What is the false-double-wall sign and how does one distinguish it from Rigler sign?
The so-called false double-wall sign refers to two dilated loops of bowel in close apposition such the luminal gas of one loop appears to outline the serosal surface of the other loop. Double wall thickness compared to single loop.
What is Rigler triad?
Something completely different (but named after the same chap: Leo George Rigler - American radiologist (1896 - 1979)). Rigler's triad is seen in gallstone ileus and consists of pneumobilia, small bowel obstruction, and a gallstone usually in the right iliac fossa.
In a normal x-ray, only the luminal surface (blue arrows) should be visible outlined by gas. The serosal surface (orange) should not be visible as it is normally in contact with other intra-abdominal content of similar density (other loops of bowel, omentum, fluid). In this case, gas abuts the serosal surface rendering it visible.
As this film has been obtained supine (note absence of air-fluid levels), ascites pools in the paracolic gutters, with fluid mixed in with gas bubbles (green arrows).