UV-A irradiance at working distance

Fluorescent magnetic particles and penetrants contain a dye that absorbs UV-A around 365 nm and re-emits in the yellow-green, where the dark-adapted eye is most sensitive. The brightness of an indication is proportional to the UV-A falling on it, so the irradiance at the part surface - not at the lamp - is what determines whether a fine indication is seen or missed. The accepted minimum is 1000 µW/cm², and lamps are certified at a stated distance, conventionally 380 mm (15 in.).

A lamp behaves approximately as a point source once you are well beyond its reflector, so the irradiance falls with the square of distance: E2 = E1 x (d1/d2)². Doubling the working distance quarters the irradiance. A lamp certified at 4000 µW/cm² at 380 mm is still legal at 760 mm, where it delivers exactly 1000, but at a metre it is below the limit even though nothing about the lamp has changed.

Ambient white light matters just as much. Fluorescent indications are seen against a black background, and white light both washes out the emission and prevents the eye from dark-adapting. The limit for fluorescent examination is 20 lx (2 fc) or less measured on the surface, and the inspector needs time in the booth - typically at least a minute, and longer after coming in from daylight - before interpreting anything.

Treat the inverse square result as a planning figure. Close to the lamp, inside the near field of the reflector, the law under-reads; LED heads with shaped optics can depart from it badly at any distance. The compliant number is the one a calibrated radiometer gives at the actual working distance, on the actual surface, with the lamp warmed up.

E2 = E1 x (d1 / d2)²
Maximum working distance for 1000 µW/cm²: d = d1 x sqrt(E1 / 1000)
Minimum UV-A at the surface: 1000 µW/cm², reference distance 380 mm (15 in.)
Maximum ambient white light for fluorescent examination: 20 lx (2 fc)