The machines will cost about $100,000 to $170,000 each, depending on the model. They are being developed by the agency as part of an ambitious technology initiative, which also includes advanced X-ray systems for inspecting carry-on bags for weapons and other contraband.

Image Credit... Chris Gash

That new X-ray technology may be capable of electronically identifying explosive chemicals, allowing the agency to drop the much-disliked rule that restricts passengers to carrying on liquids or gels solely in containers holding 3.4 ounces or less, packed in a single quart-size zip-top plastic bag.

Passengers undoubtedly would welcome that advance. It is far less clear what the reaction will be once people realize they will be asked to pose in a machine that transmits a naked body image to a screener who, the agency says, is in a “remote location” and “unable to associate the image with the passenger being screened.”

In the airports where the whole-body imaging machines are being tested, less than 2 percent of passengers presented with the option of using them are choosing not to, Mr. Kane said.

The development of these machines has been widely known for years. But until now it was assumed that the machines would be used only as an option for the relatively small number of passengers chosen for secondary inspections. The machines’ excellent performance changed the agenda, Mr. Kane said.

“My first reaction is that it will slow down the lines,” Mr. Schneier, the security technology consultant and a longtime agency critic, said Monday.

“It’s almost like an M.R.I. scan,” he said. “You stand there and hear the machine whirr around you for a few seconds and it’s done. But that’s still a lot longer than walking through the arch and seeing if you beep.”