Elliptical DWDI source offset

On small-bore pipe the source is placed outside and the film on the far side, so the beam passes through both walls and both halves of the weld appear on one radiograph. If the source sits exactly in the plane of the weld the two images superimpose and neither can be interpreted. Offsetting the source along the pipe axis tilts the beam, and the two weld images separate into the characteristic ellipse.

The geometry is straightforward projection. Place the pipe axis along z with the weld at z = 0, the source offset axially by o at a distance SOD from the near surface. The ray reaching the film-side weld arrives in the weld plane, while the ray that grazed the source-side weld lands displaced by S = o x OD / SOD. Rearranged, the offset needed for a chosen separation is o = S x SOD / OD.

The separation aimed for is conventionally three quarters to one full weld width, enough to read both halves cleanly without pushing the source-side image off the diagnostic length of the film. Too little offset and the images overlap; too much and the beam obliquity distorts the weld and stretches the penetrated thickness beyond what the density band will tolerate.

ASME BPVC Section V, Article 2, T-271.2 restricts the elliptical technique to pipe of 3.5 in outside diameter or less, and requires a minimum of two exposures 90 degrees apart. Above that diameter the images cannot be separated without unacceptable distortion and double-wall single-image with at least three exposures is used instead.

Image separation S = o x OD / SOD
Source offset o = S x SOD / OD
Beam obliquity angle = atan(o / SOD)
Penetrated thickness = 2 x wall / cos(angle)
SFD = SOD + OD