# 6.098 Digital and Computational Photography Advanced Computational Photography. Bill Freeman Frédo Durand MIT - EECS

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1 6.098 Digital and Computational Photography Advanced Computational Photography Bill Freeman Frédo Durand MIT - EECS

2 Administrivia PSet 1 is out Due Thursday February 23

3 Digital SLR initiation? During Fredo s office hours Friday Feb 17 2:30-4pm in the green-couch area in Stata D4 south I ll have a couple of SLRs, but try to bring one if you can.

4 Overview Lens and viewpoint determine perspective Aperture and shutter speed determine exposure Aperture and other effects determine depth of field Film or sensor record image

5 Reference The slides use illustrations from these books

6 More references

7 Plan Pinhole optics Lenses Exposure

8 7-year old s question Why is there no image on a white piece of paper?

9 It receives light from all directions From Photography, London et al.

10 Pinhole From Photography, London et al.

11 Demo!

12 Focal length f s Film/ sensor pinhole scene

13 Demo!

14 Focal length: pinhole optics What happens when the focal length is doubled? Projected object size is doubled Amount of light gathered is divided by 4 f d 2f s Film/ sensor pinhole scene

15 Questions?

16 Pinhole size? From Photography, London et al.

17 Diffraction limit Optimal size for visible light: sqrt(f)/28 (in millimiters) where f is focal length From Wandell

18 Problem with pinhole? Not enough light! Diffraction limits sharpness

19 Solution: refraction! From Photography, London et al.

20 Lenses gather more light! But need to be focused From Photography, London et al.

21 Thin lens optics Simplification of geometrical optics for wellbehaved lenses All parallel rays converge to one point on a plane located at the focal length f f All rays going through the center are not deviated Hence same perspective as pinhole

22 Demo!

23 How to trace rays Start by rays through the center

24 How to trace rays Start by rays through the center Choose focal length, trace parallels f

25 How to trace rays Start by rays through the center Choose focal length, trace parallels You get the focus plane for a given scene plane All rays coming from points on a plane parallel to the lens are focused on another plane parallel to the lens f

26 Focusing To focus closer than infinity Move the sensor/film further than the focal length f

27 Thin lens formula D f D

28 Thin lens formula Similar triangles everywhere! D f D

29 Thin lens formula Similar triangles everywhere! y /y = D /D y D f D y

30 Thin lens formula Similar triangles everywhere! D D f y y /y = D /D y /y = (D -f)/d y

31 Thin lens formula = 1 D D f D f D

32 Minimum focusing distance By symmetry, an object at the focal length requires the film to be at infinity. film Rays from infinity Rays from object at f

33 Extensions tubes Allow us to put sensor/film farther focus closer

34 Field of view & focusing What happens to the field of view when one focuses closer? It's reduced film focused close film focused at infinity

35 Questions? html

36 Focal length in practice 24mm 50mm 135mm

37 Perspective vs. viewpoint Telephoto makes it easier to select background (a small change in viewpoint is a big change in background.

38 Perspective vs. viewpoint Martin Scorcese, Good Fellas Moves camera as you zoom in Better known as the Hitchcock Vertigo effect

39 Perspective vs. viewpoint Portrait: distortion with wide angle Why? Wide angle Standard Telephoto

40 Focal length & sensor What happens when the film is half the size? Application: Real film is 36x24mm On the 20D, the sensor is 22.5 x 15.0 mm Conversion factor on the 20D? On the SD500, it is 1/1.8 " (7.18 x 5.32 mm) What is the mm zoom on the SD500? f d ½s Film/ sensor pinhole scene

41 Sensor size Similar to cropping source: canon red book

42

43 Recap Pinhole is the simplest model of image formation Lenses gather more light But get only one plane focused Focus by moving sensor/film Cannot focus infinitely close Focal length determines field of view From wide angle to telephoto Depends on sensor size More in the lens lecture

44 Questions?

45 Exposure Get the right amount of light to sensor/film Two main parameters: Shutter speed Aperture (area of lens)

46 Shutter speed Controls how long the film/sensor is exposed Pretty much linear effect on exposure Usually in fraction of a second: 1/30, 1/60, 1/125, 1/250, 1/500 Get the pattern? On a normal lens, normal humans can hand-hold down to 1/60 In general, the rule of thumb says that the limit is the inverse of focal length, e.g. 1/500 for a 500mm

47 Main effect of shutter speed Motion blur From Photography, London et al.

48 Effect of shutter speed Freezing motion Walking people Running people Car Fast train 1/125 1/250 1/500 1/1000

49 Shutter Various technologies Goal: achieve uniform exposure across image From Camera Technology, Goldberg

50

51 Flash synch speed? Fastest shutter speed for which the shutter opens completely at some instant. For faster speeds, it opens and closes at the same time and exposes a slit. Modern high-speed flash synch uses multiple flash bursts From Photography, London et al.

