Film posters are an outlier in the movie advertising matrix. “When the trailers are no longer played and the promotional campaign winds down, the poster remains,” outlines Poster House, the New York museum hosting an exhibition celebrating the work of Dawn Baillie. Of course, not all posters are born equal. Only the strongest visuals will become lodged in our collective consciousness long after they were first shown, and Baillie has more than a few of these to her name.

Curated by Angelina Lippert, The Anatomy of a Movie Poster charts Baillie’s four decades in the industry, exploring the evolutions in her own work as well as the trends, tastes and developments that came and went in the wider industry.

Having grown up in Hollywood, Baillie was immersed by proxy in cinema culture more than most. Yet she was introduced to the art of film poster design like most of us: as an audience member. It was the design for The Omen, released in 1976, that sold it to her, and after graduating from Otis Art Institute of Parsons School of Design, Baillie cracked her way into the industry when she joined Seiniger Advertising.

During the three years she spent working her way up there, Baillie’s projects included designing the teaser poster for Indiana Jones and the Last Crusade, as well as the famous theatrical release poster for Dirty Dancing.

Baillie’s talent was noticed by the industry, which landed her a full time art director position at the agency Dazu, where she created one of the most iconic posters of all time for Jonathan Demme’s The Silence of the Lambs. The poster features a stark portrait of Jodie Foster whose mouth is covered by a hawkmoth, photographed from a specimen loan from the Natural History Museum of Los Angeles, with tiny nude figures superimposed onto the insect’s back in the shape of a skull.

Unusually, Baillie worked on the poster in almost complete isolation, save for the computer technician who aided with the computer finishing, a new process at the time. The differences between the analogue and digital techniques are shown in two versions of the poster on display at the exhibition, which also presents less widely seen alternative teaser poster designs in different colourways featuring Foster and co-star Anthony Hopkins.

Baillie’s introduction to computer-based methods is something she took into her next venture, when she broke away to form BLT with Dazu colleagues Clive Baillie (who she later married) and Rick Lynch, making her the first woman founder in a US print agency.

At BLT, Baillie’s portfolio of posters includes The Truman Show, Zoolander, Chicago, Little Miss Sunshine, True Grit, and Birdman. She has also been a frequent collaborator of Wes Anderson, having worked on posters for The Royal Tenenbaums, The Grand Budapest Hotel, Isle of Dogs, and Asteroid City.

While the exhibition is filled with many recognisable poster designs, it also reveals the less widely known rationale behind the design decisions.

Although what we see has come from Baillie and her collaborators, the show captures the various requirements imposed by the industry – from actors’ contractual obligations to stipulations made by the Motion Picture Association – which determine which designs are used over others. It shows the inner workings of a complex machine that’s typically hidden from audiences, and Baillie’s staunch dedication to crafting powerful, remarkably flexible film poster advertising in the face of it all.

The Anatomy of a Movie Poster is at Poster House, New York until September 8; posterhouse.org