5 The Simple Magnifier F F’ AA’

6. March 02002 Chuck DiMarzio, Northeastern University 10100-2-6 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 ?

7. March 02002 Chuck DiMarzio, Northeastern University 10100-2-7 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.

8. March 02002 Chuck DiMarzio, Northeastern University 10100-2-8 Microscope Two-Step Magnification –Objective Makes a Real Image –Eyepiece Used as a Simple Magnifier F’ F A’ A F’ F

9. March 02002 Chuck DiMarzio, Northeastern University 10100-2-9 Microscope Objective F’ F A’ A F’ F

10. March 02002 Chuck DiMarzio, Northeastern University 10100-2-10 Microscope Eyepiece F’ F A2A2 A F A2’A2’

11. March 02002 Chuck DiMarzio, Northeastern University 10100-2-11 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

12. March 02002 Chuck DiMarzio, Northeastern University 10100-2-12 Microscope Effective Lens

13. March 02002 Chuck DiMarzio, Northeastern University 10100-2-13 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.

14. March 02002 Chuck DiMarzio, Northeastern University 10100-2-14 Stops, Pupils, and Windows (1) Intuitive Description –Pupil Limits Amount of Light Collected –Window Limits What Can Be Seen Pupil Window

15. March 02002 Chuck DiMarzio, Northeastern University 10100-2-15 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

16. March 02002 Chuck DiMarzio, Northeastern University 10100-2-16 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’

17. March 02002 Chuck DiMarzio, Northeastern University 10100-2-17 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’

18. March 02002 Chuck DiMarzio, Northeastern University 10100-2-18 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

19. March 02002 Chuck DiMarzio, Northeastern University 10100-2-19 Microscope Field Stop F’ F Field Stop = Exit Window Entrance Window

20. March 02002 Chuck DiMarzio, Northeastern University 10100-2-20 f-Number & Numerical Aperture F’ F A A’ f D is Lens Diameter  00.20.40.60.81 0 1 2 3 4 5 NA, Numerical Aperture f#, f-number f-Number Numerical Aperture

21. March 02002 Chuck DiMarzio, Northeastern University 10100-2-21 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

22. March 02002 Chuck DiMarzio, Northeastern University 10100-2-22 Field of View Film= Exit Window

23. March 02002 Chuck DiMarzio, Northeastern University 10100-2-23 Chief Ray Aperture Stop Field Stop Exit Pupil Chief Ray passes through the center of every pupil

24. March 02002 Chuck DiMarzio, Northeastern University 10100-2-24 Hints on Designing A Scanner Place the mirrors at pupils Put Mirrors Here

25. March 02002 Chuck DiMarzio, Northeastern University 10100-2-25 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

26. March 02002 Chuck DiMarzio, Northeastern University 10100-2-26 Examples of Aberrations (1) -10-50510 -0.5 0 0.5 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

27. March 02002 Chuck DiMarzio, Northeastern University 10100-2-27 8.599.51010.5 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 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?

28. March 02002 Chuck DiMarzio, Northeastern University 10100-2-28 Spherical Aberrations -505 10 -6 10 -5 10 -4 10 -3 10 -2 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 1 -0.500.5 -5 0 5 p, Position Factor q, Shape Factor n=4 n=2.4 n=1.5

29. March 02002 Chuck DiMarzio, Northeastern University 10100-2-29 Ray Tracing Fundamentals

30. March 02002 Chuck DiMarzio, Northeastern University 10100-2-30 Ray Tracing (1)

31. March 02002 Chuck DiMarzio, Northeastern University 10100-2-31 Ray Tracing (2)

32. March 02002 Chuck DiMarzio, Northeastern University 10100-2-32 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.

33. March 02002 Chuck DiMarzio, Northeastern University 10100-2-33 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