Radiographic Exposure Time, Unsharpness, and Source Decay

Exposure follows the INVERSE SQUARE of source-to-film distance, so a 50 percent increase in distance costs 2.25 times the shot. Geometric unsharpness -- source size times material thickness over distance -- falls only in direct proportion, so the trade is always the same shape: unsharpness improves linearly and exposure worsens quadratically. WHETHER THE LONGER SHOT IS WORTH BUYING DEPENDS ENTIRELY ON THE CODE'S UNSHARPNESS LIMIT FOR THE THICKNESS, and that is the comparison worth making before the shot rather than after. If the short distance already passes, the extra distance buys nothing the code asks for and costs real time on a production radiograph; if it fails, the minimum distance that meets the limit is the number wanted, not an arbitrary increase. SOURCE DECAY IS THE ERROR THAT NEEDS NOTHING TO GO WRONG. An Ir-192 source loses half its activity in about 74 days, so a technique sheet written two months ago and used unchanged underexposes by nearly half -- and the failure mode is a light radiograph that may still be interpreted rather than rejected, which puts a technique fault into an accepted film. Cobalt-60 at about 5.3 years is far more forgiving, and the half-life is entered here so both are covered. This computes time, distance and unsharpness on entered figures. It does not select a source, an energy or a film class, supply an exposure chart or a density requirement, determine the required image quality indicator or its placement, evaluate film density, penetrameter sensitivity or artifacts, address the technique for the geometry (single-wall, double-wall, elliptical), or interpret a radiograph. It is not a radiation safety calculation -- the restricted-area boundary is a separate question. The applicable code section, the written radiographic procedure, and the certified radiographer and interpreter govern.

exposure scales with the INVERSE SQUARE of source-to-film distance, t2 = t1 x (d2/d1)^2; geometric unsharpness Ug = source size x material thickness / distance falls only in direct proportion; and source activity decays as 0.5^(days / half-life), Ir-192 at 73.83 days and Co-60 at 1,925.3 days.

Radiographic technique arithmetic. The unsharpness LIMIT comes from the applicable code section for the thickness and is entered, as is the half-life so both common industrial sources are covered.

One inverse-square relation, one geometric ratio, and one exponential decay.

Estimate. AHJ and licensed professional govern.

Field names used by the API: base_exposure_s, base_distance_in, new_distance_in, source_size_in, material_thickness_in, days_elapsed, half_life_days, unsharpness_limit_in, new_exposure_s, ug_base_in, ug_new_in, decay_factor, decayed_exposure_s, activity_pct

• Unsharpness limit is entered it varies with thickness and code sectionthe applicable code
• Half-life is entered Ir-192 73.83 days, Co-60 1,925.3 dayspublished nuclide data
• Not a radiation safety calculation the restricted-area boundary is a separate question10 CFR Part 34 or the state equivalent