Ray theory can be carried into a shadow zone using rays of complex launch angle but the search for eigenrays is usually impractical. A new approach first finds the ``measurement front,'' i.e., the continuous curve of ray depth, as a function of arrival time at a fixed range. The measurement front folds back on itself when the rays touch a caustic. The measurement front can be continued beyond the caustic into the shadow zone using rays of complex launch angle. Points at a fixed depth on the measurement front represent ray arrivals at a hydrophone. Waveforms can be calculated directly from the ray arrivals. Airy functions are used for ray amplitudes near caustics.