A new method for optically encoding the spectral output of multislit spectrometers is proposed. It is based on sequential measurements of the total intensity of light in combinations of selected spectral bands. The resulting encoded optical information is obtained as a set of simultaneous linear algebraic equations, and spectrum reconstruction is accomplished through the use of matrix inversion techniques. This encoding method avoids the problems associated with frequency transform encoding, because it is not based on the usual Fourier or Fresnel transforms. Rather, it makes use of the theory of simultaneous linear algebraic equations.
John A. Decker, Jr. and Martin O. Harwitt, "Sequential Encoding with Multislit Spectrometers," Appl. Opt. 7, 2205-2209 (1968)