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 eta = TWa + e, where the components of eta 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.