We show that two superimposed time-and-space-domain holograms in a per
sistent spectral hole-burning material can produce destructive interfe
rence, even if the path-length difference of the writing beams is cons
tant. The cancellation of the amplitudes in the -1 diffraction order o
ccurs when the two holograms have specially chosen spectral envelopes
that represent a pair of complementary functions. By controlling the s
pectrum of the holograms we are able to perform coherent subtraction a
nd addition of images.