‘A teacher affects eternity,” Henry Adams once said. “He can never tell where his influence stops.” It might not stop at all if his influence has substance and his students are great enough.

Francis M. Naumann’s inaugural exhibition — in new, expanded quarters in Midtown — is a testament to Man Ray’s influence on modern photography. It pays special tribute to his formative influence on his most distinguished studio assistant, Berenice Abbott, who, in turn, taught Naomi Savage at the New School. The arc of transmission came to completion when Savage, Man Ray’s niece, later studied in her uncle’s studio.

It is an exciting exhibition not only for the quality of the vintage photographs on view but, also, for its showcasing of the critical role of inheritance in artistic practice. The fragmentations of Modernism have been noted frequently enough. Here, stress is on the continuities of a common practice — variable but still reciprocal — that discards the shibboleth of supreme originality.

Born Emmanuel Rudnitsky, Man Ray (1890-1976) wanted recognition as a painter but made his greatest mark as a professional photographer. He is often cited as the inventor of the photogram, a cameraless means of reproduction that achieves an image with the placement of an object on light-sensitive paper. The object appears in silhouette on the print.

Who really created the first photogram? Man Ray laid claim to the process by calling his photograms “rayograms.” But in the swamps of art historical dispute, the extent of his initiative is still contested. Did he discover the technique, or did László Moholy-Nagy (a “filcher,” according to El Lissitzky)? And how to account for Christian Schad, who produced his own versions of the photogram, dubbed “schadographs”? The secrecy of the darkroom remains impenetrable.

In the history of technology, coming first or establishing the claim of coming first is of prime importance. (Think of the race between Alexander Bell and Elisha Gray for a patent on the telephone.) The photogram, however, was not a technological advance. It was a playful use of an existing technology. (Man Ray’s tribute to the primacy of that technology is a 1930s photo of a monument to Nicéphore Niepce, credited with the first photographs in the 1820s. Niepce preceded and later partnered with the younger Louis Daguerre; the photo underscores the exhibition’s theme of the communal aspects of innovation.)

We can take Man Ray at his word when he said, “There is no progress in art, any more than there is in making love. There are just different ways of doing it.” In the end, what matters is not the process by which an image is produced, but the character and significance of the image itself. For that reason, “Teacher-Student/Student-Teacher” makes a splendid season opener for lovers of photography and photographers themselves.

The Man Ray selection includes marvelous, moody gelatin silver prints of Paris in the ’20s, limpid portraiture, and a sly photographic collage, in the manner of Harnett’s trompe l’oeil montages, that commemorates the artist’s friendship with surrealist poet Paul Éluard. Three rayographs represent a span of 23 years. “Black Circles with Springs” (1943) is clever but, like much surrealist imagery, oddly affectless.

The earlier “Scarf Plume” (c. 1920) was clearly a model for Savage who, judging by what is displayed here, infused the process with a poetry all her own.

Ohio-born Abbott, Man Ray’s most distinguished student, became his studio assistant in Paris in 1924. The artist was tired of assistants who thought they knew more than he did; he wanted to hire a complete blank. Abbott, who understood nothing of photography, was just right. Her superior ability to possess and record life on a majestic scale was not evident when she took the job.

Her photographs of the great and near-great are uncompromising.

Peggy Guggenheim, Abbott’s first patron, holds the head of a sharp-snouted dog at a severe angle. Despite her having financed Abbott’s independence from Man Ray, the portrait has her looking spoiled and predatory. Abbott’s iconic 1928 portrait of James Joyce is a series of visual rhymes and telling contradictions. The jaunty tilt of his hat parallels the diagonal print on his tie and the angle of his arm on a chair back; bravura is offset by his glasses (he suffered from glaucoma) and the head of his cane.

Returning to New York in 1929, the architectural contrasts of a changing city convinced Abbott that a portrait of New York was more compelling than portraits of people. The iconography of Manhattan, viewed through her camera eye, remains a testament to the vitality of her vision as much as a document of the American urban experience.

For a photographer dedicated to documentation over artistic expression, Abbott endowed her subjects with grandeur. Parallel to her resistance to the modernist “cult of non-intelligibility” represented by Man Ray was a gift for inflecting the facts of a motif with deep regard for their abstract qualities. Her “scientific” photography is breathtaking. “Swinging Wrench” (1958) is an elegant stop-action study of motion that recalls Muybridge. “Magnetic Objects” (1940s) is a magical approximation of metal sculpture formed by scissors, a pen knife, and pins hanging from a magnet.

Savage (1927-2005), who inherited her uncle’s skill as well as his patented techniques, is a surprise. She had her first exhibition at the Museum of Modern Art in 1962; three more followed over the next 16 years. It was an exhilarating start to a career that combined her uncle’s passion for innovation and experimentation with a greater capacity for emotional depth. She devised a form of photographic engraving in which the actual metal photographic plate itself is the art.

The very act of transmission is an act of renewal; the potentialities of a process, a technical approach, or a subject change with the moment and the artist. The remarkable body of work on view remains a lesson in itself to new generations of photographers.

Until October 31 (24 W. 57th St., between Fifth and Sixth avenues, 212-582-3201).