Although he is one of the most important American photographers of his generation, Lee Friedlander remains an enigma. Born in Washington in 1934, he came to prominence in 1967 in the “New Documents” exhibition at the Museum of Modern Art, which featured his work alongside that of Garry Winogrand and Diane Arbus.

All three photographers were inheritors of the documentary photography tradition. This genre of photography began during the 1930s, when image-makers such as Walker Evans and Berenice Abbott were inspired to document the Great Depression’s bleak and shocking counter-narrative to the American Dream. Influenced by the ideas of modernism, these photographers focused on the gritty, unromantic, quotidian detail of the world around them.

Arbus’s illuminations of social misfits and Winogrand’s wide-angle snapshots of edgy, agitated crowd scenes clearly belong to this genre of social reportage. Superficially, Friedlander fits in there too. With a repertoire of subjects ranging from street scenes to nudes, self-portraits and factory workers, he has spent decades documenting the warp and weft of the American vernacular.

Yet his extraordinary formal composition has always set him apart from his peers. The contrast of a streetlamp with a skyscraper and a telegraph wire; the play of light and shade on a shop window, the icy zigzag of a woman’s naked body against a dark rectangle of blanket – in their rhythmic juxtaposition of plane, line and angle his images borrow the vocabulary of avant-garde abstraction. At times, they show a debt to the formal play of cubism and constructivism; at others they gesture towards a neo-Dadaist anarchy of signs.

His new exhibition reveals what happens when Friedlander turns his painterly, avant-garde lens on the landscapes of North American parks. Featuring 36 photographs taken over a 20-year period, the show is devoted to the public spaces, including Central Park and Brooklyn’s Prospect Park, designed by Frederick Law Olmsted.

Considered North America’s leading 19th-century landscape architect, Olmsted possessed a quasi-utopian vision. He believed that access to public green spaces was a human right in a democracy and that the pastoral, when properly designed, could nourish and heal urban communities.

Decrying the tendency to construct parks so prim and manicured they were, in his words, “natty as a silk hat”, Olmsted created rolling spaces in which woods, lakes, streams and lawns wove together into an organic entity. This naturalistic approach led Olmsted himself to be considered an artist. “He paints with lakes and wooded slopes, with lawns and banks and forest-covered hills, with mountain sides and ocean views,” said Daniel Burnham, his friend, fellow architect and urban planner. More intriguingly, in 1973 the land artist Robert Smithson wrote an essay in which he implied that Central Park, in its dynamic decay and evolution over time, was a forerunner of conceptualism. Certainly Olmsted’s landscapes, with their sweeping slopes, substantial trees, curved bridges and mirror-like lakes, provide Friedlander with ample opportunities for the quietly dramatic compositions he loves. Perhaps the most rigorously formal is “Central Park, NYC, 1994”. Bisected by a sinuous, wrought-iron bridge, the stark bulk of a tree trunk skims the edge of a distant skyscraper, creating a powerful contrast of horizontals and verticals which recalls the quirky geometry of Bauhaus design. Also meticulously constructed is “Cherokee Park, Louisville, Kentucky 1994”, which is dominated by a thick, graffiti-carved branch which unspools out of a stump like a neo-Dadaist message.

Friedlander’s genius in capturing and cropping images permits him to transform natural shadows into spectacular forms. Here he is perfectly served by his technique of shooting in black and white on gelatin-silver print, a method that results in silky, metallic monochromes ideal for rendering contrasts of light and shade. A crazy paving-style lattice of shadows is created by a leafless tree standing in splendid isolation on a grassy knoll; another tree – although it does not itself appear – casts a sinister design like a multi-fingered palm print on an empty slope; a pointilliste canopy of horse chestnut leaves, like the upper half of an abstract diptych, reaches down to the panel of light-dappled grass trapped in its shade.

Yet Friedlander, unlike, say, Ansel Adams, never sacrifices nature’s material reality – its innate tattiness – for the sake of dramatic form. Even at their most artistic, his pictures brim with nature’s detritus: leaves lie scattered on the ground; trees are gnarled and pockmarked with crevices. Often, trees function as vertical focal points, but some works are devoid of any obvious centre.

Lacking the composed theatre evident elsewhere, these photographs highlight those pockets of the natural landscape we see but do not notice.

Lyrical and sumptuous though his images are, it’s clear that Friedlander’s relationship with Olmsted’s parks is ambiguous. In a brief foreword to the catalogue, he describes them as “wild oases in the confines of cities”. Yet Olmsted’s vision encompassed structured spaces for human recreation: playgrounds, boating lakes, football fields, cafés. Interesting, then, that there is not one human being in Friedlander’s pictures.

Buildings are, however, occasionally present. Perhaps the most memorable photograph of all is “Central Park, New York City, 1993”. A patch of grass, shot from below to seem unnaturally tall and field-like in its expanse, is framed by full-leafed trees. Yet this image of rampant, flourishing nature butts up against an abrupt, unforgiving bank of skyscrapers. Ultimately, Friedlander confronts the viewer with a landscape charged with tension, not only between modern cities and their interior jungles but also between artists and the subjects they struggle to contain.

‘Lee Friedlander: A Ramble in Olmsted Parks’ is at The Metropolitan Museum of Art, New York, until May 11. www.metmuseum.org