Iterative Joint Ptychography-Tomography with Total Variation Regularization

Abstract

In order to determine the 3D structure of a thick sample, researchers have recently combined ptychography (for high resolution) and tomography (for 3D imaging) in a single experiment. 2-step methods are usually adopted for reconstruction, where the ptychography and tomography problems are often solved independently. In this paper, we provide a novel model and ADMM-based algorithm to jointly solve the ptychography-tomography problem iteratively, also employing total variation regularization. The proposed method permits large scan stepsizes for the ptychography experiment, requiring less measurements and being more robust to noise with respect to other strategies, while achieving higher reconstruction quality results.

Improved ptychographic inspection of EUV reticles via inclusion of prior information

“…TV is commonly employed due to its effectiveness in smoothing noise -by favouring images that have a sparse gradient -while preserving edges. In recent years there have been a number of studies reporting implementations of TV regularized ptychography [20][21][22]. In this work we have taken a different approach and instead of considering a regularizer that promotes generic properties of the reconstructed image (like its sparsity or the sparsity of its gradient), the regularizer R α (O) has been designed to promote adhesion to a given prior image (object):…”

“…Recent works have reported the use of total variation as regularizer for denoising in ptychography [20][21][22]. Here we compare results obtained using the two different regularizers R α (O j ) = α||O j (r) − O p, j (r)|| 2 and R α T V (O j ) = α TV ||∇O j (r)|| 1 .…”

“…the derivations necessary to minimize (15) are analogous to the ones that can be found elsewhere [21] and are here omitted. Problem ( 13) is minimized per probe position, the subproblem with respect to O j is solved via a steepest descent, the subproblem with respect to p has a closed-form solution in the form of a soft-thresholding operator, and α TV has been computed by the L-curve and it is equal to 1e-6 [37].…”

“…In the context of CDI, prior information about the amplitude of the ptychographic illumination function enabled subwavelength imaging at the edges of the lines of a periodic object [19]. Recent studies have further shown the benefits that stem from the inclusion of the total variation (TV) prior in the ptychographic algorithms [20][21][22].…”

A priori information in ptychographic image reconstruction for EUV mask metrology

“…The constrained optimization problem is solved similarly to Chang et al 14 and Enfedaque et al 15 using a Lagrange multiplier technique called alternating direction method of multipliers (ADMM). As the problem is non-smooth, one cannot directly apply a gradient based optimization technique.…”