Few people have an adequate understanding of what these machines actually do. The technology you're referring to is backscatter X-ray. Unlike a medical X-ray, which shines X-rays through your body to produce a shadow image on a photographic plate, backscatter X-ray uses far lower intensity that cannot penetrate your body. Instead, it reads the X-rays reflected back off of the person, or "backscattered".
The concern is because X-rays are ionizing radiation. Ionizing radiation is that which is at a high enough energy level that it can strip electrons and change chemistry, which is one potential cause of cancer. The dosage of radiation from X-rays is measured in microsieverts. To put a medical X-ray into perspective with an airport backscatter X-ray, a chest X-ray delivers 100 microsieverts; an airport scan delivers .02 microsieverts. You'd have to get scanned 5,000 times to equal the radiation dosage from a single chest X-ray. 10 microsieverts, or about 500 airport scans, is considered a negligible risk.
Why negligible? Just existing on the Earth, we're all being exposed to ionizing radiation constantly. You're being hit by cosmic gamma rays right now, and other natural sources, to the tune of some 3,000 microsieverts per year, equivalent to some 150,000 airport scans.
Flying in an airplane, you have less atmosphere to protect you, so you're exposed to more; about 20 microsieverts on a coast-to-coast flight. One backscatter X-ray airport scan gives you the same radiation you'd receive by flying in the airplane for four minutes. It is so small it's not even worth counting.
But if 1/500th of negligible is still too much for you, try the competing airport scan technology: Millimeter wave scanning. These use radio waves. Radio waves are not ionizing radiation, so they pose no plausible threat to health at all.
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On another note, I prefer anything that might (and I say "might" as this is pretty much speculation) help prevent my airplane from blowing up in flight. And, personally, I much prefer some security monkey in an observation room seeing an image of my private parts than having same monkey fumble in my croch :shock:
Thanks a lot- bring it on, those scanners!