2nd Response to "Feasibility of 3D reconstruction from a single 2D diffraction measurement"

TL;DR

This paper defends the validity of ankylography for 3D reconstruction from single 2D diffraction data, providing theoretical critique, numerical experiments, and detailed procedures to support its applicability.

Contribution

It offers a rebuttal to critiques of ankylography, clarifies its theoretical basis, and supplies practical methods for reconstruction using the HIO algorithm with positivity constraints.

Findings

Ankylography can be applicable to general samples.

Numerical experiments support the feasibility of ankylography.

Detailed procedures enable reproducibility of reconstructions.

Abstract

We present our 2nd response to Thibault's commentary article [1] and his reply [2], in which he commented upon our ankylography paper [3] and our 1st response [4]. In this article, we further explain why we think Thibault's theoretical analysis is flawed and his interpretation of our experiment is incorrect. Furthermore, we provide a quantitative analysis and a numerical experiment to illustrate why ankylography can in principle be applicable to general samples. Finally, we present detailed procedures for our numerical experiment on ankylographic reconstructions, which uses the traditional HIO algorithm only with the positivity constraint [5]. We welcome anyone (including Thibault) interested in ankylography to perform numerical experiments and verify our results. We will be very happy to provide any help if needed.