Exposure transfer

The most reliable exposure chart a crew owns is the last shot that came out right. Transferring it to the next joint means applying four independent multiplicative corrections to a known-good time.

Distance follows the inverse square law, (d2/d1)^2. Activity is inversely proportional, A1/A2, which handles both decay between shots and swapping projectors. Film class is the ratio of relative exposures, roughly 3.2 between D7 and D4. Thickness is exponential: each extra half value layer of steel in the beam doubles the required exposure, so the correction is 2^((x2-x1)/HVL).

The thickness term is the one that catches people out. It is not linear. Going from 25 mm to 32 mm of steel with iridium is only 7 mm more material, but at an HVL of 12.7 mm that is 0.55 of a half value layer, a 47 percent increase in exposure. Going from 25 mm to 50 mm nearly quadruples it.

Transfer is valid across a modest range. Push it far and the effective beam quality changes - the beam hardens as it passes through more steel, so the effective HVL rises and the calculation over-predicts. Beyond about two half value layers of change, shoot a step wedge and redraw the chart rather than extrapolating.

t2 = t1 x (d2/d1)^2 x (A1/A2) x (F2/F1) x 2^((x2 - x1) / HVL)
HVL = half value layer of the material for that source
F = film relative exposure factor