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Refractive-index profile and modal dispersion in single-mode optical fibers are computed from the measured far-field exit radiation pattern of the fundamental mode. Instead of Fourier transforming the far-field numerically, the near-field is calculated by fitting a series of Gauss-Laguerre functions to the far-field. The coefficients of the series are simply found by matrix inversion and determine directly the refractive-index profile and the modal dispersion within the framework of a scalar theory. The main advantage of the proposed method lies in its inherent insensitivity against random measurement errors. Further possible applications (determination of cutoff wavelength, near-field and refractive-index profile of integrated-optical waveguides with rectangular cross section) are briefly discussed.