1. Basic Principles of Imaging and Lenses

2. Light

3. Electromagnetic
Radiation
Light
Photons

4. These three are the same…
Light
pure energy
Electromagnetic Waves
energy-carrying waves emitted by vibrating electrons
Photons
particles of light

6. EM Radiation Travels as a Wave
c = 3 x 108 m/s

8. EM Radiation Carries Energy
• Quantum mechanics tells us that for photons E = hf
where E is energy and h is Planck’s constant.
• But f = c/l
• Putting these equations together, we see that
E = hc/l

9. Electromagnetic Wave Velocity
The speed of light is the same for all seven forms of light.
It is 300,000,000 meters per second or 186,000 miles per second.

10. The Electromagnetic Spectrum
Radio Waves - communication
Microwaves - used to cook
Infrared - “heat waves”
Visible Light - detected by your eyes
Ultraviolet - causes sunburns
X-rays - penetrates tissue
Gamma Rays - most energetic

12. The Multi-Wavelength SunUV
Visible
X-Ray
Composite
Radio
Infrared

13. EM Spectrum Relative Sizes

14. The Visible Spectrum
Light waves extend in wavelength from about 400 to 700 nanometers.

15. Transparent Materials
Transparent - the term applied to materials through which light can pass in straight lines.

16. Opaque Materials
Opaque - the term applied to materials that absorb light.

17. Are clouds transparent or opaque to visible light?
Answer: opaque
Are clouds transparent or opaque to ultraviolet light?
Answer: almost transparent

18. Special Things About a Light Wave
• It does not need a medium through which to travel
• It travels with its highest velocity in a vacuum
• Its highest velocity is the speed of light, c,
equal to 300,000 km/sec
• The frequency (or wavelength) of the wave determines
whether we call it radio, infrared, visible, ultraviolet,
X-ray or gamma-ray.

19. A Brief History of Images
1544
Camera Obscura, Gemma Frisius, 1558

20. Camera Obscura
"When images of illuminated objects ... penetrate through a small hole into a very dark room ... you will see [on the opposite wall] these objects in their proper form and color, reduced in size ... in a reversed position, owing to the intersection of the rays". Da Vinci
(Russell Naughton)
Slide credit: David Jacobs

21. A Brief History of Images
1558
1568
Lens Based Camera Obscura, 1568

22. Jetty at Margate England, 1898.
(Jack and Beverly Wilgus)
Slide credit: David Jacobs

23. A Brief History of Images
1558
1568
1837
Still Life, Louis Jaques Mande Daguerre, 1837

24. A Brief History of Images
1558
1568
1840?
Abraham Lincoln?

25. A Brief History of Images
1558
1568
1837
Silicon Image Detector, 1970
1970

26. A Brief History of Images
1558
1568
1837
1970
Digital Cameras
1995

27. A Brief History of Images
1558
1568
1837
1970
Hasselblad HD2-39
1995
2006

28. Geometric Optics and Image Formation
TOPICS TO BE COVERED :
1) Pinhole and Perspective Projection
2) Image Formation using Lenses
3) Lens related issues

29. Pinhole Cameras Pinhole camera - box with a small hole in it
Image is upside down, but not mirrored left-to-right
Question: Why does a mirror reverse left-to-right but not top-to-bottom?
The point to make here is that each point on the image plane sees light from only
one direction, the one that passes through the pinhole.

30. Pinhole and the Perspective Projection
Is an image being formed
on the screen?
YES! But, not a “clear” one.
(x,y)
screen
scene
image plane
effective focal length, f’
optical
axis y x z
pinhole

31. Magnification y z x d f’ optical axis Pinhole d’ planar sceneB d f’
optical
axis z A
Pinhole A’ d’ x
planar scene
image plane B’
From perspective projection:
Magnification:

32. Properties of Projection
Points project to points
Lines project to lines
Planes project to the whole or half image
Angles are not preserved
Degenerate cases
Line through focal point projects to a point.
Plane through focal point projects to line

33. Distant Objects are Smaller
Size is inversely proportional to distance.
Note that B’ and C’ labels should be switched.

34. Parallel Lines Meet Common to draw film plane
in front of the focal point.
Moving the film plane merely
scales the image.

