They’re not doing that, and there’s an easy way to tell. If you’re in a theater playing a digital print (the marquee at the ticket booth should have a “D’’ next to the film’s name), look back at the projection booth.

“When you’re running a 2-D film, that polarization device has to be taken out of the image path. If they’re not doing that, it’s crazy, because you’ve got a big polarizer that absorbs 50 percent of the light.’’

A description of the problem comes from one of several Boston-area projectionists who spoke anonymously due to concerns about his job. We’ll call him Deep Focus. He explains that for 3-D showings a special lens is installed in front of a Sony digital projector that rapidly alternates the two polarized images needed for the 3-D effect to work.

The uniting factor is a fleet of 4K digital projectors made by Sony — or, rather, the 3-D lenses that many theater managers have made a practice of leaving on the projectors when playing a 2-D film. Though the issue is widespread, affecting screenings at AMC, National Amusements, and Regal cinemas, executives at all these major movie theater chains, and at the corporate offices of the projector’s manufacturer, have refused to directly acknowledge or comment on how and why it’s happening. Asked where his company stands on the matter, Dan Huerta, vice president of sight and sound for AMC, the second-biggest chain in the US, said only that “We don’t really have any official or unofficial policy to not change the lens.’’

Why, then, do so many of the movies look so terrible? This particular night “Limitless,’’ “Win Win,’’ and “Source Code’’ all seemed strikingly dim and drained of colors. “Jane Eyre,’’ a film shot using candles and other available light, appeared to be playing in a crypt. A visit to the Regal Fenway two weeks later turned up similar issues: “Water for Elephants’’ and “Madea’s Big Happy Family’’ were playing in brightly lit 35mm prints and, across the hall, in drastically darker digital versions.

A walk through the AMC Loews Boston Common on Tremont Street one evening in mid-April illustrates the problem: gloomy, underlit images on eight of the multiplex’s 19 screens (theaters 5, 8, 9, 10, 11, 13, 15, and 18, to be specific). These are the auditoriums using new digital projectors that are transforming the movie exhibition business, machines that entirely do away with celluloid. The “film’’ comes in the form of a software file, and the projector pumps it onto the screen at high intensity.

As if rising ticket prices and chatterbox patrons weren’t enough, moviegoers in the Boston area are being left in the dark thanks to the regular misuse of the lenses on new digital projection equipment at many of the region’s major theater chains. But almost no one at the theaters or their corporate headquarters is willing to talk about it.

If they talk about it at all, the chains claim that individual multiplex managers are the ones to decide whether to switch out the 3-D lens for 2-D showings. Dan Huerta, Vice President of Sight and Sound for AMC, the second-biggest chain in the US, said, “Obviously, if we know there’s a 2-D movie that’s going to be shown through a 3-D lens, we would have to make sure that the manager or a technical person could make the call.’’

A spokeswoman for Norwood-based National Amusements, the ninth-largest chain in the country, responded to detailed questions by saying “We are not experiencing any issues with the Sony 4K systems.’’

After multiple requests, Sony declined through a spokesman to respond to questions about its digital projection equipment. Executives at the major theatrical chains are equally unwilling to discuss the matter. When contacted for this article, a spokesman for Regal, the nation’s largest multiplex operator, e-mailed the following statement: “Patron response has been overwhelmingly positive toward digital cinema and all of the associated entertainment options provided by this technology.’’

So why aren’t theater personnel simply removing the 3-D lenses? The answer is that it takes time, it costs money, and it requires technical know-how above the level of the average multiplex employee. James Bond, a Chicago-based projection guru who serves as technical expert for Roger Ebert’s Ebertfest, said issues with the Sonys are more than mechanical. Opening the projector alone involves security clearances and Internet passwords, “and if you don’t do it right, the machine will shut down on you.’’ The result, in his view, is that often the lens change isn’t made and “audiences are getting shortchanged.’’

