Light, vision, and photography

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  • An electro-magnetic (EM) wave is a signal carrying energy through space/time, with a physical value at each space-time point given by the strength of its electrical and magnetic fields. These fields oscillate perpendicular to each other, and perpendicular to the path of the wave (EM waves are transverse).
  • EM waves travel through a vacuum (no medium)
  • EM waves travel at a fixed speed c = approximately 3 x 10^8 (300 million) meters/second, or 3 x 10^5 (300,000) km/sec, or 186,000 miles/sec (compare to sound at roughly 340.29 meters/sec, or 1116 ft/sec, or 768 mph. Light is nearly a million times faster than sound - nearly instantaneous by comparison. The difference enables us to estimate the remoteness of a lightning flash.)
  • Like periodic sound waves, periodic EM waves are characterized by their:
    • Period: T
    • Frequency: f = 1/T
    • Wavelength: L = c*T = c/f, i.e. c = f*L, f=c/L (higher frequency implies lower wavelength)
    • Amplitude: A
    • Power: proportional to A^2 , where A is the root mean square amplitude, as for sound. But also proportional to frequency!
    • Here is an animation, showing EM wave propagation. Also [1].
  • Like sound waves, EM waves can be analyzed as the sum of sine and cosine waves at different frequencies and amplitudes, using the Fourier theorem
  • Light comprises a frequency range within the EM spectrum in the visible range: 750 - 390 nanometers (billionths of a meter), i.e. frequencies in the range 400 to 790 terahertz (tera = trillion = 10^12), corresponding to colors ROYGBIV (red-orange-yellow-green-blue-indigo-violet)
    • Waves (transverse, longitudinal)(1D, 2D, 3D).
    • Inverse square law: the spread of wave energy is proportional to the square of the distance from the source. If the power (energy per unit time) is constant, then intensity (power per unit area) is inversely proportional to the square of the distance. What this means: a flashlight's intensity at 8 feet is only a quarter its intensity at 4 feet.
    • Reflection: a wave will bounce off a reflective boundary, partially (glass) or fully (mirror).
    • Diffraction: while light shadows appear relatively sharp (compared to sound shadows), a light wave can travel around an obstacle significantly smaller than its wavelength (see periodic waves, below), and will spread after passing through a hole.
    • Refraction: a wave changes direction when the medium changes.
    • Light waves are tranverse traveling electromagnetic waves through space (no medium) in 3D.

Terms for light and optics

  • Watt: unit of power, 1 joule/second
    • a joule is the energy required to exert a force of 1 newton on an object over one linear meter (recall that a Pascale is a unit of pressure: the force of 1 newton spread over 1 sq meter)
    • a newton is the force required to accelerate a kilogram 1 m/s each second
  • Radiant flux: measure of power in EM radiation. The unit of radiant flux is the watt.
  • Luminous flux: measure of visible power of light source, i.e. power that is perceived by the eye (= radiant flux adjusted for wavelength)
  • Lumen: unit of luminous flux, i.e. watts but measuring only what is perceived by the eye (Technical definition: One lumen is defined as the luminous flux of light produced by a light source that emits one candela of luminous intensity over a solid angle of one steradian)
  • Lux: measure of luminous flux per unit area = one lumen per square meter
  • Luminous intensity: measure of power in EM radiation per solid angle unit
  • Candela: unit of luminous intensity (the luminous intensity emitted by an ordinary candle is approximately 1 candela)

