Penghan Lu (Jülich / DE), Shengbo You (Sheffield / GB), Thomas Schachinger (Vienna / AT), Frederick Allars (Sheffield / GB), Yan Lu (Jülich / DE), Rafal Edward Dunin-Borkowski (Jülich / DE), Andrew M. Maiden (Sheffield / GB; Didcot / GB)
Abstract text (incl. figure legends and references)
Ptychography measures a correlated matrix of diffraction patterns with sufficient real space overlapping between adjoining data, and reconstructs both amplitude and phase of the object as well as of the probe. In a ptychographic measurement, the multiply of real space sampling, i.e. scanning step size, ΔR (Fig. 1a) and reciprocal space sampling, Δθ (Fig. 1b), should be smaller than half of the wavelength [1]. A factor of ½ here is because only amplitude information is recorded in the diffraction patterns and phase information is lost (phase problem). We can then define a sampling figure of merit S = λ / 2 / Δθ / ΔR (λ, wavelength), which must be larger than 1. In practice S is usually larger than 3 and typically takes a value of 10 to 20 (oversampling). With the additional information of the target reconstructed image pixel size (related to spatial resolution) p, detector pixel numbers Nd, one can determine the scanning step size ΔR = Nd * p / 2 / S. Depending on the overlapping ratio, a proper probe size can then be calculated, especially for defocused probe ptychography.
Instead of applying defocus aberration, one could realise the desired enlarged probe in focus by adding certain population of vortices in the probe (Fig. 2c) [2, 3]. This can be realised with a patterned Si3N4 thin film phase mask putting in the condenser aperture plane. It would produce a structured enlarged probe with rather uniform intensity level over a wide lateral extent (Fig. 2d). If instead using an amplitude mask or a phase mask with wrong phase shift, the central spot will be much brighter than the surrounding structures and therefore diminish the advantages of the structured illumination. Following the calculation above, we can also determine the population of vortices, if the desired probe size and image pixel size is given, so the fabricated phase mask can match with the designed experimental set up.
Structured illumination is also of vital importance in near-field ptychography. In this case, the probe becomes a full-field illumination and the detector measures Fresnel (near-field) instead of Fraunhofer diffraction. Without a structured probe, each diffraction image carries the same information except it is laterally shifted, and thus the ptychography reconstruction reduces to a single phase retrieval loop. We have experimentally demonstrated near-field ptychography with electrons using a thin film phase diffuser [4] and now extended this with an amplitude mask (Fig. 2a, b) which proves to work well and avoids the inelastic scattering from the phase diffuser.
References
[1] D. J. Batey et al., Physical Review A 89, 043812 (2014).
[2] P. M. Pelz et al., Scientific Reports 7, 9883 (2017).
[3] W. Van den Broek et al., Microscopy and Microanalysis 25 (S2), 58 (2019).
[4] F. Allars et al., Ultramicroscopy 231, 113257 (2021).
Fig. 1. Illustration of real space sampling (a) and reciprocal space sampling (b) in ptychographic measurements.
Fig. 2. (a-b) Amplitude diffuser for near-field ptychography. (a) SEM image of a FIB-fabricated amplitude diffuser. (b) Experimentally reconstructed amplitude of the probe from a near-field electron ptychography measurement using the diffuser in (a). (c-d) Phase diffuser for far-field ptychography. (c) Design of a phase diffuser. (d) Experimentally measured in-focus probe structured by a FIB-fabricated Si3N4 thin film phase diffuser based on the design in (c).