“I walked into the room and I could barely see, and my stomach dropped,’’ the filmmaker said. “The first screening looked spectacular and the second was so dark, it was daytime versus nighttime. If they’re doing this for a big screening, I can’t imagine what they do for regular customers. That’s no way to see a movie.’’

That’s dark enough for Hollywood director Peter Farrelly to complain loudly when his comedy “Hall Pass’’ had its promotional screening in two of the Common’s theaters prior to opening this past February. Farrelly went from one screening where the 3-D lens had been removed to a second in which the lens was still on, and he couldn’t believe his eyes.

The difference can be extreme. Chapin Cutler, a cofounder of the high-end specialty projection company Boston Light & Sound, estimates that a film projected through a Sony with the 3-D lens in place and other adjustments not made can be as much as 85 percent darker than a properly projected film.

If you see two beams of light, one stacked on top of the other, that’s a Sony with the 3-D lens still in place. If there’s a single beam, it’s either a Sony with the 3-D lens removed or a different brand of digital projector, such as Christie or Barco.

Yet some theater employees scoff at that notion. “I can tell you who’s not [making the call], and it’s not the manager,’’ said one projectionist who has worked at a number of area theaters, including the Common, and who also preferred to remain anonymous. This man — let’s call him the Phantom Projectionist — believes that unspoken AMC corporate policy is to keep 3-D lenses on for 2-D showings.

“If we knew a house would be opening ‘Harry Potter’ and it wasn’t going to be 3-D,’’ he said, “I would ask them to swap the lens out and it would either go nowhere or come back with a negative from the regional technician, usually with the impression that it came from above.’’

Digital projection can look excellent when presented correctly. Go into Theater 14 at the Common, newly outfitted with a Christie 4K projector, and you’ll see a picture that is bright and crisp, if somewhat colder than celluloid. (You’ll also hear a busted sound channel that makes the actors sound tinny and faraway— but that’s a different article.)

Digital is the future — the Common plans to be all-digital by July — if only because it saves studios millions of dollars a year on processing film prints. Why, then, did Regal and AMC sign contracts in early 2009 — and National Amusements in June 2010 — with Sony, the one manufacturer whose projectors feature the external 3-D lens that’s too expensive and difficult to easily remove for 2-D showings?

The reason appears to be a basic business quid pro quo. Sony provides projectors to the chains for free in exchange for the theaters dedicating part of their preshow ads to Sony products. Unfortunately, the 3-D boom took off in late 2009 and Sony had to come up with a retrofitted solution. Said the Phantom Projectionist, “To me it feels like they’re serving people pigeon burgers and telling them its grade-A beef.’’

But what if audiences don’t notice or don’t care that they’re eating pigeon burgers? When queried by a reporter, moviegoers exiting showings at the Common recently were hard-pressed to pinpoint problems with what they’d just seen.

An older couple leaving the under-illuminated 7:15 “Win Win’’ showing thought the film looked fine; another patron praised its “creative lighting.’’ Walking out of the 7:05 showing of “Source Code,’’ Gerry Jurrens, 62, of Kingston, N.J., admitted that “in some places it seemed a little grainy, but it still looks better than what I’ve got at home.’’

Educating audiences and overcoming this inertia can be difficult. Boston Light & Sound’s Cutler said, “We have a tendency to walk in the door, we’ve paid our money, bought our popcorn, and we want to sit down and watch something. We’re loath to get up and leave because we’ve put that much effort in.’’

Still, the basic benchmarks of quality are easy to spot. In the opinion of the anonymous Deep Focus, “You should have a good, bright, clear, sharp picture and clean sound. That’s really it. It should be very easy to run a good show off digital and it stuns me that the chains can’t even manage to do that.’’

Herb Nipson agrees, and with four decades experience as a Boston-area projectionist he’s worth listening to. “I think audiences have to be a lot more proactive now,’’ he said, “because audiences are the only group that has any real concern for the quality of the image. They’re the only ones watching it.’’

Ty Burr can be reached at tburr@globe.com.

© Copyright 2011 Globe Newspaper Company.