Phase retrieval using through-focus images in Lorentz transmission electron microscopy.

In this study, we report on phase retrieval by the maximum likelihood method with conjugate gradient method (CG-MAL) using through-focus images in Lorentz transmission electron microscopy (LTEM). The method was evaluated using 32 simulated and experimentally obtained through-focus images of magnetic bubbles; these images were collected under a defocus range from approximately -3 mm to 3 mm. Consequently, we obtained the magnetic domain structures of the magnetic bubbles in both the simulation and the LTEM experiment. Furthermore, the CG-MAL method showed better convergence behavior than other iterative phase retrieval methods. Therefore, the method can also be widely and effectively applied to the observation of magnetic domain structures other than magnetic bubbles when highly defocused through-focus images are used.