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We argue that the Scanning Tunneling Microscope (STM) images of resonantstates generated by doping Zn or Ni impurities into Cu-O planes of BSCCO arethe result of quantum interference of the impurity signal coming from severaldistinct paths. The impurity image seen on the surface is greatly affected byinterlayer tunneling matrix elements. We find that the optimal tunneling pathbetween the STM tip and the metal (Cu, Zn, or Ni) $d_{x^2 - y^2}$ orbitals inthe Cu-O plane involves intermediate excited states. This tunneling path leadsto the four-fold nonlocal filter of the impurity state in Cu-O plane thatexplains the experimental impurity spectra. Applications of the tunnelingfilter to the Cu vacancy defects and ``direct'' tunneling into Cu-O planes arealso discussed.Comment: 4 pages, 4 eps figures. Version published in PR

Impurity States and Interlayer Tunneling in High Temperature Superconductors