Fig. 2: Bragg ptychography and sampling principles.

a In the (x, y, z) laboratory frame, a finite size beam illuminates a crystalline thin film sample in Bragg geometry, while a 2D detector collects the coherent diffracted pattern, so that the incident and exit wave vectors (k_i and k_f, respectively) fulfil the Bragg condition. The 3D information is acquired by rotating the sample in the vicinity of the Bragg angle θ_B, along the rocking curve, i.e. at the θ₁ …θ_N positions. The intensity information is recorded as a function of (q₁, q₂, and q₃), the components of the wave-vector transfer q. Using a recently developed formalism⁴⁰, this sampling depicts a direct space frame (r₁, r₂, r₃). It implies sampling rates along the three directions, that ensure that the illuminated volume (delimited by the green line) is contained within the numerically retrieved direct space (shown as an orange rectangle). The probe frame is also defined as (p₁, p₂, p₃). b A typical hard x-ray probe profile presented at the focal plane and (c) numerically propagated along the beam axis (see Methods). The dashed rectangle corresponds to the accessible region based on the parameters used during the acquisition of the BP dataset. The full extent of the probe, visible outside this rectangle, is only retrieved through the implementation of the angular up-sampling approach. Along the propagation direction, note the probe invariance over distances as large as a few hundreds of micrometres. The hue rendering colour scale is indicated in (b). d Sufficiently small sampling steps of Δθ are needed to fulfil the numerical sampling relation. This relation is depicted in the plot, as a function of the probe size W and the sample thickness T.