1. MIT 2.71/2.710 09/22/04 wk3-b-1 Imaging Instruments (part I) Principal Planes and Focal Lengths (Effective, Back, Front) Multi-element systems Pupils & Windows; Apertures & Stops the Numerical Aperture and f/# Single-Lens Camera Human Eye Reflective optics Scheimpflug condition

2. MIT 2.71/2.710 09/22/04 wk3-b-2 Focal Lengths & Principal Planes generalized optical system (e.g. thick lens, multi-element system) EFL: Effective Focal Length (or simply “focal length”) FFL: Front Focal Length BFL: Back Focal Length FP: Focal Point/Plane PS: Principal Surface/Plane

3. MIT 2.71/2.710 09/22/04 wk3-b-3 The significance of principal planes /1 thin lens of the same power located at the 2 nd PS for rays passing through 2 nd FP optical system

4. MIT 2.71/2.710 09/22/04 wk3-b-4 The significance of principal planes /2 thin lens of the same power located at the 1 st PS for rays passing through 1 st FP optical system

5. MIT 2.71/2.710 09/22/04 wk3-b-5 Reminder: imaging condition (thin lens) object image chief ray

6. MIT 2.71/2.710 09/22/04 wk3-b-6 The significance of principal planes /3 object multi-element optical system image? magnification?

7. MIT 2.71/2.710 09/22/04 wk3-b-7 The significance of principal planes /4 object multi-element optical system lateral hold, where f= (EFL)

8. MIT 2.71/2.710 09/22/04 wk3-b-8 Numerical Aperture medium of refr. index n half-angle subtended by the imaging system from an axial object Numerical Aperture Speed (f/#)=1/2(NA) pronounced f-number, e.g. f/8 means (f/#)=8. Aperture stop the physical element which limits the angle of acceptance of the imaging system

9. MIT 2.71/2.710 09/22/04 wk3-b-9 Aperture / NA: physical meaning medium of refr. index n The Numerical Aperture limits the optical energy that can flow through the system Later we will also learn that the NA also defines the resolution (or resolving power) of the optical system

10. MIT 2.71/2.710 09/22/04 wk3-b-10 Entrance & exit pupils multi-element optical system image through preceding elements image through succeeding elements entrance pupil exit pupil

11. MIT 2.71/2.710 09/22/04 wk3-b-11 The Chief Ray Starts from off-axis object, Goes through the center of the Aperture

12. MIT 2.71/2.710 09/22/04 wk3-b-12 The Field Stop Limits the angular acceptance of Chief Rays

13. MIT 2.71/2.710 09/22/04 wk3-b-13 Entrance & Exit Windows multi-element optical system image through preceding elements image through succeeding elements entrance window exit window

14. MIT 2.71/2.710 09/22/04 wk3-b-14 All together entrance window exit window entrance pupil exit pupil field stop aperture stop

15. MIT 2.71/2.710 09/22/04 wk3-b-15 All together entrance window exit window entrance pupil exit pupil field stop aperture stop

16. MIT 2.71/2.710 09/22/04 wk3-b-16 Example: single-lens camera object plan e image plan e size of film or digital detector array

17. MIT 2.71/2.710 09/22/04 wk3-b-17 Example: single-lens camera object plan e Aperture Stop & Entrance Pupil image plan e

18. MIT 2.71/2.710 09/22/04 wk3-b-18 Example: single-lens camera object plan e image plan e Exit Pupil (virtual) Aperture Stop & Entrance Pupil

19. MIT 2.71/2.710 09/22/04 wk3-b-19 Example: single-lens camera chief ray Field Stop & Exit Window object plan e

20. MIT 2.71/2.710 09/22/04 wk3-b-20 Example: single-lens camera Entrance window Field Stop & Exit Window chief ray

21. MIT 2.71/2.710 09/22/04 wk3-b-21 Example: single-lens camera Entrance window Field Stop & Exit Window Exit Pupil (virtual) Aperture Stop & Entrance Pupil

22. MIT 2.71/2.710 09/22/04 wk3-b-22 Example: single-lens camera Entrance window Field Stop & Exit Window Exit Pupil (virtual) Aperture Stop & Entrance Pupil

23. MIT 2.71/2.710 09/22/04 wk3-b-23 Example: single-lens camera Aperture Stop vignetting

24. MIT 2.71/2.710 09/22/04 wk3-b-24 Imaging systems in nature “Physical” architecture matches survival requirements and processing capabilities Human eye: evolved for – adaptivity (e.g. brightness adjustment) – transmission efficiency (e.g. mexican hat response) – bypass structural defects (e.g. blind spot) – other functional requirements (e.g. stereo vision) Insect eye: similar, but muchsimpler processor (human brain = ~10 11 neurons; insect brain = ~10 4 neurons)

