We present a method to analyze binary-lens microlensing light curves with onewell-sampled fold caustic crossing. In general, the surface of chi^2 showsextremely complicated behavior over the 9-parameter space that characterizesbinary lenses. This makes it difficult to systematically search the space andverify that a given local minimum is a global minimum. We show that for eventswith well-monitored caustics, the caustic-crossing region can be isolated fromthe rest of the light curve and easily fit to a 5-parameter function. Four ofthese caustic-crossing parameters can then be used to constrain the search inthe larger 9-parameter space. This allows a systematic search for all solutionsand thus identification of all local minima. We illustrate this technique usingthe PLANET data for MACHO 98-SMC-1, an excellent and publicly availablecaustic-crossing data set. We show that a very broad range of parametercombinations are compatible with the PLANET data set, demonstrating thatobservations of binary-lens lightcurves with sampling of only one causticcrossing do not yield unique solutions. The corollary to this is that the timeof the second caustic crossing cannot be reliably predicted on the basis ofearly data including the first caustic crossing alone. We investigate therequirements for determination of a unique solution and find that occasionalobservations of the first caustic crossing may be sufficient to derive acomplete solution.
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