Abstract: A method includes extracting phase due to fringe count error (FCE) in spectra formed by an interferometer. The exemplary method includes the steps of: (a) forming an earth scene spectrum; (b) forming a background reference spectrum; and (c) forming a phase extraction function, Rk, where k is a kth channel of the interferometer. The phase extraction function is formed from the earth scene spectrum and background reference spectrum. The method may also include the steps of (d) using recursive least squares (RLS) to extract phase from the Rk function; and (e) providing the extracted phase to a user to correct the FCE. Step (c) may include forming a term in the Rk function that includes a positive or a negative sign of a square root. Step (d) may include determining whether the sign is negative or positive using the RLS.