Abstract : 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.