Fig. 1. Spectral diversity in diffraction. (a), (b) A binary object is illuminated by a beam containing the 27th and 29th harmonics (at 38.4 and 35.7 nm wavelength), either (a) with a flat intensity and phase or (b) with order-dependent OAM. (c), (d) Difference of the monochromatic diffraction patterns between the two wavelengths (I35.7 nm−I38.4 nm) for (c) flat and (d) OAM beam illumination. The dynamic range of the camera is set to ≈20 and 15 bits for the flat beam and OAM beam, respectively, such that the number of photons in the incoherent sum of the monochromatic diffraction patterns is equal to 2.27×108 in both cases.

Fig. 2. Scanning diversity and reconstruction quality of simulated data sets. (a) Logarithmic scale diffraction patterns are shown for beams with radii of curvature R=∞, R=7.5  mm, and R=4.2  mm, all illuminating the center of the object at scan position 0. (b) Three monochromatic probes at 38.25 nm wavelength with increasing quadratic phase and identical Gaussian intensity profile (30.5 μm 1/e2 diameter). (c) Diversity metrics D1norm, D2norm, cosine, and JSD by comparing diffraction patterns between adjacent scan positions for a scan grid with the first 20 scan points, as a function of the quadratic phase of the probe. (d) The example FRC by comparing independent reconstructions within the data sets of three monochromatic probes. The intersection of FRC curves and 1 bit threshold line determines the object resolution. (e) Reconstruction quality calculated from the FRC as a function of the quadratic phase of the probe. The colored dots are extracted from (d).

Fig. 3. Experimental setup. (a) The driving NIR laser is focused by an f=300  mm focal length lens into an argon gas jet. An Al filter blocks the fundamental, and the high harmonics are refocused by a pair of broadband multilayer mirrors onto the sample. A CCD camera is placed approximately 10 cm from the focal plane. (b), (c) Intensity profile of the driving laser at the gas jet plane for generating (b) Gaussian and (c) OAM XUV beams. (d)–(f) Polychromatic beam intensities for (d) Gaussian, (e) vortex, and (f) structured beam, computed upstream from the sample plane at distances 8.1, 6, and 1.625 mm (mask plane), respectively. (g) Measured and reconstructed spectrum of the XUV radiation after the mirrors, plotted along with the reflectivity curve of the XUV mirrors. (h) Scanning electron microscope image of the imaging target. (i)–(k) Polychromatic diffraction patterns from illumination of the central part of the object with (i) Gaussian, (j) vortex, and (k) structured beam.

Fig. 4. Reconstruction results from ptychographic measurements for (a) Gaussian, (b) vortex, and (c) structured probes. Right: amplitude of reconstructed objects. Top left: zoomed-in areas of the object. Bottom left: dominant modes of the reconstructed probes of the five brightest harmonics. Scale bars in all figures correspond to 20 μm.

Fig. 5. Reconstruction results from synthetic ptychographic datasets with (a)–(d) Gaussian, (e)–(h) vortex, and (i)–(l) structured probes. (a), (e), (i) Amplitude of the reconstructed object. (b), (f), (j) Zoomed-in area of the object group 9/elements 5 and 6. (c), (g), (k) Probe reconstructions of the five brightest harmonics. (d), (h), (l) FRC computed by comparing object reconstructions with true object. Scale bars in all figures correspond to 20 μm.

Fig. 6. Diversity metrics for different probe beam structures. (a) Scanning diversity of polychromatic diffraction patterns. (b) Spectral diversity between diffraction patterns at wavelengths of 35.6 and 38.3 nm. (c) Spectral diversity between diffraction patterns at wavelengths of 38.3 and 41.4 nm. The solid lines indicate the mean values of comparing adjacent scan positions (for scanning diversity) or wavelengths (for spectral diversity) over the whole diffraction patterns series, while the shaded areas have a width of one standard deviation.

Fig. 7. Fisher information for different probe beam structures. The shape of the violin plots describes the distribution of Fisher information per diffraction pattern (for a total of 219 scanning positions). The Fisher information is normalized by the average information achievable with a Gaussian probe. (a) Fisher information associated with a parameter s that determines the overall size and scale of the phase object shown as an inset plot. (b) Fisher information associated with the phase ϕ of the phase object shown as an inset plot.

Fig. 8. Complementary object and probe reconstructions for experimental data. (a)–(c) Complex-valued representations of the reconstructed object for (a) Gaussian, (b) vortex, and (c) structured beams. (d)–(e) Amplitude of the partially coherent 27th harmonic (38.3 nm) beams at the object plane. (g)–(i) Amplitude and complex-valued plots of the incoherent modes of the 27th harmonic. In all complex-valued plots, brightness corresponds to amplitude and hue to phase. Scale bars in all figures are equal to 20 μm.

Fig. 9. Scanning diversity metrics for different normalization strategies. (a) Global normalization, (b) local normalization, and (c) local normalization on total flux. The solid lines indicate the mean values of comparing adjacent scan positions for scanning diversity over the whole diffraction patterns series, while the shaded areas have a width of one standard deviation. Note the different horizontal and vertical scales.

Fig. 10. Spectral diversity metrics for monochromatic diffraction patterns at 38.3 and 41.4 nm for different normalization strategies. (a) Global normalization, (b) local normalization, (c) local normalization including spectral weights, and (d) local normalization on total flux. The solid lines indicate the mean values of comparing wavelengths over the whole diffraction patterns series, while the shaded areas have a width of one standard deviation. Note the different horizontal and vertical scales.