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	     CS 448 - Camera designs and features, April 16, 2002

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		       *** Quick review of perspective ***

Common assumptions:
	1.  Light leaving an object travels in straight lines
	2.  These lines converge to a point (more or less) at the eye
		o both can be verified from simple observation
		o known by ancients

"Natural perspective":
	3a. More distant objects subtend smaller visual angles
		-> drawing from Euclid (3c BC), in Kemp, fig 31, p. 27

"Linear perspective":
	3b. A perspective image is formed by the intersection of these
	    lines with a "picture plane" (the surface of the painting)
		-> drawing from Piero (1474), Kemp, fig. 32, p. 28

A few exercises in perspective:
	1. How many vanishing points can there be in a perspective drawing?
		o an infinite number, one per direction of lines in the scene

	2. Does a pair of lines parallel to the picture plane converge?
		o No.
		o Consider buildings seen from across the street in wide-angle.
		o Recall difference between projection onto plane
		versus visual angle when viewed.

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		      *** Perspective in photography ***

Viewpoint versus field of view:
	o definition parts #1 and #2 say nothing about the lens;
	  for a given viewpoint, all lenses observe the same lines of sight;
	  lenses only narrow the field of view; we'll come back to #3 shortly
	o zooming versus dollying
		-> old man, Hedgecoe, p. 105
	o extreme wide-angle versus extreme telephoto
		-> compression in telephoto shots, postcard of MemChu and hills
		-> workers on Golden Gate Bridge, Peterson, p. 57

Perspective, lenses, and apertures:
	o a lens actually performs a 3D perspective transform, not just 2D
		-> see link (below) to my drawing
	o Where is the center-of-projection in a lens?
		- for a thin lens: at the optical center
		- for a thick lens: at the first principle point,
		  equal to the first nodal point for a lens in air
			-> Hecht, p. 212
	o aperture stop
		- ideally, placed on first principle plane
		- in practice, placed immediately in front or behind lens,
		  or somewhere in the middle for a complicated lens system
	o telecentric stops 
		- located at front (object) or back (image) focal point
		- object: no change in magnification with changes in focus
		- image: orthographic view of the world
			-> Kingslake, Optical System Design, p. 88

Click here to see my drawing of the 3D perspective transform. It also includes a geometric demonstration of why depth of field rises as the square of the viewing distance. I gave this formula in class (see later in the notes), but I didn't have time to back it up by covering the remaining parts of this drawing.

The view camera:
		-> general layout, Ansel Adams, p. 30
	o rotating the back parallel to a scene plane ("swing back")
		= eliminates a vanishing point
		= oblique projection
			-> Adams, p. 144
		o we can replace this with a perspective warp after-the-fact

	o sliding the back parallel to the front ("rising front")
		= off-axis projection
			-> Adams, p. 143
		o we can replace this with a larger field of view,
		  but we sacriface sensor resolution

	o tilting the lens relative to the back rotates the plane of focus
		o Scheimpflug condition: back, lens, and focus planes intersect
			-> see drawing, proof requires applying Snell's law
			-> Adams, fig. 10-10, p. 153
		o e.g. to keep ground plane in focus
			-> Adams, p. 152 and fig. 10-9, p. 153
		o or a page of text
			-> London, p. 310
		o we *can't* replace this adjustment with post-processing!

	o tilting the lens or sliding the back also causes vignetting,
	  because light falling on the sensor drops off away from its center
		- apparent area of aperture drops as cos(theta),
		- illumination on an oblique surface drops as cos(theta),
		- distance to that surface increases as cos(theta) and
		- light drops as distance^2,
		- so light drops as cos^4(theta)

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		     *** Other components of a camera ***

Depth of field (mostly already covered by Steve):
	o depth of field = far limit - near limit =
		= (2 N C U^2) / F^2 where: (Goldberg, p. 10)
			N = f-number of aperture
			C = allowable size of circle of confusion
			U = distance to scene = focus setting
			F = focal length of lens, so
		- d.o.f. increases with smaller aperture, i.e. larger f-number 
			-> Adams, p. 49
		- d.o.f. increases as square of distance to scene
		- d.o.f. decreases as square of focal length of lens

