An Efficient and Robust Self-Calibration Algorithm for Translation Position Errors in Ptychography

Ptychography, one kind of the large-field-of-view and high-resolution computational imaging, is consistently hampered by the motion errors of linear translation stages, i.e., the resolution of lensless ptychographic microscope cannot break through the positioning accuracy of its translation stages. Here, an accurate, fast, and robust self-calibration algorithm is proposed to refine the translation position errors of translation stages in ptychography imaging online. The proposed algorithm employs a dynamic weighting function to accelerate the correction of the center translation position through “parallel cross correlation” registration within the centrosymmetric and axisymmetric array probes, which requires neither careful dynamic parameter adjustment nor high magnification subdivision pixel operations during the iteration process and can effectively escape from local optimums and avoid violent convergence oscillations and crosstalk. Simulations and experiments are carried out comparatively with the heuristic simulated annealing algorithm and the single-probe “serial cross correlation” algorithm, and preliminary results indicate that the proposed algorithm can achieve the refinement accuracy of a few thousandths of a pixel within a 100 iterations and deliver orders of magnitude increase in calibration accuracy, convergence speed, and noise immunity. Furthermore, verification experiments are also performed using the linear variable displacement transducer (LVDT) to measure the translation position errors, and results demonstrate that the comparison residuals are less than ±0.5
$\mu \text{m}$
, verifying the effectiveness and feasibility of the proposed algorithm. These significant advances significantly expand its potential applications, encompassing positioning errors calibration and measurement in ptychography, tomography, and in-line holography microscopy.