Vibration of low amplitude imaged in amplitude and phase by sideband versus carrier correlation digital holography

Sideband holography can be used to get field images (E0 and E1) of a vibrating object for both the carrier (E0) and the sideband (E1) frequency with respect to vibration. Here we propose to record E0 and E1 sequentially and to image the product E1E0* or the correlation 〈E1E0*〉. We show that these quantities are insensitive to the phase related to the object roughness and directly reflect the phase of the mechanical motion. The signal to noise can be improved by averaging E1E0* over a neighbor pixel, yielding 〈E1E0*〉. Experimental validation is made with a vibrating cube of wood and a clarinet reed. At 2 kHz, vibrations of amplitude down to 0.01 nm are detected.