  We present a power spectrum analysis of the Herschel-SPIRE observations of
the Polaris flare, a high Galactic latitude cirrus cloud midway between the
diffuse and molecular phases. The SPIRE images of the Polaris flare reveal for
the first time the structure of the diffuse interstellar medium down to 0.01
parsec over a 10 square degrees region. These exceptional observations
highlight the highly filamentary and clumpy structure of the interstellar
medium even in diffuse regions of the map. The power spectrum analysis shows
that the structure of the interstellar medium is well described by a single
power law with an exponent of -2.7 +- 0.1 at all scales from 30" to 8 degrees.
That the power spectrum slope of the dust emission is constant down to the
SPIRE angular resolution is an indication that the inertial range of turbulence
extends down to the 0.01 pc scale. The power spectrum analysis also allows the
identification of a Poissonian component at sub-arcminute scales in agreement
with predictions of the cosmic infrared background level at SPIRE wavelengths.
Finally, the comparison of the SPIRE and IRAS 100 micron data of the Polaris
flare clearly assesses the capability of SPIRE in maping diffuse emission over
large areas.
