  We present FIR and sub-mm images of the Crab nebula, taken with ISOPHOT on
board ISO and with the SCUBA on the JCMT. The ISOPHOT observations were made at
60, 100, 170 micron, with FWHM of equivalent area Gaussian beams of 44, 47 and
93 arcsec, respectively. The 850 micron SCUBA image has a Gaussian FWHM of 17
arcsec. The 60 and 100 micron images show clear excess of emission above that
expected from an extrapolation of the synchrotron spectrum of the Crab nebula
from lower frequencies. The ISOPHOT images reveal that about half this excess
is attributable to two peaks, separated by approximately 80 arcsec. We also
present spectra taken using the LWS on board ISO, which show that the FIR
excess is not due to line emission. The lower resolution 170 micron image does
not show any excess emission. These findings are consistent with a picture in
which the FIR excess is due to emission from a small amount of warm dust which
radiates predominantly at 60 and 100 micron micron but not at 170 micron, and
which is superimposed on a synchrotron spectrum which gradually steepens
towards shorter wavelengths throughout the FIR and MIR spectral range. The dust
geometry is consistent with a torus of diameter approximately 0.8 pc created by
the supernova progenitor, superimposed upon a broadly distributed component
which may be supernova condensates in the filaments. The dust-to-gas ratio in
the filaments is comparable to the interstellar value. To study spectral index
variations in the radio synchrotron emission we compared the 850-micron image
with a 20-cm VLA image. These images are very similar, implying that there is
little variation in spectral index across the face of the remnant between these
wavelengths.
