Fig. 4

Unique identification of prolate pill-shaped structures. a Measured image (intensity in arbitrary units) and b matching simulation result of the wide-angle diffraction of a pill-shaped prolate droplet (logarithmic intensity in arbitrary units, color bar applies also to d–f). The structure shape and orientation are visualized in yellow. The optical axis of the extreme ultraviolet beam is directed into the image plane, the tilt angle between the symmetry axis of the particle and the optical axis is 35°; the semi-minor axes a = b = 370 nm and the semi-major axis c = 950 nm; for optical parameters see “Methods” section. c Illustration of the origin of bent streaks occurring when a tilted rod-type structure diffracts the light. The constructive interference is analogous to the specular reflection at the surface of a macroscopic rod. Two particular bundles of constructively interfering rays are explicitly sketched, please note that the different ray colors do not refer to wavelengths, but are applied to facilitate distinction. d Simulated wide-angle diffraction image of a wheel-shaped oblate particle (semi-major/-minor axes as in b, tilt angle of 80° between the symmetry axis and the optical axis, which is directed into the image plane). If the oblate particle’s symmetry axis is neither oriented along the optical axis nor perpendicular to it, the diffraction patterns exhibit straight streaks to only one side. e, f Comparison of simulated wide-angle diffraction images of a prolate e and an oblate structure f aligned to the scattering plane, i.e., at 90° tilt angle between the symmetry axis and the optical axis, other parameters as in b, d. Though the 2D projections are similar and the 2D outlines identical, the intensity distributions of the straight streaks are clearly different and decay much faster for wheel-type than for pill-type shapes