Potential and Challenge of Ankylography

TL;DR

Ankylography is a promising technique for 3D structure determination from a single view, with recent advances and ongoing challenges in extending its applicability to larger objects and practical use.

Contribution

This paper provides an updated understanding of ankylography's potential, clarifies misconceptions, and discusses future directions for its development.

Findings

Ankylography can reconstruct 3D structures of small objects from spherical shell diffraction data.

Reconstruction is feasible for objects up to 14x14x14 voxels, and sometimes larger for less dense structures.

The method's potential extends to other fields involving Fourier coefficient analysis within spherical shells.

Abstract

The concept of ankylography, which under certain circumstances enables 3D structure determination from a single view [1], had ignited a lively debate even before its publication [2,3]. Since then, a number of readers requested the ankylographic reconstruction codes from us. To facilitate a better understanding of ankylography, we posted the source codes of the ankylographic reconstruction on a public website and encouraged interested readers to download the codes and test the method [4]. Those who have tested our codes confirm that the principle of ankylography works. Furthermore, our mathematical analysis and numerical simulations suggest that, for a continuous object with array size of 14x14x14 voxels, its 3D structure can usually be reconstructed from the diffraction intensities sampled on a spherical shell of 1 voxel thick [4]. In some cases where the object does not have very dense structure, ankylography can be applied to reconstruct its 3D image with array size of 25x25x25 voxels [4]. What remains to be elucidated is how to extend ankylography to the reconstruction of larger objects, and what further theoretical, experimental and algorithm developments will be necessary to make ankylography a practical and useful imaging tool. Here we present our up-to-date understanding of the potential and challenge of ankylography. Further, we clarify some misconceptions on ankylography, and respond to technical comments raised by Wei [5] and Wang et al. [6] Finally, it is worthwhile to point out that the potential for recovering 3D information from the Fourier coefficients within a spherical shell may also find application in other fields.