Fig. 1. Iterative flowchart of the parallel cross-correlation ptychographic self-calibration method for the translation position errors

Fig. 2. Schematic diagrams of the principle of weighted probe matrix correction. (a) Probe matrix correction principle; (b) weighting coefficient acceleration principle

Fig. 3. Simulation input information. (a) Sample and probe amplitude; (b) sample and probe phase; (c) scanning trajectory

Fig. 4. Reconstructed amplitude phase maps

Fig. 5. Illuminated probe calibration position distributions with an initial position error of ±15 pixel. (a) Simulated annealing method; (b) particle swarm method; (c) serial cross-correlation method; (d) parallel cross-correlation method

Fig. 6. Global position error convergence curves for different initial position errors. (a) ±15 pixel; (b) ±10 pixel; (c) ±5 pixel

Fig. 7. Global position error convergence curves under different noise intensities. (a) 40 dB; (b) 30 dB; (c) 20 dB

Fig. 8. Reconstructed amplitude phase maps with a detector noise of 20 dB

Fig. 9. Ptychographic imaging setup with transmissive geometry. (a) Experimental prototype system; (b) original diffraction field

Fig. 10. Illuminated probe calibration position distributions. (a) Simulated annealing method; (b) particle swarm method; (c) serial cross-correlation method; (d) parallel cross-correlation method

Fig. 11. Ptychographic imaging results of USAF-1951. (a) Particle swarm method; (b) simulated annealing method; (c) serial cross- correlation algorithm; (d) parallel cross-correlation method

Fig. 12. Comparison and validation experimental results of USAF-1951. (a) RMS error convergence curves; (b) line trace

Fig. 13. Imaging of frog blood biological specimen. (a)(b) Reconstructed amplitude phase images by mPIE method;(c)(d) reconstructed amplitude phase images by parallel cross-correlation method