52 Your best friend Use a tripod! It will always enhance sharpness Avoid camera shake More about shake & stabilization in lens lecture

53 Aperture Diameter of the lens opening (controlled by diaphragm) Expressed as a fraction of focal length, in f-number f/2.0 on a 50mm means that the aperture is 25mm f/2.0 on a 100mm means that the aperture is 50mm Disconcerting: small f number = big aperture What happens to the area of the aperture when going from f/2.0 to f/4.0? Typical f numbers are f/2.0, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, f/32 See the pattern?

54 Aperture & physical lens size On telephoto, the lens size is directly dictated by the max (that is min) f number Other lenses, not always clear The aperture can be internal or not Zoom lenses usually have a variable maximal aperture Why?

55 Main effect of aperture Depth of field From Photography, London et al.

56 Depth of field sensor lens Point in focus Object with texture

57 Depth of field We allow for some tolerance Depth of field sensor Depth of Max focus acceptable circle of confusion sensor lens lens Point in focus Object with texture Point in focus Object with texture

58

59 Depth of field What happens when we close the aperture by two stop? Aperture diameter is divided by two Depth of field is doubled Diaphragm Point in focus sensor lens Object with texture

60 Depth of field From Photography, London et al.

61 Depth of field & focusing distance What happens when we divide focusing distance by two? Similar triangles => divided by two as well Half depth of field Half depth of field Point in focus sensor lens

62 Depth of field & focusing distance What happens when we divide focusing distance by two? Similar triangles => divided by two as well From Photography, London et al.

63 SLR viewfinder & aperture By default, an SLR always shows you the biggest aperture Brighter image Shallow depth of field help judge focus Depth of field preview button: Stops down to the aperture you have chosen Darker image Larger depth of field

64 Questions?

65 Questions?

66 Exposure Two main parameters: Aperture (in f stop) Shutter speed (in fraction of a second) Reciprocity The same exposure is obtained wit an exposure twice as long and an aperture area half as big Hence square root of two progression of f stops vs. power of two progression of shutter speed Reciprocity can fail for very long exposures From Photography, London et al.

67 Reciprocity Assume we know how much light we need We have the choice of an infinity of shutter speed/aperture pairs What will guide our choice of a shutter speed? Freeze motion vs. motion blur, camera shake What will guide our choice of an aperture? Depth of field, diffraction limit Often we must compromise Open more to enable faster speed (but shallow DoF)

68 From Photography, London et al.

69 From Photography, London et al.

70 From Photography, London et al.

71 Questions?

72 Metering Photosensitive sensors measure scene luminance Usually TTL (through the lens) Simple version: center-weighted average Assumption? Failure cases? Usually assumes that a scene is 18% gray Problem with dark and bright scenes

73 From Photography, London et al.

74 Metering Centered average Choice on Nikon Spot Smart metering Nikon 3D matrix Canon evaluative Incident Measure incoming light Next slide From the luminous landscape

75 Nikon 3D Color Matrix Learning from database of 30,000 photos Multiple captors (segments) Exposure depends on Brightness from each segments Color Contrast Distance Focus (where is the subject)

76 Exposure & metering The camera metering system measures how bright the scene is In Aperture priority mode, the photographer sets the aperture, the camera sets the shutter speed In Shutter-speed priority mode, the photographers sets the shutter speed and the camera deduces the aperture In both cases, reciprocity is exploited In Program mode, the camera decides both exposure and shutter speed (middle value more or less) In Manual, the user decides everything (but can get feedback)

77 Pros and cons of various modes Aperture priority (My favorite, I use it 90% of the time) Direct depth of field control Cons: can require impossible shutter speed (e.g. with f/1.4 for a bright scene) Shutter speed priority Direct motion blur control Cons: can require impossible aperture (e.g. when requesting a 1/1000 speed for a dark scene) Note that aperture is somewhat more restricted Program Almost no control, but no need for neurons Manual Full control, but takes more time and thinking

78 Recap: Metering Measure scene brightness Some advanced modes that take multiple sources of information Still an open problem

79 Questions?

80 Sensitivity (ISO) Third variable for exposure Linear effect (200 ISO needs half the light as 100 ISO) Film photography: trade sensitivity for grain Digital photography: trade sensitivity for noise From dpreview.com

81 Questions?

82 From Photography, London et al.

83 From Photography, London et al.

84 From Photography, London et al.

85 From Photography, London et al.

86 From Photography, London et al.

87 Useful for landscape to get depth of field from foreground to infinity Ansel Adams

88 From Photography, London et al.

89 From Photography, London et al.

90 Tilt-shift lens 35mm SLR version

91 Next time: color

92 Appendix

93 Equation of projection From Ponce & Forsyth

94 Equation of projection Cartesian coordinates: We have, by similar triangles, that (x, y, z) (f x/z, f y/z, -f) Ignore the third coordinate, and get (x,y,z) (f x/z, f y/z)

95 Effect of projection Points go to points Lines go to lines Planes go to a half plane Parallel lines go to converging lines Polygons go to polygons Degenerate cases: Line through the pinhole go to points Planes through the pinhole go to a line Parallels parallel to the image plane stay parallel Planes parallel to the image plane goes to full planes

96 Next time: color

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