Film density adjustment
Photographic density is the logarithm of the ratio of incident to transmitted light through the processed film: D = log10(I_in / I_out). A density of 2.0 passes one hundredth of the light, 3.0 one thousandth. The relationship between exposure and density is the characteristic curve, and it is emphatically not linear – it is an S shape, flat in the toe, steep through the useful working range, flattening again at the shoulder.
Because the curve is steep in the working range, correcting density is not a matter of scaling exposure by the density ratio. Between density 2.0 and 3.0 the film gradient is around 4 to 5, so a full unit of density costs only about 0.2 in log exposure – a factor of 1.6 to 1.7 in time, not 1.5 times as a naive ratio would suggest. Below density 1.5 the film is in the toe, the gradient collapses, and contrast sensitivity is lost even though the image looks acceptable on a bright viewer.
Codes fix a working range for exactly this reason. ASME BPVC Section V, Article 2, T-282.2 requires a density between 1.8 and 4.0 for single-film X-ray radiographs and between 2.0 and 4.0 for gamma radiographs, measured through the area of interest. ISO 17636-1 requires a minimum of 2.0 for class A and 2.3 for class B. A radiograph outside the range is rejected regardless of how good the IQI reading is, because the contrast the code assumes is not present.
The correction here uses a representative class C4 to C5 characteristic curve. For accurate work on a specific emulsion and processor, expose a step wedge and plot your own curve – film speed drifts with developer age and temperature.
Worked example
| Exposure time used | 12 min |
| Density achieved | 1.5 |
| Density wanted | 2.5 |
| Radiation source | gamma |
| Relative exposure at density achieved | 0.73 |
| Relative exposure at density wanted | 1.33 |
| Exposure correction factor | 1.822 |
| Corrected exposure time | 21.86 min |
From the characteristic curve, density 1.5 corresponds to relative exposure 0.73 and density 2.5 to 1.33. The correction factor is 1.33 / 0.73 = 1.822, so t2 = 12 x 1.822 = 21.86 min. Note that the correction is not the naive density ratio of 2.5/1.5 = 1.67: relative exposure is a logarithmic scale, and over this span the curve is climbing out of the toe, so the exposure actually has to rise by more than the density ratio suggests.
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