Trevor Paglen, an artist and photographer finishing his Ph.D. in geography at the University of California, Berkeley, has managed to document some of this hidden world. The 75 patches he has assembled reveal a bizarre mix of high and low culture where Latin and Greek mottos frame images of spooky demons and sexy warriors, of dragons dropping bombs and skunks firing laser beams.

“Oderint Dum Metuant,” reads a patch for an Air Force program that mines spy satellite images for battlefield intelligence, according to Mr. Paglen, who identifies the saying as from Caligula, the first-century Roman emperor famed for his depravity. It translates “Let them hate so long as they fear.”

Wizards appear on several patches. The one hurling lightning bolts comes from a secret Air Force base at Groom Lake, northwest of Las Vegas in a secluded valley. Mr. Paglen identifies its five clustered stars and one separate star as a veiled reference to Area 51, where the government tests advanced aircraft and, U.F.O. buffs say, captured alien spaceships.

The book offers not only clues into the nature of the secret programs, but also a glimpse of zealous male bonding among the presumed elite of the military-industrial complex. The patches often feel like fraternity pranks gone ballistic.

The book’s title? “I Could Tell You but Then You Would Have to Be Destroyed by Me,” published by Melville House. Mr. Paglen says the title is the Latin translation of a patch designed for the Navy Air Test and Evaluation Squadron 4, at Point Mugu, Calif. Its mission, he says, is to test strike aircraft, conventional weapons and electronic warfare equipment and to develop tactics to use the high-tech armaments in war.

“The military has patches for almost everything it does,” Mr. Paglen writes in the introduction. “Including, curiously, for programs, units and activities that are officially secret.”

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He said contractors in some cases made the patches to build esprit de corps. Other times, he added, military units produced them informally, in contrast to official patches.