Exposure

   
Aperture, Focal Length, f/stop, & Aperture Area Table (click)
Exposure Values Table (click)

    
Light, for our purposes (photographic) may be described as being composed of discrete and quantifiable packets of energy called photons. Light is known to exhibit wave behaviors as well but for the purposes of this discussion, we may focus on its particle nature, except with regard to spectral sensitivity mapping of films and sensors.

This limitation is practicable because both films and sensors are changed incrementally by light. In the case of film or other photo-sensitive materials, photons are absorbed by metal-halide grains (most typically, Silver Bromide) that together with gelatin provide the chemical “sensor” of the film. When a photon is absorbed by a Silver-Halide grain, a Bromine ion (Br-) looses an electron, converting into elemental Bromine and a Silver ion (Ag+) absorbs the electron creating a Silver atom. The silver atom migrates to a potential latent image site caused by impurities in the crystal structure of the grain and forms a latent image that will be changed into an image after being treated by chemical developing and fixing agents. It is believed the Bromine atom reacts with the gelatin. Therefore, there is an incremental effect and relationship between the formation of image / image density and the number of photons (of appropriate wavelength) entering a Silver-Halide grain.*

Now consider a digital sensor composed of an array of photo-sensitive sites where each site can absorb photons and convert them into an electrical signal that is proportional to the number of photons absorbed. CMOS sensors converting them directly to a voltage using a a photo diode to establish a voltage differential across a (FET) transistor and indexing the photo sites with a 2D array. CCD sensors develop  discrete charges at each photo site and then dump the charges serially. Both sensor types feed the sensor’s analog outputs into analog to digital converters that convert each photo site’s voltage into a number representing its magnitude.

There are of course certain inefficiencies in both systems. Both media require a minimum light intensity, in the case of film, to create a linear response and to overcome absorption and dispersion within the film base and the gelatin emulsion. In the case of digital sensors, to significantly overcome the circuitry’s inherent noise so as to establish a good signal to noise (s/n) ratio (where the signal strength is significantly higher than the base noise level.)

How does this relate to exposure? Both mechanisms have both lower and upper limits to their functionalities. Each photographic site (the Silver-Halide grain in the case of film and the pixel in the case of the digital sensor,) must receive enough photons to initiate a recordable response but not too many so as to exceed the site’s absorptive ability. The medium’s absorptive capability is generally referred to its dynamic range and is often expressed in terms of the number of stops (or whole EV numbers) the medium is capable of recording. Each full stop represents a difference of 2 times (or 1/2,) a dynamic rage of 8 stops is equal to 2^8 or 256:1. 12 stops = 2^12 or 4096:1, and 14 stops = 2^14 or 16,384:1.

Practical Exercise: Determine your digital camera’s dynamic range.

  1. Choose a uniformly well lit white surface such as a wall.
  2. Mount your camera on a tripod an face it towards the surface taking care not to cast a shadow on the surface.
  3. Set the camera to its lowest ISO setting.
  4. Using the built-in metering system, make one exposure.
  5. Look at the exposure data and note the shutter speed and the f/stop.
  6. Set the camera’s mode dial to M (manual) and set the aperture and shutter speed to match those of the exposure just made.
  7. Reduce the shutter speed by 1/2 and make another exposure.
  8. Repeat step #7 eight more times each time reducing the shutter sped by 1/2 of the previous exposure.
  9. Re-set the shutter speed to that used in step #4 (the first exposure made.)
  10. Repeat steps #7-8 except instead of reducing the shutter speed by 1/2, double it instead.
  11. Examine the first series of exposures (steps #7-8) and determine the last exposure that appears different (lighter) than the previous exposure.
  12. Examine the secondt series of exposures (step #10) and determine the last exposure that appears different (darker) than the previous exposure.
  13. The total number of exposures that show gradations plus the center image (remembering to include one pure white and one pure black) is the dynamic range of your camera’s sensor expressed in full stops (or EVs.)

Exposure value

Exposure value is a base-2 logarithmic scale defined by (Ray 2000, 318 **)

EV = log2N2/t

where
N is the relative aperture (f-number)
t is the exposure time (“shutter speed”) in seconds
EV 0 corresponds to an exposure time of 1 s and a relative aperture of f/1.0. If the EV is known, it can be used to select combinations of exposure time and f-number, as shown in EV Table.
Each increment of 1 in exposure value corresponds to a change of one “step” (or, more commonly, one “stop”) in exposure, i.e., half as much exposure, either by halving the exposure time or halving the aperture area, or a combination of such changes. Greater exposure values are appropriate for photography in more brightly lit situations, or for higher ISO speeds.

* A detailed description of the Gurney Mott Theory of Latent Image Formation may be found at The Photographic Latent Image

** Ray, Sidney F. 2000. Camera Exposure Determination. In The Manual of Photography: Photographic and Digital Imaging, 9th ed. Ed. Ralph E. Jacobson, Sidney F. Ray, Geoffrey G. Atteridge, and Norman R. Axford. Oxford: Focal Press. ISBN 0-240-51574-9