Maximum-likelihood refinement for coherent diffractive imaging

Abstract

We introduce the application of maximum-likelihood (ML) principles to the image reconstruction problem in coherent diffractive imaging. We describe an implementation of the optimization procedure for ptychography, using conjugate gradients and including preconditioning strategies, regularization and typical modifications of the statistical noise model. The optimization principle is compared to a difference map reconstruction algorithm. With simulated data important improvements are observed, as measured by a strong increase in the signal-to-noise ratio. Significant gains in resolution and sensitivity are also demonstrated in the ML refinement of a reconstruction from experimental x-ray data. The immediate consequence of our results is the possible reduction of exposure, or dose, by up to an order of magnitude for a reconstruction quality similar to iterative algorithms currently in use.

On-the-fly scans for X-ray ptychography

“…2(a)-2(c) were performed using 100 iterations of the difference map algorithm 11,18 and 300 iterations of likelihood optimization 19 with a Poissonnoise model, a flat disc of 10 lm diameter as initial illumination in the n ¼ 1 mode, and a random noise in the higher modes. The computational cost scales linearly with the number of modes and the number of recorded diffraction patterns.…”

Parallel ptychographic reconstruction

“…With the addition of linear phase ramp corrections [47], we expect the synchronous implementation to be robust and applicable to samples of varying materials, regardless of their scattering strength and feature contrast. More desirable features to be included in the future are: correcting for positioning errors caused by temperature changes or motor drifts [48,49], the maximum-likelihood refinement method for post-processing the results [50], and additional phase retrieval algorithms such as the difference map method.…”

Coherent X-ray imaging across length scales

“…Another important property of ptychography is that a beam stop is not required, as in conventional CDI, since the illumination beam diverges after the sample, thus reducing in intensity before being incident on the detector. Figure 16 shows images illustrating ptychographic imaging of a porous hydroxyapatite sphere [70]. The data for these images was acquired at the Swiss Light Source (cSAXS beamline) at a photon energy of 6.2keV.…”