We present an alternative method for the complete characterization of linear passive optical devices using the measurement of the spectral power density of an intermediate interferometric transfer function. Important advantages of this method compared to other published methods are the simplicity of the interferometric setup and the fact that iterative algorithms are not required. This method makes use of spectral interferometry to implement an intermediate transfer function which is mathematically related to the optical device transfer function and whose phase response is proven to be minimum. This last fact permits the unique retrieval of the phase response from the magnitude response using the Hilbert transform (in particular, minimum-phase reconstruction algorithms). Therefore, the whole intermediate transfer function (amplitude and phase responses) can be obtained using only power measurements. Once the intermediate interferometric function has been fully established, the complete optical device transfer function is reconstructed by inverting the mathematical relation between them. We have applied the proposed method to the characterization of fiber Bragg gratings, obtaining results that are in close agreement with the original transfer functions.