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.

t2 = t1 x relE(D2) / relE(D1)
relE = relative exposure from the characteristic curve
Density D = log10(incident light / transmitted light)