# Film Characteristic Curves

In film radiography, the number of photons reaching the film determines how dense the film will become when other factors such as the developing time are held constant. The number of photons reaching the film is a function of the intensity of the radiation and the time that the film is exposed to the radiation. The term used to describe the control of the number of photons reaching the film is “exposure.”

## Film Characteristic Curves Different types of radiographic film respond differently to a given amount of exposure. Film manufacturers commonly characterize their film to determine the relationship between the applied exposure and the resulting film density. This relationship commonly varies over a range of film densities, so the data is presented in the form of a curve such as the one for Kodak AA400 shown to the right. The plot is called a film characteristic curve, sensitometric curve, density curve, or H and D curve (named for developers Hurter and Driffield). "Sensitometry" is the science of measuring the response of photographic emulsions to light or radiation. A log scale is used or the values are reported in log units on a linear scale to compress the x-axis. Also, relative exposure values (unitless) are often used. Relative exposure is the ratio of two exposures. For example, if one film is exposed at 100 keV for 6mAmin and a second film is exposed at the same energy for 3mAmin, then the relative exposure would be 2. The image directly to the right shows three film characteristic curves with the relative exposure plotted on a log scale, while the image below and to the right shows the log relative exposure plotted on a linear scale. Use of the logarithm of the relative exposure scale makes it easy to compare two sets of values, which is the primary use of the curves. Film characteristic curves can be used to adjust the exposure used to produce a radiograph with a certain density to an exposure that will produce a second radiograph of higher or lower film density. The curves can also be used to relate the exposure produced with one type of film to exposure needed to produce a radiograph of the same density with a second type of film.

## Adjusting the Exposure to Produce a Different Film Density

Suppose Film B was exposed with 140 keV at 1mA for 10 seconds and the resulting radiograph had a density in the region of interest of 1.0. Specifications typically require the density to be above 2.0 for reasons discussed on the film density page. From the film characteristic curve, the relative exposures for the actual density and desired density are determined and the ratio of these two values is used to adjust the actual exposure. In this first example, a plot with log relative exposure and a linear x-axis will be used. From the graph, first determine the difference between the relative exposures of the actual and the desired densities. A target density of 2.5 is used to ensure that the exposure produces a density above the 2.0 minimum requirement. The log relative exposure of a density of 1.0 is 1.62 and the log of the relative exposure when the density of the film is 2.5 is 2.12. The difference between the two values is 0.5. Take the anti-log of this value to change it from log relative exposure to simply the relative exposure and this value is 3.16. Therefore, the exposure used to produce the initial radiograph with a 1.0 density needs to be multiplied by 3.16 to produce a radiograph with the desired density of 2.5.  The exposure of the original x-ray was 10 mAs, so the new exposure must be 10 mAs x 3.16 or 31.6 mAs at 140 keV.

## Adjusting the Exposure to Allow Use of a Different Film Type

Another use of film characteristic curves is to adjust the exposure when switching types of film. The location of the characteristic curves of different films along the x-axis relates to the film speed of the films. The farther to the right that a curve is on the chart, the slower the film speed. It must be noted that the two curves being used must have been produced with the same radiation energy. The shape of the characteristic curve is largely independent of the wavelength of the x-ray or gamma radiation, but the location of the curve along the x-axis, with respect to the curve of another film, does depend on radiation quality. Suppose an acceptable radiograph with a density of 2.5 was produced by exposing Film A for 30 seconds at 1mA and 130 keV. Now, it is necessary to inspect the part using Film B. The exposure can be adjusted by following the above method, as long at the two film characteristic curves were produced with roughly the same radiation quality. For this example, the characteristic curves for Film A and B are shown on a chart showing relative exposure on a log scale. The relative exposure that produced a density of 2.5 on Film A is found to be 68. The relative exposure that should produce a density of 2.5 on Film B is found to be 140. The relative exposure of Film B is about twice that of Film A, or 2.1 to be more exact. Therefore, to produce a 2.5 density radiograph with Film B the exposure should be 30mAs times 2.1 or 62 mAs.