WASHINGTON  President Obama, who emphasizes American innovation, says modernizing the federal Patent and Trademark Office is crucial to “winning the future.” So at a time when a quarter of patent applications come from California, and many of those from Silicon Valley, the patent office is opening its first satellite office  in Detroit.

That is only one of the signs that have many critics saying that the office has its head firmly in the 20th century, if not the 19th.

Only in the last three years has the office begun to accept a majority of its applications in digital form. Mr. Obama astonished a group of technology executives last year when he described how the office has to print some applications filed by computer and scan them into another, incompatible computer system.

“There is no company I know of that would have permitted its information technology to get into the state we’re in,” David J. Kappos, who 18 months ago became director of the Patent and Trademark Office and undersecretary of commerce for intellectual property, said in a recent interview. “If it had, the C.E.O. would have been fired, the board would have been thrown out, and you would have had shareholder lawsuits.”