So far, this is what I was quickly able to copy:
The other issue besides privacy that has surrounded backscatter X-raying has to do with radiation exposure. Most of us do not get X-rayed on a regular basis; and when we do get X-rayed in a hospital or doctor's office, we've got a lead vest thrown over our vital organs. But at airports, there's no lead vest. So are people who travel a lot going to be subjected to dangerous levels of radiation if they get backscattered too often? Most experts say no. According to the Health Physics Society (HPS), a person undergoing a backscatter scan receives approximately 0.005 millirems (mrem, a unit of absorbed radiation). American Science and Engineering, Inc., actually puts that number slightly higher, in the area of .009 mrem. According to U.S. regulatory agencies, 1 mrem per year is a negligible dose of radiation, and 25 mrem per year from a single source is the upper limit of safe radiation exposure. Using the HPS numbers, it would take 200 backscatter scans in a year to reach a negligible dose -- 1 mrem -- of radiation. You receive 1 mrem from three hours on an airplane, from two days in Denver or from three days in Atlanta. And it would take 5,000 scans in a year to reach the upper limit of safety. A traveler would have to get 100 backscatter scans per week, every week, for a year, in order to be in real danger from the radiation. Few frequent flyers fly that frequently.
It has been evaluated by the Food and Drug Administration's Center for Devices and Radiological Health, the National Institute of Standards and Technology and the Johns Hopkins University Applied Physics Laboratory
I like you.

Quick response, matter of fact, citing sources and giving further info to read. I'll openly acknowledge that I don't know what the dangers might be (whoa, I just had a weird deja vu moment -- I need to check my posts from a couple years ago...), but I have a hard time trusting citations of studies from the government without independent review. I can't find these studies online -- the actual studies, not just quotes about them and assurances that everything tested out A-OK -- but maybe I'm not looking hard enough. But again, the letter I linked simply asserts that:
"The X-ray dose from these devices has often been compared in the media to the cosmic ray exposure inherent to airplane travel or that of a chest X-ray. However, this comparison is very misleading: both the air travel cosmic ray exposure and chest Xrays have much higher X-ray energies and the health consequences are appropriately understood in terms of the whole body volume dose. In contrast, these new airport scanners are largely depositing their energy into the skin and immediately adjacent tissue, and since this is such a small fraction of body weight/vol, possibly by one to two orders of magnitude, the real dose to the skin is now high.
In addition, it appears that real independent safety data do not exist. A search, ultimately finding top FDA radiation physics staff, suggests that the relevant radiation quantity, the Flux [photons per unit area and time (because this is a scanning device)] has not been characterized. Instead an indirect test (Air Kerma) was made that emphasized the whole body exposure value, and thus it appears that the danger is low when compared to cosmic rays during airplane travel and a chest X-ray dose."
The response from one agency, according to medindia.net, was,
"The Office of Science and Technology responded this week to the scientists' letter, saying the scanners have been "tested extensively" by US government agencies and were found to meet safety standards.
But Sedat told AFP Friday: "We still don't know the beam intensity or other details of their classified system.""
So the government essentially said, "Trust us, we tested it exhaustively," but refuse to release (or at least, have not released despite prompting) their test info yet?
Maybe it is safe. I still wouldn't enjoy getting an X-ray, but I would submit if I had to for medical reasons. But this is not medically needed. Even if it is found to be completely safe, I find this particular process/policy abhorrent.
Maybe I'm a prude for not wanting anyone but my doctor or someone I know, love and trust to see me naked (or touch me in places I would NEVER feel comfortable allowing a stranger to touch), but up until now I've had the right to be a prude. Now some people are saying I DON'T have that right, if I want to fly?
Well, if this policy is still in place next time I fly, I guess I'll submit to the pat-down and fill out a comment card when it's over. Until then, I'll write letters, as suggested previously, and hope logic eventually prevails.
And for a country that seems to worship on the alter of reason and logic (after all, don't people frequently dismiss "feelings" and "opinions" as invalid tools for argument?), this seems like a highly illogical and nonsensical "security" measure.