The idea of halftone printing originates from William Fox Talbot. In the early 1850s he suggested using "photographic screens or veils" in connection with a photographic intaglio process. Several different kinds of screens were proposed during the following decades. One of the well known attempts was by Stephen H. Horgan while working for the New York Daily Graphic.
Halftone Botanicals by Tristan Benedict-Hall
They published "the first reproduction of a photograph with a full tonal range in a newspaper" on March 4, 1880 (entitled "A Scene in Shantytown") with a crude halftone screen.
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