Micrograting design to retrieve IR spectra in the long wavelength region

To design microgratings, which can be used for correlation spectroscopy in the 725–1450 cm^?1 range, a gradient searching Davidon–Fletcher–Powell (DFP) algorithm was successfully applied to retrieve target spectra of SF₆, ethylene, SO₂, and NH₃. Owing to a unique fit parameter treatment, the DFP algorithm produced stable convergence for the minimization and provided superior matches between the diffraction spectrum and the target spectrum to those provided by the phase retrieval algorithm (PRA) or the extended PRA. In addition, the diffraction efficiencies for the micrograting line profiles obtained from the DFP algorithm were at least an order of magnitude greater than those from the PRA or the extended PRA. We also evaluated the effects of number of line element reduction or the dimensional errors in the line elements on the spectrum shape. The line depth error would not change the main spectral features but increase noise features. However, the line width error affects more sensitively the spectrum shape and the diffraction efficiency.