Experimental results of imaging using the diffraction pattern without an objective lens have been presented using different sources; x-ray, electron beam, and tabletop light sources of lasers. The imaging using the diffraction pattern is called as dffractive imaging. In recent years, diffractive imaging has developed into a powerful application for single-molecule imaging. Using this method, one can reconstruct the structure of an object by achieving phase retrieval from a diffraction pattern in the Fourier domain.
We study diffractive imaging in terms of experiment using electron beam and theory of phase retrieval.
Atomic Resolved Imaging
At 30 kV, the atomic structure of a single-wall carbon nanotube is obtained at a resolution of 0.12 nm, which is only 18 times the wavelength of the electron beam. The intensity differences between a single carbon atom and two overlapping atoms can be clearly distinguished, which demonstrates the present method’s potential for use in chemical identification. These results show that the low-voltage diffractive imaging has the capability to directly observe the electrostatic potential of materials at atomic resolution. The present method can generally be applied to biologically important ones.
Figure: Atomic resolved imaging of single-wall carbon nanotube （SWCNT）. Top : SWCNT. Bottom left: Magnification of white box. Bottom right: Atomic arrangement. We cooperated with Hitachi, Ltd. in doing the work. Hitachi Review
DNA on Graphene
In 1953, Watson and Crick begun their memorial paper with the following; “We wish to suggest a structure for the salt of deoxyribose nucleic acid (D.N.A.). This structure has novel features which are of considerable biological interest.” The title of the paper is MOLECULAR STRUCTURE OF NUCLEIC ACIDS (A Structure for Deoxyribose Nucleic Acid). It is well known that the diffraction pattern obtained by DNA crystal was a conclusive evidence for elucidating the structure of DNA. Generally speaking, crystallization is essential for atomic-resolved structure analysis. However, huge biological materials remain unresolved structures due to non-crystallized nature.
The diffractive imaging is one of the most promising methods for challenging this problem. The video shows our imaging target of a single DNA on a graphene.
Phase problems arise from the lost Fourier phase in measuring the diffraction waves. Reconstructing the phase information using the diffraction pattern of a target object yields the target image, and it is called phase retrieval. Concerning the theoretical research for phase retrieval, a generalized phase retrieva algorithm based on information measures was presented by Shioya and Gohara. Their result reveals that the ER algorithm is a kind of generalized phase retrieval algorithm based on the density power divergence. And also, a new iterative phase retrieval based on the maximum entropy method for the diffractive imaging was introduced.
Figure: Back-and-forth iteration of Fourier transformation between two complex function spaces, Object space and Fourier space.
- Free software, Diffractive Imager, is supplied by System In Frontier Inc.
- S. Hattanda, H. Shioya, Y. Maehara, K. Gohara:
K-means clustering for support construction in diffractive imaging,
J. Opt. Soc. Am. A, 31(3), 2014.
- O. Kamimura, Y. Maehara, T. Dobashi, K. Kobayashi, R. Kitaura, H. Shinohara, H. Shioya, and K. Gohara:
Low-voltage electron diffractive imaging of atomic structure in single-wall carbon nanotubes,
Appl. Phys. Lett., 98(17), 174103.1-3, 2011.
- H. Shioya,Y. Maehara, and K. Gohara:
Spherical shell structure of distribution of images reconstructed by diffractive imaging,
J. Opt. Soc. Am. A, 27(5), pp.1214-1218, 2010.
- H. Shioya, Y. Maehara, S. Watanabe, K.Gohara:
An Information-Theoretic Approach to Phase Retrieval,
International Journal of Information and Management Sciences, 21, pp.1-11, 2010.
- K. Kawahara, K. Gohara, Y. Maehara, T. Dobashi, and O. Kamimura:
Beam-divergence deconvolution for diffractive imaging,
Phys. Rev. B, 81(8),081404.1-081404.4(R),2010.
- O. Kamimura, T. Dobashi, K. Kawahara, T. Abe, and K. Gohara:
10-kV diffractive imaging using newly developed electron diffraction microscope,
Ultramicroscopy, 110(2), 130-133, 2010.
- H. Shioya and K. Gohara:
Maximum entropy method for diffractive imaging,
J. Opt. Soc. Am. A, 25(11),pp.2846-2850, 2008.
- O. Kamimura, K. Kawahara, T. Doi, T. Dobashi, T. Abe, and K. Gohara:
Diffraction microscopy using 20 kV electron beam for multiwall carbon nanotubes,
Appl. Phys. Lett., 92(2), 024106.1-024106.3, 2008.
- H. Shioya, K. Gohara:
Generalized phase retrieval algorithm based on information measures,
Optics Communications, 266(1), pp.88-93, 2006.