Schmidt, who was born on the island of Naissaar, in Estonia, received little education. After working in Gothenburg, Sweden, he went in 1901 to study engineering at Mittweida in Germany, near Jena. He set up his own workshop in 1904 in Mittweida and manufactured high-grade mirrors to be used in telescopes. He also built some reflecting telescopes, including one for the Potsdam Astrophysical Observatory, and set up his own observatory. In 1926 he moved to the Hamburg Observatory in Bergedorf. As a master craftsman he worked unaided even though he had lost his right arm as a boy. He was also an alcoholic and claimed to have his best ideas after prolonged drinking bouts. He died in a mental hospital.

His name is known to all astronomers as the designer of one of the most basic items of observatory equipment, the Schmidt telescope. This was built to overcome some of the penalties inherent in the design of the large parabolic reflectors like the Mount Wilson 100-inch (2.5-m) telescope. Parabolic mirrors are used rather than spherical ones in telescopes to correct the optical defect known as spherical aberration and thus allow the light from an object to be accurately and sharply focused. This accurate focusing only occurs, however, for light falling on the center of a parabolic mirror. Light falling at some distance from the center is not correctly focused owing to a different optical distortion in the image, known as coma.

This limits the use of parabolic reflectors to a narrow field of view and thus precludes them from survey work and the construction of star maps. Schmidt replaced the primary parabolic mirror with a spherical mirror, which though coma-free did however suffer from spherical aberration, thus preventing the formation of a sharp image. To overcome this fault Schmidt introduced a ‘corrector plate’ through which the light passed before reaching the spherical mirror. It was so shaped to be thickest in the center and least thick between its edges and the center. In this way a comparatively wide beam of light passing through it is refracted in such a way as to just compensate for the aberration produced by the mirror and produce an overall sharp image on a (curved) photographic plate.

Schmidt's first hybrid reflector/refractor was ready and installed in the Hamburg Observatory in the early 1930s. Observatories have since used the Schmidt telescope to photograph large areas of the sky. The whole sky has now been surveyed with these instruments and the results, which include the very faintest objects down to a magnitude of 21, are published in the Palomar Sky Survey and the Southern Sky Survey.