Viewfinder:
	o 35mm format (24mm x 36mm)
		- separate viewfinder
			-> Ansel Adams, p. 12-13
		- single-lens reflex (SLR)
			-> mirror and pentaprism, Goldberg, p. 137
	o medium format (2 1/4 x 2 1/4 inch)
		- twin lens reflex
			-> Adams, p. 22-23
		- single lens reflex
			-> Adams, p. 24-25
	o large format (4 x 5 inch, 5 x 7, 8 x 10, 11 x 14)
		- ground glass screen
			-> Adams, p. 30-31, i.e. a view camera
Focusing aids:
	o split wedge
		- two prisms
			-> Goldberg, p. 12
		- gather light from two regions in lens
			-> Goldberg, p. 18
		- If image is well focused, the two images coincide, else not
			-> Goldberg, p. 14-15

Autofocus systems: (from Goldberg)
	o active methods
		- time of flight using ultrasonic chirp, or
		- triangulation using narrow beam of infrared light
		- both fail at long distances, dark or reflective objects, etc.
	o passive methods
		- these methods require a reasonably bright scene

		- two-view methods (for non-SLR cameras) compares 1D images
		  from two viewpoints using 1D CCD strip, looks for match
			-> Goldberg, p. 33

		- contrast method compares contrast of images at three depths,
		  if in focus, image will have high contrast, else not
			-> Goldberg, p. 36
			-> Canon EOS D30?

		- phase methods compares two parts of lens at the sensor plane,
		  if in focus, entire exit pupil sees a uniform color, else not
		- assumes object has diffuse BRDF

	o use depth info to drive zoom lens, to keep object fixed size in image
		(Goldberg, p. 47)
	o rubber focus: vary focus, hoping that sharp edges will dominate blurs
		(Goldberg, p. 50)
		- related to conventional tomography

Exposure metering: (Goldberg, p. 55-60)
	o zonal systems
		- e.g. spot versus area

	o exposure systems expect (and force) a gray average
		- fails on snow or coal bins

	o special algorithms
		- recognizing and metering for faces
		- detecting backlit scenes

Shutters:
	o leaf shutter
			-> Adams, p. 82
		- speeds down to 1/500 second
		- center of lens (not image!) gets light for longer than edges
	o focal-plane shutter
			-> Adams, p. 83, or Goldberg, p. 70
			-> My Canon has vertical-travel focal-plane shutter
		- capable of faster speeds, but
		- distorts fast-moving objects
			-> Lartigue, Grand Prix auto race, in Adams, p. 85
	o rotary shutters for movie cameras (Goldberg, p. 86)
		- Arriflex had a two-segment mirror

	o synchronization with (electronic) flash
		- electronic flash is brief, 1/500 to 1/50,000 sec
		- if focal-plane shutter, must be fully open during flash,
		  which typically limits speed to 1/90 sec (p. 86)

Miscellaneous notes on camera technology:
	o motors
		- Canon ultrasonic motors
			-> Goldberg, p. 216
	o batteries and energy management
		- Q. What takes the most power?  A. Flash, by 3x
			-> Goldberg, p. 224

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			     *** Sources cited ***

Perspective:

	Martin Kemp,
	The Science of Art,
	Yale University Press, 1990.

	Allison Cole,
	Perspective,
	Dorling Kindersley, 1992.

	Leonardo Da Vinci,
	Leonardo on Painting,
	translated by M. Kemp and M. Walker,
	Yale University Press, 1989.

Camera technology:

	* Ansel Adams,
	The Camera,
	Little, Brown, and Co., 1976.
	(chapter on view-camera adjustments handed out in class)

	Eugene Hecht,
	Optics, second edition,
	Addison-Wesley, 1987.

	Rudolph Kingslake,
	Optics in Photography,
	SPIE Press, 1992.

	Rudolph Kingslake,
	Optical System Design,
	Academic Press, 1983.

	Norman Goldberg,
	Camera technology: the dark side of the lens,
	Academic Press, 1992.

Photographic technique:

	John Hedgecoe,
	The Photographer's Handbook, third edition,
	Alfred A. Knopf, 1993.

	Barbara London and John Upton,
	Photography, fifth edition,
	HarperCollins, 1994.

	Bryan Peterson,
	Learning to See Creatively,
	Watson-Guptill, 1988.

* handed out in class

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