The basic work on sensitometry was carried out in Britain in the 1880s by Ferdinand Hurter (1844-98) and Vero C. Driffield (1848-1915), whose results were published in 1890. Their work is elegantly summarized by a graph that plots density D against the logarithm of the exposure, log H: this is variously known as the D/log H (formerly D/log E) curve, the H & D curve (from their initials), and the characteristic curve.
Density is a logarithmic value. In a negative, if one area transmits twice as much light as another, the density difference is 0.30, the logarithm (to base 10) of 2. If it transmits ten times as much, the density difference is 1.0, the logarithm of 10. And so forth.
Negative density is measured from a baseline of film base-plus-fog density (fb + f). Film base has a density of about 0.03 for roll-film and sheet film, and 0.3 for 35 mm film, which has a grey dyed base to reduce halation and permit daylight loading of cassettes. ‘Fog’ refers to those silver halide crystals that develop anyway, whether or not they are exposed to light. It is (or should be) uniform throughout the emulsion, but varies according to the emulsion, the developer, and the development time.
For prints, reflection values are used. If one area reflects twice as much light as another, the density difference is again 0.30. Measurements are taken from a baseline of ‘paper base white’, the brightest white of which the material is capable.
Exposure is normally measured in lux seconds (formerly called metre-candle-seconds). The logarithm is taken because this gives a more convenient, compact, and easily comprehensible curve than plotting the actual (non-logarithmic) lux second values.
Characteristic curves vary widely in shape, but all follow the same basic form: the curve in Fig. 1 describes a typical black-and-white negative film in a typical developer. It may be divided into several sections:
• Threshold. Below a certain level of exposure, there is no density at all. This is a result of the ‘inertia’ of the material in question.
• Toe. At first, the increase in density with exposure is slow, and the slope of the curve is all but flat. By convention, the dark areas of the negative on the toe are called the shadows, though of course they may be any dark area: a black velvet dress in full sun may be darker than anything in open shadow in the same scene.
• Straight-line portion. Sooner or later, the relationship between density and (log) exposure becomes more or less linear. This region is known as the straight-line portion of the curve, though it is seldom absolutely straight. The slope of this curve is known as ‘gamma’ and is an indication of the contrast of the material: a steep slope (higher gamma) means more contrast, a gentle slope, less.
• Shoulder. There is a limit to how much density a given emulsion can deliver, no matter how much exposure it receives. The absolute limit is normally abbreviated to Dmax (maximum density), but before this is reached, the slope of the curve slowly decreases, so that each subsequent lux second gives less and less density.
• Region of solarization. With some (not all) materials, with gross overexposure, the density may actually begin to fall again with increasing exposure: more exposure means less density. This was first seen when the sun recorded as a clear dot in the negative, instead of the black dot one would expect, hence the term ‘solarization’. It is of little or no consequence in modern practical photography, and should not be confused with the Sabatier effect or pseudo-solarization.
With reversal film, or any other direct positive, maximum density corresponds with complete lack of exposure, and minimum density results from maximum exposure. The curve therefore goes ‘backwards’ (see Fig. 2), the curve for a typical colour slide material.
Speed points
One of the most useful things about the H&D curve is that it can be used to establish film speed. The earliest criteria were based on the threshold: the minimum exposure required to give any density at all. For a given threshold speed, however, a short-toe film will be effectively faster than one with a long toe because there is more usable density at low exposures. Another possibility is to produce the slope of the straight-line portion of the curve downwards until it intersects the exposure axis, and use this as the speed point. This takes no account of toe speed and is greatly distorted by development time: the longer the development time, the steeper the curve, and the higher the speed.
The original DIN (Deutsche Industrie Norm) standard in the early 1930s addressed the latter problem by developing the film to the maximum possible contrast (‘gamma infinity’). This was admirably standardized but bore little resemblance to real-life photography. The speed point on this curve was taken as a density of 0.10 above fb + f: a somewhat arbitrary figure, but a conveniently round number, easily measured adequately with a basic densitometer.
Later in the 1930s, L. A. Jones at Kodak determined a better speed point. He reasoned that the first useful density is when the slope of the curve (on the toe) becomes steep enough to provide useful differentiation of tone with increasing exposure. Empirically, he found that this occurred at 30 per cent of the average slope (gamma) of the straight-line portion, measured between the speed point and a point 1.5 log exposure units further along the curve (32×the exposure, or five stops more). This is the fractional gradient speed point criterion, and it is relatively little affected by development: the higher the overall gamma, the steeper the toe gradient needs to be in order to reach 30 per cent of it. This became the basis of the ASA (American Standards Association) film speed system until the late 1950s.
The disadvantage of the fractional gradient system is that the speed point is quite hard to find. In 1959, therefore, the ASA standard adopted the DIN criterion of 0.10 above fb + f, with a standard slope defined as one that gives a density of 0.80 above the speed point for an increase in exposure of 1.3 log units. The slope of this curve is therefore 0.80/1.30 = 0.61538, normally rounded to 0.62. At the same time, the one-stop safety factor that had previously been built into black-and-white film speeds was dropped, so published film speeds doubled overnight, though of course actual film speeds remained constant.
The only significant change since then is that the old ‘standard’ ISO (International Standards Organization) developer has been dropped, and manufacturers can now use any developer they like. Most use ‘middle of the road’ developers such as Kodak D-76, though speed-increasing developers can deliver up to 2/3 stop extra speed while still adhering to ISO criteria of shadow density and contrast, and fine-grain developers typically wipe off up to one stop in speed, so an ‘ISO 400’ film may range from ISO 200 to ISO 650, depending on developer.
Speed points for colour negative films are similarly determined, though the speeds of each individual colour emulsion must be taken into account.
The speed points for transparency film are necessarily more complex. They are based on a maximum exposure point, which gives a density of 0.20 above fb + f, and a minimum exposure point, which is either where the shoulder of the curve begins or 2.0 above minimum density, whichever is lower. The speed point is the geometric mean of these two exposure points.
Fig. 1 (Idealized) D/logH curve for a B&W negative emulsion
Fig. 2 (Idealized) D/logH curve for a transparency emulsion
— Roger W. Hicks
Bibliography
- The Photographic Researches of Ferdinand Hurter and Vero C. Driffield (1920, repr. 1974).
- Eggleston, J., Sensitometry for Photographers (1984).
- Hicks R., and Schulz, F., Perfect Exposure: From Theory to Practice (1999)
