Fig. 5: Carbon K-edge phase imaging and phase and absorption spectroscopy of the CNT sample.

a Average over the phase images at all photon energies from a C 1 s energy stack (282–296 eV, 0.5 eV spacing) recorded using defocus ptychography with a 1.0 μm spot size. A scale factor of −1 was applied. b Phase image at 284.7 eV, corresponding to the C 1 s → π* absorption resonance. c Comparison of phase and amplitude spectra taken from the areas indicated by red and blue rectangles in (b). Linear vertical polarization, which highlights horizontal CNT, was used. The lines are smoothed versions of the measured data (points). The vertical line highlights the energy of the minimum of the C 1 s → π* phase resonance, which is 0.5 eV below the peak of the C 1 s → π* resonance in the absorption spectrum. (see Supplementary Table 1 for acquisition details).