Mr. Sittig has also projected Cinerama and recalled the suspense of the experience. He remembered a screening of “The Wonderful World of the Brothers Grimm” at the TCM Classic Film Festival in Los Angeles in 2012, the last year that true three-strip Cinerama was presented in the United States. (Beginning with “It’s a Mad Mad Mad Mad World” in 1963, films under the Cinerama banner were just rebranded 70-millimeter, projected from a single strip.) A film break, he said, required 45 minutes of maintenance.

The same problems of alignment and consistent illumination that dogged the Cinerama presentations of the 1950s and early 1960s also troubled the restorations. Each shot had three pieces, sometimes sourced from different elements, and they hadn’t always faded at the same rate. “The trick here is to make it look like it’s one image across the screen, and that became sort of a dance of death,” said David Strohmaier, the unofficial director of Cinerama restorations, who worked for free and estimates that 80 percent of the restoration work was done at his home.

He and his producing partner, Randy Gitsch, couldn’t have made new film prints even if they had the budget for them: The original negatives were too worn. “The only way for this stuff to survive was what we did,” Mr. Strohmaier said. True aficionados can still make pilgrimages to the ArcLight Dome in Los Angeles or the National Science and Media Museum in Bradford, England, which occasionally hold analog Cinerama screenings. The Seattle Cinerama reopened in 1999 after an overhaul that included a restored Cinerama screen.

Image A Cinerama theater. Credit... Cinerama, via Museum of Modern Art, New York

“Fortunately, you don’t need any of those theaters to show real Cinerama because you have the luxury of digital Cinerama,” Mr. Gitsch said. Referring to Cinerama’s inventor, he added, “We’d like to think that Fred Waller’s original concept would have been to make one seamless picture, and you can’t really do that very well with three pieces of film.” The presentations at MoMA, which will use a single digital projector, will have “smilebox” letterboxing, approximating the illusion of depth that original moviegoers got from the extreme curvature of the screen.