She was born in New York City in 1796 as Sarah Porter Stima. Although little is known about her, it is believed that she married Harlow Mather in 1819 and that they had a son in Brooklyn, New York, where her family lived for the rest of her life, and where her invention, the underwater telescope or periscope, was produced.
Later, he improved the design to give it a more modern approach. Through the design thinking process, he worked to create an object to examine what is beneath the surface of seawater, for example the hull of ships and any submerged objects.
This device, patented by Sarah Mather in April 1845, consisted of a turpentine lamp in a glass globe that was submerged in water. The device allowed the hull of a ship and other submerged objects or details to be examined from the deck. “The nature of my invention consists in constructing a tube with a lamp attached to one end of it which can be sunk in water to illuminate objects, and a telescope for viewing and inspecting them underwater…” She herself assumed these benefits: “...for examining the hulls of ships, for examining or discovering objects underwater, for fishing, for blasting rocks to clear channels and other uses”. In July 1864 she introduced an “Improvement in Underwater Telescopes” to her previous invention, US Patent No. 43,465. Its innovation was key in the American Civil War, as it allowed shipwrecks to be detected, helped the North discover the Confederates' maritime movements, and also participated in search missions for missing ships.
Currently, there are multiple uses for the device that Sarah Mather invented. Underwater telescopes continue to be used in search and rescue missions for boats and planes that land at sea. They are also used in shipwreck discovery missions in history and have revealed many historical remains of the past. And it has also been applied to maritime research and the development of the naval industry. Likewise, they are used in the military field due to being able to anticipate the movement of submarines, missiles and other potential threats. Currently, the concepts of the underwater telescope are being applied in medicine. Part of the endoscopic technology of modern underwater telescopes has been used in holograms, which serve as a visual representation of the interference pattern.