Analog (traditional) photography


  • pinhole camera: with an infinitesimal pinhole, everything is always in focus. Problem: no light gets through such a pinhole!
    • pinhole: an infinitesimal hole
    • light path: from every point in the scene reflecting light in all directions, one and only one ray passes through the pinhole; there is therefore no blur.
    • film: captures a focused inverted image, since every visible point in the scene is represented by a single point on the film.
  • lens
    • If we make the pinhole bigger, we let in more light - but the image goes out of focus.
    • The function of the lens is to focus this light
    • Problem: only points a fixed distance from the lens will be focused on the film - points at this distance lie on the focal plane. You must refocus the lens to change this distance. The distance between lens and film is called the focal length of the lens - and it is fixed.
    • Clarification: there is actually a range of points that are nearly in focus - the distance in front of and behind the focal plane is called the depth of field. Outside this range focus will be poor.
  • A lens camera improves upon the pinhole camera by using a lens to focus light. An SLR camera typically allows you to change lenses.
    • lens and its focal length
    • Each lens has a characteristic focal length. The longer the focal length, the narrower the angle of view
    • Let us start with a "normal" lens, around 53 degrees (about 50 mm).
    • A longer focal length means the film captures a smaller angle, which automatically blows up the image - a "telephoto" lens. Such lenses reduce foreshortening and make judgments of relative distance difficult. The image will also be darker, because less light is coming in, creating other problems. But they allow you to see at a distance. However such lenses are also very obtrusive and may give the impression that you are "spying" on people.
    • A short focal length means the film captures a wider angle, which automatically squeezes more image into the frame - a "wide" lens. Such lenses may introduce distortions at the extreme (e.g. fish-eye effect) but they let in lots of light.
    • A zoom lens allows you to vary the angle, between wide and telephoto. Most point and shoot, and all video, cameras contain such a lens. It's useful - no doubt - but the optics are inferior to using multiple lenses.
    • f-stop: The f-stop is a measure of lens aperture. It represents the ratio of focal length to diameter. A longer focal length, or a smaller diameter, both let in less light - varying as the square of these values. So a higher f-stop lets in less light, all other factors being equal. The advantage: the narrower aperture will be better focused at a range of distances - the depth of field increases.
    • shutter speed
    • shutter speed: the amount of time the shutter remains open, usually expressed as the reciprocal of the time value (e.g. "8" = 1/8th second).
  • Taking a good, well-lit photograph
    • To take a good photograph means ensuring adequate light, but not too much. Basically you want the most brightly illuminated point not to exceed the range of the film, and you want the darkest point to just barely register on the film. As for audio recordings: you want to fit the entire dynamic range (brightest to darkest) into the range of the film (and the same goes for the CCD, when using digital cameras).
    • Another factor is ensuring adequate perspective: not being too far away (reducing the foreshortening effect: apparent distances between objects are reduced), nor too close up (exaggerating it: apparent distances between objects are increased). See this comparison of water bottles of equal size using different lenses.
    • How to ensure adequate light? There are six factors: distance, focal length, f-stop, shutter speed, film speed, artificial lighting (e.g. flash). These depend on basic physical principles, especially the inverse square law. As always there are lots of tradeoffs....
      • Distance: getting closer to your subject will ensure there is more light (but may be tricky from a fieldwork standpoint)
      • Focal length: a wider angle lens will let in more light (but may not provide sufficient zoom)
      • f-stop: given a particular lens, a lower f-stop number lets in more light (but decreases depth of field)
      • shutter speed: all other things being equal, a slower shutter speed lets in more light (but increases the problems of shake and blur; the former problem can be mitigated with a tripod, but the latter problem is harder)
      • film speed: a faster film will require less light, but is also more grainy (in the digital domain you will also decrease your signal/noise ratio by increasing the gain)
      • artificial light: obviously lighting the scene will help; floodlights require lots of power and setup and are tricky and expensive; a flash is fine, but the inverse square law means that objects further from the camera quickly are dark.
  • film development (chemistry) and printing

camera types

  • SLR 35 mm. Mirror shows you what the camera sees. Makes camera bulky. Use behind the lens built-in light meter for accuracy. Interchangeable lenses, manual settings allow maximal control.
  • Rangefinder, or "point and shoot". Quiet, light, tiny, inexpensive, typically fully automated (though settings may allow some manual functions). But rangefinder is not accurate (parallax error), meter is not behind lens, lens is usually not interchangeable, lens is small and poorer quality, can’t apply filters. Come in 35mm and other film sizes. Good for speed.
  • Twin-lens reflex. Like rangefinder but accepts larger format film. Older style.
  • View. See exactly what you will photo on ground glass. Insert film plate, and take picture. Simplest, oldest type of camera. Can make large negatives. 4x5 is common.

Digital photography

The theory of digital cameras is exactly the same as for analog cameras, up until the final stage: instead of film, there is a CCD (charge coupled device) comprising an array of light sensors, or pixels.


  • Sampling and quantization error: as for audio there are only a fixed number of pixels, and each one measures the incident light using a finite number of states. By contrast, film chemistry is more "continuous".
  • Codecs: there is a process of encoding light to become numeric, and (in the reverse direction) decoding numbers to become light.
  • Pixel and megapixel (sampling rate)
  • Bit depth (sample size)

Camera types

  • DSLR: digital version of SLR (above): provides maximum control, higher quality optics, AD capture, processing, interchangeable lenses, BUT more weight, bulk, cost
  • point and shoot: digital version of rangefinder (above): provides less quality and control, BUT less weight, bulk, cost
  • smaller cameras installed in laptops, tablets, and phones: minimal quality and control, BUT more readily available

Note that digital cameras have blurred the lines between photography and videography (and audiography), so you may be able to get away with a smaller number of multipurpose devices....however specialized devices will always have an edge: with less to do, they do it better.

File formats

As for audio (mp3, ogg, wav, etc.) there are a multitude of image file formats. These differ according to:

  • the codec (the way the image is digitally encoded as pixels
    • color depth per pixel (8 bit pixel = 256 colors; 24 bit pixel = over 16 million colors, or "truecolor")
  • compression scheme - lossy or lossless
  • raster or vector: whether a map of pixels or set of vectors is stored. Normally real-world images are not stored as vectors, which are used for computer graphics

Here are some of the more common ones:

  • tiff, Tagged Image File Format: may be uncompressed (~ wav) or compressed, lossy or lossless
  • jpg, Joint Photographic Experts Group: compressed, usually lossy (~ mp3)
  • PNG, portable network graphics - a lossless, open-source compression scheme
  • GIF: graphics interchange format. 8 bit palette provides limited color range (256). Often used also for animations.
  • BMP: Windows bitmap format, an uncompressed pixel representation
  • SVG: a common and open vector graphics standard


  • Adobe Photoshop: commercial
  • The Gimp: open source equivalent. Note that you'll need to install and run X11 on Mac OS X before starting the Gimp.