We present "HERA", a novel hyperspectral camera based on a Fourier-transform approach. Two delayed replicas of the optical field entering an imaging system are produced by an ultra-stable common-path birefringent interferometer that combines compactness, high delay precision, long-term stability and insensitivity to vibrations. Each pixel of a bidimensional sensor records a high contrast interferogram as a function of the relative delay between the two replicas. An appropriate Fourier transformation of the dataset produces spectrally resolved images that exhibit high contrast and spatial resolution, only limited by the lens and the sensor. Examples of application in cultural heritage will be reported.