## Sensitometry

The word “sensitometry” is derived from two Latin words meaning “sensitivity” and “measurement”. It is the science of measuring how photographic emulsions respond to exposure and processing.

An invisible image is formed when film is exposed to light; this is called a latent image. When the film with the latent image is processed, a visible image is formed on the camera negative film. Sensitometry is the relationship between exposure and the resultant image over the sensitivity range of the emulsion. How much exposure is required to produce an image that is very light gray, slightly darker gray, very dark gray or black?

How much exposure is required to produce an image that is very light gray, slightly darker gray, very dark gray or black? Sensitometry is a way of measuring how much light is required to expose the film to produce the slightest darkening (after processing) and increasing amounts of darkening all the way to a very dark gray and black, when the film is fully exposed.

Curiously, the human eye does not see equal increments in brightness equally. As brightness increases, the steps must increase in size. The eye has a logarithmic response – each step must be ten times as bright as the previous one for the eye to respond equally. A brightness series of 1, 10, 100, 1000, 10,000 looks like equal steps and has logarithmic brightness values (powers of 10) of 0, 1, 2, 3 and 4. In sensitometry, we need to measure quantities in ways that are equivalent to the ways we perceive the images. This is the first example: we use logarithmic exposures in sensitometry.

Let’s talk about camera stops for a moment. Those of you with adjustable 35 mm still cameras will know that exposure is made up of light intensity (the lens stop) and the exposure time. The formula is E (Exposure) = I (Intensity) times T (Time).

Every f/stop provides a doubling of the exposure. This series of f/stop numbers will be familiar. If we take the logarithm of the number 2 (doubling), the answer is 0.3010 or almost exactly 0.3. This is a number we shall need to remember, as it is used in many applications – exposure, filters, printing, etc.

## Densitometry

Densitometry is simply the measurement of the degree of darkening in the film image. We shall need to define the units used – density, and describe the measuring device used – densitometer.

The measurement of density simply compares the intensity of the light falling on the film sample (incident light – Ii) with the intensity of the light transmitted by the film-transmitted light (It). Moving from left to right in this diagram, the darker the film image, the less the transmitted light.

If we take the ratio of the transmitted light to the incident light It/Ii, we get a quantity called “Transmittance”. Its value is 1.0 for clear film and decreases to very small numbers for dense film. Alternately, we can use the ratio of the incident light to the transmitted light which is called “opacity”. Its values range from zero for clear film to figures of 100,000 for the densest film – also awkward numbers. But recall what we said about the logarithmic brightness response of the human eye. We should also measure density in logarithmic units. The log of opacity is called Density.

## Characteristic Curve

As we plot the densities vs. their exposures, going from low exposures/low densities to high exposures/high densities and join the points together, we obtain an S-shaped curve. Below a certain exposure, no image density is formed, then it increases steadily until it can go no higher. This is called the characteristic curve for one color layer of this film. It is also sometimes called the “H and D” curve, not because the axes are log exposure (symbol – H) and density (symbol – D), but for the two English photographic scientists, Hurter and Driffield, who discovered this curve.

The names of the parts of the characteristic curve are:

• Dmin: or minimum density, representing the unexposed film, where the density is due to the film base and a few silver halide crystals that have developed spontaneously without exposure.
• Toe: The most sensitive crystals have been exposed, representing the darkest parts of the image, i.e., the shadows, or underexposure.
• Straight-line portion: Density increases in a linear manner, proportional to exposure, representing most of the tones in the image.
• Shoulder: almost all the crystals are now exposed, representing the bright highlights of the scene.
• Dmax: all the crystals are now exposed, representing burned-out highlights. Usually the cinematographer will avoid exposing the Dmax.

## Useful Parameters from Characteristic Curve

We can derive a number of useful metrics or “parameters” from the characteristic curve:

• Speed is measured as the exposure required to produce a certain density above Dmin.
• Contrast or gamma is the slope or gradient of the straight-line portion measured by dividing the increase in density between the speed point and a point at a specified exposure above the speed point by the increase in exposure or delta D over delta H.
• The latitude or exposure range of the film is the range of exposure over the usable portion of the curve, from the start of the toe up to the end of the shoulder, avoiding Dmin or Dmax.

The speed of an emulsion is indicated by the position of the curve, and particularly the speed point, along the exposure axis.  Fast emulsions lie to the left (little exposure required) while slow emulsions lie to the right (greater exposure required).  There are several different metrics for speed, depending on the type of film, e.g., we use EI or Exposure Index for camera films.

The contrast of the emulsion is the gradient or slope of the straight-line portion, measured between the speed point and a point higher in exposure by a specified amount.  The increase in density between these points is greater the higher the contrast. Each type of film has a typical contrast, ranging from about 0.6 for negative films to 3.0 or greater for print paper.