SARANAC, Mich. — Of all the cartons of organic eggs sold in the United States, more than 1 in 10 originates from a complex here that houses more than 1.6 million hens.

They’re sold under the Eggland’s Best label.

“The entire process is organic,” Greg Herbruck, president of Herbruck’s Poultry Ranch says in a promotional video.

Details of the operation are not publicly available, however, and he declined a Washington Post reporter’s request for a visit, citing the possibility that it could infect the flock with disease, such as avian flu.

But according to people familiar with the operation, as well as a building plan, each of the nine long rectangular barns at Herbruck’s holds about 180,000 birds, or more than three hens per square foot of floor space, according to sources, who spoke on the condition of anonymity because they had not been authorized to speak for the company.

None of the birds is allowed to set foot outside, sources said.

Under USDA requirements, organic livestock are supposed to have access to the “outdoors,” get “direct sunlight” and “fresh air.” The rules prohibit “continuous total confinement of any animal indoors.” Organic livestock are supposed to be able to engage in their “natural behavior,” and for chickens, that means foraging on the ground for food, dust-bathing and even short flights.

Katherine Paul of the Organic Consumers Association said the Herbruck’s operation betrays consumer expectations.

“This is not at all what consumers expect of an organic farm,” she  said, when told about Herbruck’s. “It’s damaging to the image of the entire industry.People will wonder, ‘Why the hell am I paying more for this?’ ”

In addition, Paul said, allowing the large egg operations to confine their hens to the barn creates an unfair advantage when hundreds of smaller family organic operations let the hens out and sustain higher costs.