dante stella stories photographs technical guestbook

More is less is more
The Devil is in the dynamic range

Having had some time to observe how people review digital equipment, whether cameras or negative scanners or whatever, I can only conclude that dynamic range is one of the most misunderstood concepts out there.  It's not that people misunderstand what it is in the abstract; rather, it is the practical application to photography that seems to be the hangup.

What is dynamic range?

There are two definitions relevant to dynamic range in photography.

One is lifted directly from electronics: in an analog electronic system, dynamic range is the ratio of the maximum signal power obtainable that does not distort compared to the noise level of the system.  This is sometimes expressed as the signal to noise ration (example: a CD player might have a 96dB signal to noise ratio).

Photographers also abuse the term dynamic range to stand for (a) the range of light levels in a scene; (b) the range of light values film can capture (or the range of opacities developed film exhibits; or (c) the range of reflectance in photo paper (example: this scene has a 500:1 contrast ratio).

How does it apply to conventional materials?

Film and paper have the ratio of Dmax (the blackest or most opaque condition possible) to Dmin (just darker than the film or paper base).  For example, if the Dmax of a film is 4.0 and the Dmin is 0.3, then the dynamic range is 3.7d. You can convert density units to stops easily. 

Start by assuming that your input and output are completely proportional.  Each 0.3 increment represents double (or half) the light.  So if you have 3.0d, you have ten stops of light. 

But because conventional materials do not have a proportional response to light, you then need to divide by the contrast index or gamma.  These measure the slope of the response curve of material as developed.  This last calculation determines how many stops of subject exposure will get the film up to its Dmax.  Different films are measured in different ways:

Contrast index for negative film.  For comparative purposes, negative film dynamic range is best estimated with respect to Contrast Index (CI).  This is average slope of the film's response measured from the toe (where response just starts picking up) to the shoulder (where the response to light starts becoming less proportional to the input).  Thus, it picks up where the film effectively "clips" - appropriately compared to what happens when a digital chip takes in more light than it can handle.  Contrast index varies with development time; more development time means higher CI.

Gamma for slide film.  On the other hand, slide films are more appropriately measured against digital by using gamma.  Gamma is the slope of the straight-line portion of the response curve (shorter and steeper because it does not include the more gently sloped toe and shoulder).  Slide film (like digital) does not really shoulder - the transparency simply becomes clear.  For this reason, only the gamma measure is relevant for slides.

So if you are dealing with negative film, divide those 10 stops by 0.58 (a typical contrast index), to reach a result of 17 stops.  If you are dealing with slide film, divide by 1.4 (a typical gamma) to get 7 stops.

For obvious reasons, machines that scan film and paper typically express their dynamic range in the same density units.  A scanner, though, does not care about how many stops of real-world exposure were recorded on the film; what matters is that it can scan though the densest part of the film or see into the darkest part of the paper without unacceptable levels of noise.

The Zone System uses a system that can best be thought of as ratios following geometric progression: 2 raised to the nth power, where n is the number of stops.  Each stop doubles the amount of light.  So a picture with one stop of range between the brightest and dimmest object has one stop of range (1:2).  The prototypical Zone system print will have a 1:256 range (eight stops) between brightest and darkest areas.

How does it apply to digital capture equipment?

Some digital cameras measure their dynamic range by signal to noise ratio.  This basically follows the formula used in electronics: what is the ratio of the highest possible value to the lowest possible (i.e., background noise).  For example, the sensor chip in the Kodak 14n that I use has a 69dB dynamic range measure this way.

To convert a dB to a ratio (roughly): divide the dB number by 20. 
Then raise 10 to this power.

69dB / 20 = 3.45

103.45 = 2818

= 2818:1

Other cameras express these values in bits (or stops).  Note that these bits have nothing to do with the number of bits in the resulting file (for reasons which will be discussed later).  For example,  the published dynamic range of a Kodak 14n measured in bits is 11.5.  Bits are equivalent to stops - which means that the sensor can capture a scene that is 11.5 stops from low to high, or a 1:2896 lighting ratio.

To convert bits to a ratio: where n is the number of bits,  2n is the ratio.

11.5 bits --> 211.5 --> 2896

= 2896:1

This should at least give you some ability to compare ranges.

What are some benchmarks?

The following are estimated (or published) dynamic ranges for a number of materials.  Remember, whether you realize the full range is highly dependent on how well controlled your exposure (and where appropriate, developing) is.  Negative films are computed according to contrast index and slide film according to gamma (see above for explanation why).

Item Numeric Stops of range in subject
Polaroid Sprintscan 120 scanner 3.9d Depends on the film being scanned.
Tmax 400 film (0.58 CI) 3.4d 19.5 stops
Tmax 100 film (0.58 CI) 3.0d 17 stops
Tri-X 35mm film (0.58 CI) 2.4d 13.5 stops
Kodak DCS Pro 14n digital 69dB 11.5 stops
Fuji Finepix S3 digital camera -- 10 stops (estimated)
Tri-X 35mm film (0.75 CI) 2.4d 10.5 stops
Nikon D2x digital camera -- 9.5 stops (measured)
Typical LCD display 500:1 9 stops
Kodachrome 25, 64, 200 (1.4 gamma) 3.7d 8 stops
Ektachrome 100 (1.4 gamma) 3.4d 7.5 stops
Human eye (no iris change) 150:1 7 stops

You will not see a lot of published figures for digital cameras.  They all claim great "dynamic range," but data is not really forthcoming and what is there tends to indicate pretty lackluster range.  Even if the data were all out there, it would not really be that useful in comparing systems - since there is no standard method of determining dynamic range.

What's the noise threshold, Kenneth?