When Jasper Johns painted his first “Flag,” in the mid-1950s, he wanted people to look freshly at a familiar image — to be jolted into seeing it anew. One of the ironies of Mr. Johns’s subsequent fame is that his painted flags have become almost as familiar a cultural symbol as the real thing.

“Jasper Johns: An Allegory of Painting, 1955–1965,” opening Sunday at the National Gallery of Art in Washington, D.C., seeks to restore Mr. Johns’s early works to their original strangeness. Whether by coincidence or by design, the exhibition includes no flags, and no numbers — another familiar Johns motif. Instead, the show, curated by the head of modern and contemporary art at the National Gallery, Jeffrey Weiss, focuses on four motifs that Mr. Weiss argues constitute a narrative in Mr. Johns’s work between 1955 and 1965: the target, the mechanical “device,” the stenciled naming of colors, and the imprint of the body.

Mr. Johns was born in Augusta, S.C., in 1930 and moved to New York City in 1949. In the mid-1950s, after destroying much of his earlier work in order to reinvent himself, Mr. Johns began painting found images like targets, flags, and numbers — images he referred to as “things the mind already knows.” Mr. Johns’s first exhibit, in 1958 at the Leo Castelli Gallery, put both him and Mr. Castelli on the map.

It is hard to overstate the impact his early paintings had, particularly on younger artists who were looking for an alternative to Abstract Expressionism. “The work looked so different from what the prevailing style was in avant-garde circles, because it was so imagistic,” an art historian at SUNY Albany, Roberta Bernstein, said in an interview.

After World War II, many artists felt that Abstract Expressionism’s relentless focus on the artist’s own psychology no longer made sense, and Mr. Johns seemed to offer new possibilities for the future of painting. The artist Ed Ruscha described to the late Kirk Varnedoe, who curated Mr. Johns’s 1996 retrospective at the Museum of Modern Art, the liberation he experienced upon encountering Mr. Johns’s work for the first time. “It was the atomic bomb of my education,” Mr. Ruscha said.

“Johns, along with Rauschenberg, helped open doors to a new artistic sensibility,” Ms. Bernstein said. “Many of the directions that emerged in the ’60s were very strongly influenced by his work.”

Among those influenced by him was Andy Warhol, who appropriated pop-culture images like Campbell’s Soup cans. Minimalist and post-minimalist artists, such as Richard Serra, Robert Morris, Eva Hesse, and Mel Bochner, were inspired by Mr. Johns’s attention to the artwork as a physical object.

Mr. Weiss chose the 83 works in this show based on the narrative he wanted to draw out, which has to do with Mr. Johns’s attempt to find a path between figuration and abstraction. “He does that by using ready-made images like the target, which is both a familiar sign and an abstract form,” Mr. Weiss said, “and also by focusing on quasi-mechanical procedures: stenciling, scraping, imprinting.”

The four motifs Mr. Weiss picked out emerge in Mr. Johns’s work sequentially: Around 1960, targets led to paintings that include the very “device” — the compass arm — used earlier to trace the concentric circles. Mr. Johns also began using stenciled words, usually names of colors. In 1962, he did a series of drawings that he created by imprinting parts of his own body — particularly his hands and face. He covered them with baby oil, then pressed and rolled himself against a sheet of draftsman’s paper tacked to the wall. He applied charcoal to the paper, which adhered to the oil, so that a ghostly human image emerged.

“He’s reintroducing the figure in a very interesting and original way,” Mr. Weiss said. “It makes its way into the work through this mechanical process, but the result is not mechanical at all; it’s quite haunting.”

The appearance of Mr. Johns’s spectral face is a startling moment in his oeuvre, and makes clear that a simple contrast between his work and that of the Abstract Expressionists — their expressivity versus his impersonality and restraint — would be wrong.

“With Johns, it seemed that there was a distancing from that kind of self-expression — a focus on issues about perception, and a way to look at the world that seemed to deflect attention away from the artist’s feelings,” Ms. Bernstein said. “But I think Johns himself reflecting upon that work understands, as do most people, that it is very much about the artist,” she continued. “It is about self-expression, just in a different way.”

The show in Washington will offer a window on this critical time in Mr. Johns’s work, and in American painting in general. “It’s an amazing show because they’ve gathered such key works from that first 10 years,” Ms. Bernstein said. “It will be quite an opportunity to see the strength of his early period.”