Inverse problems are frequently encountered in many fields of natural science and engineering, e.g., retrieval of atmospheric parameters from remote sensing spectral measurements is a typical inverse problem. Inverse problems are well known to be ill-posed because small perturbations in the measured data can lead to extreme perturbations of the retrieved solution. Physically meaningful solutions can be found by regularization, i.e., by introducing additional information, e.g., by using quadratic constraints. The L-curve criterion is a convenient tool to automatically find the optimal weighting of this constraint. A numerically robust implementation delivers additional diagnostics of the inverse problem and allows an efficient implementation of the L-curve criterion. After solving the inverse problem the quality of the solution has to be investigated. Thus, a detailed assessment of all error sources is mandatory. The methods for solving inverse problems and the detailed error analysis developed in this work are applied to the determination of the middle atmospheric OH concentration from far infrared spectra. In the theoretically oriented ESA study PIRAMHYD three satellite based limbsounding instruments (Fabry-Perot interferometer, Fourier transform spectrometer, and heterodyne spectrometer) were compared. The higher sensitivity of low spectral resolution instruments to systematic error sources was a major result of this study. Furthermore pointing error was identified to be the dominant error source for all instruments. In the second application data measured by the vertical sounding heterodyne spectrometer THOMAS flown in the MAHRSI validation campaign were analysed. Agreement of MAHRSI mesospheric and upper stratospheric OH measurements and the OH concentration determined by THOMAS within the overall error of the THOMAS measurements has been shown. (orig.)103 refs.Available from TIB Hannover: RA 437(1999-48) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman