Anna Atkins? Constance Talbot?
Well, according to Roddy Simpson, a former secretary of the Scottish Society for the History of Photography and currently a photographic researcher at Glasgow University, he thinks the accolade should be bestowed upon Jessie Mann, who lived in Edinburgh in the 1840s.
Miss Mann, from Perthshire, was an assistant to Edinburgh-based photographic pioneers David Octavius Hill and Robert Adamson, may have been the first female to use photographic machinery to capture images of people and places.
You can read the rest of the report here.
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Perhaps another candidate to consider is "Mrs. Fletcher." According to Graham Garrett in his Biographical Index of Daguerreotypists in Canada, 1839-1871, Mrs. Fltecher was active in Canada as early as 1841. On her arrival with her husband in Pictou, Nova Scotia in July, 1841, she describes herself in an advertisement as a "Professor and Teacher of the Photogenic Art" and declares she was "prepared to execute Daguerreotype minatures in a style unsurpassed by any American or European Artist." Garrett goes on to state that a Mrs. Fletcher was "experimenting with the daguerreotype process in Cambridgeport, Massachusetts at an early period, (ca. 1839-40), according to an undated manuscript memoir written sometime later by the prominent Boston daguerreotypist, A. S. Southworth.