A new methodology able to model and reconstruct the transverse trace space of low-emittance electron\nbeams accelerated in the bubble regime of laser-plasma interaction is presented. The single-shot\nmeasurement of both the electron energy spectrum and the betatron radiation spectrum is shown to\nallow a complete measurement of the transverse emittance, including the correlation term. A novel\ntechnique to directly measure the betatron oscillation amplitude distribution is described and tested at the\nSPARC-LAB test facility through the interaction of the ultrashort ultraintense Ti:Sa laser FLAME with a\nHe gas-jet target. Via the exposed technique the beam transverse profile is also retrieved. From the study of\nthe electron transverse dynamics inside the plasma bubble, the nonlinear correlation between the betatron\namplitude and the divergence, i.e. the angle with respect the acceleration axis, is found. The angular\ndistribution of the electron beam inside the bubble is retrieved. The knowledge of the trace-space density\nallows a more accurate measurement of the transverse emittance with respect to previous paradigms.
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