This paper analyzes the systematic errors in Hadamard transform optical instruments caused by moving masks, incorrect mask alignment, faulty mask fabrication, missing data, diffraction, etc. and describes techniques for reducing or eliminating these errors. In a great many cases the behavior of the instrument can be characterized by a single matrix equation of the form 71 = TWa + e, where the components of 71 are the measurements, T is a matrix characterizing the instrument, W specifies the mask configurations, a is a vector containing the unknown spectral intensities, and the components of e are small random errors.

We have constructed a Hadamard Transform Spectrometer (HTS) which simultaneously obtains fifteen infrared spectra, each having 255 spectral elements.Spectra are obtained essentially in real time through use of a minicomputer with 8K words of memory and a CRT display. This permits operation of the instrument in the field.