Hecht was born in Glogau, then in the German Empire (now Głogów in Poland), the son of Mandel Hecht and Mirel Mresse. The family migrated to the USA in 1898, settling in New York City. His studies and talents led to Columbia University making him professor of biophysics in 1928.
In June 1917 Hecht received his Ph.D. and married Celia Huebschmann. Their daughter Maressa was born in 1924.
Hecht began his study into light sensitivity with clams (Mya arenaria) and insects. His specialty was photochemistry, the kinetics of the reactions initiated by light in the receptors. He made contributions to the knowledge of dark adaptation, visual acuity, brightness discrimination, color vision, and the mechanism of the visual threshold.
He spent time as a post-doctoral researcher with the group of Edward Charles Cyril Baly at the University of Liverpool, UK. Baly was a pioneer in the application of the technique of spectroscopy in chemistry, and Hecht took this further by applying it to biological molecules.
Hecht's responsibility in showing the protein character of rhodopsin was recounted by historians of protein science:
According to biographer Pirenne, Hecht was a "brilliant lecturer and expositor." Pirenne continues, 
:The lack of synthesis discernible in present-day knowledge and teaching perturbed him, and he took an active interest in all the human implications of science. He dealt with persons and ideas on the basis of their intrinsic worth,...