35. Vanishing Points Each set of parallel lines meets at a different point
The vanishing point for this direction
Sets of parallel lines on the same plane lead to collinear vanishing points.
The line is called the horizon for that plane
Good ways to spot faked images
scale and perspective don’t work
vanishing points behave badly
supermarket tabloids are a great source.

37. Model 0: Pinhole Projection

38. The Equation of Pinhole Projection
Cartesian coordinates:
We have, by similar triangles, that (x, y, z) -> (f x/z, f y/z, f)
[multiply by f/z]
Ignore the third coordinate, and get
3D object point  2D image point

39. Model 1: Weak Perspective Projection
Issue
Perspective effects, but not over the scale of individual objects
Collect points into a group at about the same depth, then divide each point by the depth of its group
Advantage: EASY
Disadvantage: WRONG

40. The Equation of Weak Perspective
s is constant for all points.
Parallel lines no longer converge, they remain parallel.
Slide credit: David Jacobs

41. Model 2: Orthographic Projection
Magnification:
When m = 1, we have orthographic projection y
optical
axis z x
image plane
This is possible only when
In other words, the range of scene depths is assumed to be much smaller than the average scene depth.
But, how do we produce non-inverted images?

42. Pros and Cons of These Models
Weak perspective has simpler math.
Accurate when object is small and distant.
Most useful for recognition.
Pinhole perspective much more accurate for scenes.
Used in structure from motion.
When accuracy really matters, we must model the real camera
Use perspective projection with other calibration parameters (e.g., radial lens distortion)
Slide credit: David Jacobs

43. Problems with Pinholes
Pinhole size (aperture) must be “very small” to obtain a clear image.
However, as pinhole size is made smaller, less light is received by image plane.
If pinhole is comparable to wavelength of incoming light, DIFFRACTION
effects blur the image!
Sharpest image is obtained when:
pinhole diameter
Example: If f’ = 50mm,
= 600nm (red),
d = 0.36mm

44. The Reason for Lenses

45. Image Formation using (Thin) Lenses
Lenses are used to avoid problems with pinholes.
Ideal Lens: Same projection as pinhole but gathers more light! i o P P’ f
Gaussian Lens Formula:
f is the focal length of the lens – determines the lens’s ability to bend (refract) light
f different from the effective focal length f’ discussed before!

46. Focus and Defocus
aperture
aperture
diameter
Blur Circle, b d
Gaussian Law:
Blur Circle Diameter :
Depth of Field: Range of object distances over which image is sufficiently well focused,
i.e., range for which blur circle is less than the resolution of the imaging sensor.

47. Problems with Lenses Compound (Thick) Lens Vignetting B A
principal planes A
nodal points
thickness
more light from A than B !
Chromatic Abberation
Radial and Tangential Distortion
ideal
actual
ideal
actual
image plane
Lens has different refractive indices
for different wavelengths.

48. Spherical Aberration
Spherical lenses are the only easy shape to manufacture, but are not correct for perfect focus.

49. Two Lens System
object
final
image
image
plane
intermediate
virtual image
lens 2
lens 1
Rule : Image formed by first lens is the object for the second lens.
Main Rays : Ray passing through focus emerges parallel to optical axis.
Ray through optical center passes un-deviated.
Magnification:
Exercises: What is the combined focal length of the system?
What is the combined focal length if d = 0?

50. Lens systems
A good camera lens may contain 15 elements and cost a many thousand dollars
The best modern lenses may contain aspherical elements

51. Insect Eye We make cameras that act “similar” to the human eye Fly
Mosquito

52. Human Eye The eye has an iris like a camera
Focusing is done by changing shape of lens
Retina contains cones (mostly used) and rods (for low light)
The fovea is small region of high resolution containing mostly cones
Optic nerve: 1 million flexible fibers
Slide credit: David Jacobs

53. Human Eye Rods Intensity only
Essentially night vision and peripheral vision only
Since we are trying to fool the center of field of view of human eye (under well lit conditions) we ignore rods

54. Human Eye
Cones
Three types perceive different portions of the visible light spectrum

55. Human Eye
Because there are only 3 types of cones in human eyes, we only need 3 stimulus values to fool the human eye
Note: Chickens have 4 types of cones

56. Human Eye vs. the Camera
We make cameras that act “similar” to the human eye

57. CCD Cameras
Slide credit: David Jacobs