In this paper we prove that the recently introduced method of signal apparition optimally separates signals from interfering sources recorded during simultaneous source seismic data acquisition. By utilizing a periodic sequence of source signatures along one source line, that wavefield becomes separately partially visible in the spectral domain where it can be isolated from interfering signals, processed, and subtracted from the original recordings, thereby separating the wavefields from each other. Whereas other methods for simultaneous source separation can recover data in triangle-shaped region in the spectral domain, signal apparition allows for the exact separation of data in a diamond-shaped region that is twice as large thereby enabling superior reconstruction of separated wavefields throughout the entire data bandwidth.