Mitigating tilt-induced artifacts in reflection ptychography via optimization of the tilt angles

Ptychography in a reflection geometry shows great promise for non-destructive imaging of 3-dimensional nanostructures at the surface of a thick substrate. A major challenge to obtain high quality reflection-ptychographic images under near-grazing conditions has been to calibrate the incidence angle used to straighten the measured curved diffraction patterns in a process referred to as 'tilted plane correction' (TPC). In this work, we leverage the flexibility of automatic differentiation (AD)-based modeling to realise an alternative approach, where the tilted propagation is included into the forward model. Use of AD allows us to jointly optimize the tilt angles with the typical probe and object, eliminating the need for accurate calibration or random search optimization. The approach was validated using datasets generated with an extreme ultraviolet (EUV) beamline based on either a tabletop high harmonic generation (HHG) source or a visible laser. We demonstrate that the proposed approach can converge to a precision of $\pm 0.05\deg$ for probe beams at $70\deg$ angle of incidence, possibly precise enough for use as a calibration approach. Furthermore, we demonstrate that optimizing for the tilt angles reduces artifacts and increases reconstruction fidelity. Use of AD not only streamlines the current ptychographic reconstruction process, but should also enable optimization of more complex models in other domains, which will undoubtedly be essential for future advancements in computational imaging.