25. MIT 2.71/2.710 09/22/04 wk3-b-25 Anatomy of the human eye Images removed due to copyright concerns W. J. Smith, “Modern Optical Engineering,” McGraw-Hill

26. MIT 2.71/2.710 09/22/04 wk3-b-26 Images removed due to copyright concerns Eye schematic with typical dimensions Photographic camera concerns Images removed due to copyright concerns

27. MIT 2.71/2.710 09/22/04 wk3-b-27 Accommodation (focusing) Remote object (unaccommodated eye) Proximal object (accommodated eye) Comfortable viewing up to 2.5cm away from the cornea

28. MIT 2.71/2.710 09/22/04 wk3-b-28 Eye defects and their correction Images removed due to copyright concerns from Fundamentals of Optics by F. Jenkins & H. White

29. MIT 2.71/2.710 09/22/04 wk3-b-29 The eye’s “digital camera”: retina Images removed due to copyright concerns http://www.mdsupport.org

30. MIT 2.71/2.710 09/22/04 wk3-b-30 The eye’s “digital camera”: retina Images removed due to copyright concerns rods: intensity (grayscale) cones: color (R/G/B) http://www.phys.ufl.edu/~avery/

31. MIT 2.71/2.710 09/22/04 wk3-b-31 Retina vs your digital camera Retina: variant sampling rate Digital camera: fixed sampling rate (grossly exaggerated; in actual retina transition from dense to sparse sampling is much smoother)

32. MIT 2.71/2.710 09/22/04 wk3-b-32 Retina vs your digital camera Retina: blind spot not noticeable Digital camera: bad pixels destructive

33. MIT 2.71/2.710 09/22/04 wk3-b-33 Retina vs your digital camera Retinal imageCCD image http://www.klab.caltech.edu/~itti/ Images removed due to copyright concerns

34. MIT 2.71/2.710 09/22/04 wk3-b-34 Spatial response of the retina – lateral connections http://webvision.med.utah.edu/ Images removed due to copyright concerns

35. MIT 2.71/2.710 09/22/04 wk3-b-35 http://www.phys.ufl.edu/~avery/ Spatial response of the retina – lateral connections

36. MIT 2.71/2.710 09/22/04 wk3-b-36 Explanation of the “flipping dot” illusion: the Mexican hat response Spatial response of the retina – lateral connections http://faculty.washington.edu/wcalvin Images removed due to copyright concerns

37. MIT 2.71/2.710 09/22/04 wk3-b-37 Temporal response: after-images http://dragon.uml.edu/psych/

38. MIT 2.71/2.710 09/22/04 wk3-b-38 Seeing 3D http://www.ccom.unh.edu/vislab/VisCourse Images removed due to copyright concerns

39. MIT 2.71/2.710 09/22/04 wk3-b-39 VIEWING POINT

40. MIT 2.71/2.710 09/22/04 wk3-b-40 The compound eye Images removed due to copyright concerns

41. MIT 2.71/2.710 09/22/04 wk3-b-41 Elements of the compound eye: ommatidia (=little eyes) “image” formation: blurry, but computationally efficient for moving-edge detection Images removed due to copyright concerns

42. MIT 2.71/2.710 09/22/04 wk3-b-42 Reflective Optics Example: imaging by a spherical mirror

43. MIT 2.71/2.710 09/22/04 wk3-b-43 Sign conventions for reflective optics Light travels from left to right before reflection and from right to left after reflection A radius of curvature is positive if the surface is convex towards the left Longitudinal distances before reflectionare positive if pointing to the right; longitudinal distances after reflection are positive if pointing to the left Longitudinal distances are positive if pointing up Ray angles are positive if the ray direction is obtained by rotating the +z axis counterclockwise through an acute angle

44. MIT 2.71/2.710 09/22/04 wk3-b-44 Reflective optics formulae Imaging condition Focal length Magnification

45. MIT 2.71/2.710 09/22/04 wk3-b-45 The Cassegrain telescope

46. MIT 2.71/2.710 09/22/04 wk3-b-46 The Scheimpflug condition The object plane and the image plane intersect at the plane of the lens. OBJECT PLANE OPTICAL AXIS LENS PLANE IMAGE PLANE