Potential of Attosecond Coherent Diffractive Imaging

Attosecond science has been transforming our understanding of electron dynamics in atoms, molecules, and solids. However, to date almost all of the attoscience experiments have been based on spectroscopic measurements because attosecond pulses have intrinsically very broad spectra due to the uncertainty principle and are incompatible with conventional imaging systems. Here we report an important advance towards achieving attosecond coherent diffractive imaging. Using simulated attosecond pulses, we simultaneously reconstruct the spectrum, 17 probes, and 17 spectral images of extended objects from a set of ptychographic diffraction patterns. We further confirm the principle and feasibility of this method by successfully performing a ptychographic coherent diffractive imaging experiment using a light-emitting diode with a broad spectrum. We believe this work clears the way to an unexplored domain of attosecond imaging science, which could have a far-reaching impact across different disciplines.

Figure 1

Schematic of the broadband CDI data acquisition and SPIRE algorithm. (a) A probe with a very broad spectrum is defined by a pinhole and scanned across a sample. At each scan position, a diffraction pattern is recorded by a detector. (b) SPIRE iterates between real and reciprocal space. In real space, the exit wave of the real and ghost modes at different wavelengths is obtained by multiplying probes by the object functions of the sample. In reciprocal space, the calculated diffraction patterns at different scan positions are compared with the corresponding experimental diffraction patterns, which is used to update the real and ghost modes of the next iteration. A detailed description of SPIRE is provided in the Supplemental Material [44].

Figure 2

Representative diffraction patterns and reconstructed spectra by SPIRE. (a) and (b) Representative diffraction patterns measured from a resolution and letter pattern, respectively, using simulated attosecond pulses. (c) Representative diffraction pattern of a test pattern using an LED. (d)–(f) Reconstructed spectra (in blue) of the resolution and letter pattern with simulated attosecond pulses and of the test pattern with the LED, respectively, where the true spectra are in red. The true spectrum of the LED in (f) was measured by a spectrometer.

Figure 3

Probe and spectral image reconstructions of a resolution pattern with simulated attosecond pulses. (a)–(c) The structure of the resolution pattern at 9.3, 6.72, and 6.2 nm, respectively. (d)–(i) Three representative probes and spectral images at different wavelengths reconstructed by SPIRE, respectively, where the spatial resolution is increased with the decrease of the wavelength. The full 17 probes and 17 spectral images are shown in Supplemental Material, Figs. S2(a) and S3(a) [44], respectively. Scale bars, $2\mu \mathrm{m}$.

Figure 4

Probe and spectral image reconstructions of a letter pattern with simulated attosecond pulses. (a)–(c) Absorption contrast images of the letter pattern at 7.75, 6.72, and 6.2 nm, respectively, where the $K$ edge of boron is at 6.6 nm. (d)–(i) Three representative probes and spectral images at different wavelengths reconstructed by SPIRE, respectively, where the image contrast of the “CDI” letters changes across the absorption edge. The full 17 probes and 17 spectral images are shown in the Supplemental Material, Figs. S4(a) and S5(a) [44], respectively. Scale bars, $2\mu \mathrm{m}$.

Figure 5

Probe and spectral image reconstructions of a test pattern from broadband LED diffraction patterns. (a)–(f) Three representative probes and spectral images reconstructed by SPIRE at 662.5, 550, and 437.5 nm, respectively. The full 17 probes and 17 spectral images are shown in Supplemental Material, Fig. S8 [44]. Scale bars, $200\mu \mathrm{m}$.