Effect of Filter Arrangement in the Estimation Accuracy of an Imaging Spectrometer

We investigate the reason why increasing the number of basis spectra in a spectral imaging device does not always improve the estimation merit. A particular filter is not the cause of this observation but the components of the inverse of the transformation matrix which map the coefficient of the basis spectra to the color of the sample. We found out that the large magnitude of the components of the inverse of the transformation matrix results in error in the calculation of the coefficients. This error leads to a drop in the spectral estimation merit even when the number of basis spectra is increased. Therefore, it is not enough that the filter used in an imaging spectrometer is not a linear multiple of other filters and nonzero to any of the wavelengths in the range of interest. Filters must also be arranged in a sequence such that the inverse of the transformation matrix will have components with small magnitude