  Difference-phase (or Hanbury Brown - Twiss type) intensity interference of
classical light is considered in higher orders in the intensity. It is shown
that, while the visibility of sum-phase (NOON-type) interference for classical
sources drops with the order of interference, the visibility of
difference-phase interference has opposite behavior. For three-photon and
four-photon interference of two coherent sources, the visibility can be as high
as 81.8% and 94.4%, respectively. High-visibility three-photon and four-photon
interference of space-time and polarization types has been observed in
experiment, for both coherent and pseudo-thermal light.
