Ptychography is an imaging technique which aims to recover the complex-valued exit wavefront of an object from a set of its diffraction pattern magnitudes. Ptychography is one of the most popular techniques for sub-30 nanometer imaging as it does not suffer from the limitations of typical lens based imaging techniques. The object can be recon- structed from the captured diffraction patterns using iterative phase retrieval algorithms. Over time many algorithms have been proposed for iterative reconstruction of the object based on manually derived update rules. In this paper, we adapt automatic differentiation framework to solve practical and complex ptychographic phase retrieval problems and demonstrate its advantages in terms of speed, accuracy, adaptability and generalizability across different scanning techniques.
"ADP: Automatic Differentiation Ptychography"
Sushobhan Ghosh, Youssef Nashed, Oliver Cossairt, Aggelos Katsaggelos
Computational Graph for ADP with probe retrieval
Traversal of the data flow graph from left to right expresses calculation of the objective function from the unknown object function to the objective expressed by E. This traversal is equivalent to functional composition of elemental operators (shown in yellow) whose analytic derivatives relative to the independent variables are
known. Gradient descent optimization is performed by applying the chain rule to backpropagate partial derivatives through the network.
Comparative PSNR plots for ADP and ePIE on step-scan
The comparisons are made on simulated step-scan data. Both algorithms are run on GPU optimized libraries (Tensorflow for ADP and PtychoLib for ePIE). The probe estimation for step-scan ADP starts after 50s.
Comparative PSNR plots for single-probe ADP and multi-probe ePIE on fly-scan data
The comparisons are made on simulated fly-scan data. Both algorithms are run on GPU optimized libraries (Tensorflow for ADP and PtychoLib for ePIE). The probe estimation for single-probe fly-scan ADP starts after 25s
Qualitative analysis of fly-scan ADP and multi- probe ePIE
(a) Simulated ground truth chip image
(b) multi-probe ePIE reconstruction
(c) single-probe ADP reconstruction
(d) Horizontal (e) vertical line plot for distance from ground truth phase in radians
Experimental results for Hynix DRAM inte- grated circuit
(a) Phase reconstruction for experimental diffraction data collected at APS, Argonne.
(b) Zoomed region for region in blue box in (a). (c) Reconstructed probe. Phase shown in color while amplitude shown as magnitude.
(d) Edge response (10%-90%) of 23 nm, suggesting a resolution of about ∆x = 23 nm.
The authors of this work were funded by IARPA RAVEN grant /No. 86101156 // FA8650-17-C-9112; National Science Foundation (NSF) CAREER grant IIS-1453192; Defense Advanced Research Projects Agency (DARPA) (REVEAL HR0011-16-C-0028); and Office of Naval Research (ONR) grant N00014-15-1-2735. The Bio- nanoprobe is funded by NIH/NCRR High End Instrumentation (HEI) grant (1S10RR029272-01) as part of the American Recovery and Reinvestment Act (ARRA)