Temporal soliton molecules in dispersion-managed fibers are characterized with an advanced FROG technique. This technique reveals phase and power profiles for complex pulse shapes where conventional techniques fail.We present an experimental characterization of amplitude and phase profiles of soliton molecules in optical fibers. Soliton molecules, recently discovered bound states of fiber-optic solitons in dispersion-managed fibers [1], hold potential for increasing the ultimate data-carrying capacity of fibers. Their binding mechanism crucially depends on phase dynamics; however, in previous art no direct phase information was accessible. Established techniques for amplitude-and-phase characterization like FROG [2] and its numerous variations [3] turn out to be inadequate for assessment of these complex pulse shapes: the algorithms do not converge in most cases.We therefore employ blind-FROG [3] combined with a novel algorithm called VAMPIRE (very advanced method of phase and intensity retrieval of E-fields) [4,5]. This procedure yields useful output every single time where conventional FROG demonstrably fails. We thus obtain, for the first time, useful phase and chirp information about soliton molecules experimentally. At the same time, our experiment constitutes the first realistic test of the VAMPIRE technique which is found to exhibit superior performance.Today's advanced fiber-optic transmission lines make increasing use of so called dispersion-managed fibers, i.e. fibers in which segments of positive and negative group velocity dispersion alternate periodically. Typically, data are coded in an RZ (return to zero) format in which a short light pulse sits in a time slot several times wider so that neighboring pulse interaction is avoided. We demonstrated recently both numerically and experimentally that at a certain much closer spacing two such signal pulses can form a stable bound state provided they are in antiphase. This compound has been called a soliton molecule [1].The power profile of this structure by necessity has a π phase jump and a central zero; one can therefore also think of the compound as being composed of two bright solitons with an intermediate dark soliton. Note that this property is also most demanding for a full field reconstruction. FROG typically fails when there are zeroes. It is presently unclear whether interferometric methods like SPIDER [6] can present a viable alternative: They seem to have difficulties with π phase jumps, and require either peak powers not available in this experiment, or extended averaging times over which interferometric phase stability is hard to maintain here.As we conducted systematic experiments to further characterize the range of existence and the stability properties of these soliton molecules, it became evident that the core reason for the binding mechanism resides in the phase dynamics inside the pulse. Also, an analytical model has been formulated [7] in which the pulse's chirp plays the central role. To get access to phase information, we therefore ...