Three-dimensional imaging of a phase object from a single sample orientation using an optical laser

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Three-dimensional imaging of a phase object from a single sample orientation using an optical laser

Chien-Chun Chen, Huaidong Jiang, Lu Rong, Sara Salha, Rui Xu, Thomas G. Mason, and Jianwei Miao

Phys. Rev. B 84, 224104 – Published 13 December 2011

Abstract

Ankylography is a new 3D imaging technique, which, under certain circumstances, enables reconstruction of a 3D object from a single sample orientation. Here, we provide a matrix rank analysis to explain the principle of ankylography. We then present an ankylography experiment on a microscale phase object using an optical laser. Coherent diffraction patterns were acquired from the phase object using a planar CCD detector and were projected onto a spherical shell. The 3D structure of the object was directly reconstructed from the spherical diffraction pattern. This work may potentially open the door to a new method for 3D imaging of phase objects in the visible light region. Finally, the extension of ankylography to more complicated and larger objects is suggested.

Received 17 July 2011

DOI:https://doi.org/10.1103/PhysRevB.84.224104

Authors & Affiliations

Chien-Chun Chen¹, Huaidong Jiang², Lu Rong¹, Sara Salha¹, Rui Xu¹, Thomas G. Mason^1,3, and Jianwei Miao^1,*

¹Department of Physics and Astronomy and California NanoSystems Institute, University of California, Los Angeles, California 90095, USA
²State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, People's Republic of China
³Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA

^*Corresponding author: miao@physics.ucla.edu

Comments & Replies

Comment on “Three-dimensional imaging of a phase object from a single sample orientation using an optical laser”

Haiqing Wei and Shiyuan Liu

Phys. Rev. B 86, 226101 (2012)

Reply to “Comment on ‘Three-dimensional imaging of a phase object from a single sample orientation using an optical laser’ ”

Chien-Chun Chen, Huaidong Jiang, Lu Rong, Sara Salha, Rui Xu, Thomas G. Mason, and Jianwei Miao

Phys. Rev. B 86, 226102 (2012)

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Vol. 84, Iss. 22 — 1 December 2011

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Images

Figure 1
Schematic layout of the experimental setup. A compound lens system, consisting of two converging lenses, was used to collimate the incident laser beam with a wavelength of 543 nm. An aperture was placed 15 mm upstream of the sample to block the unwanted scattering from the lenses. A phase object made up of SU-8 epoxy photoresist was supported on a silicon nitride membrane 100 nm thick. To increase the depth of the sample along the beam axis, the silicon nitride membrane was tilted about 45° relative to the incident beam. Coherent diffraction patterns were recorded by a liquid-nitrogen-cooled CCD camera with 1340 × 1300 pixels and a pixel size of 20 μm × 20 μm, placed at a distance of 31.5 mm from the sample. A beam stop was positioned in front of the CCD camera to block the direct beam.Reuse & Permissions
Figure 2
(a) DIC microscope image of the phase object, consisting of four alphabet letters (WWWA). (b), (c) The high and low spatial resolution diffraction patterns acquired by a planar CCD detector. The low spatial resolution pattern was used to reduce the missing center. (d) Two spherical diffraction patterns on a 3D Cartesian grid. The centrosymmetry of the two spherical patterns is because the sample is a weak phase object. The size of the 3D array is $1691 \times 1691 \times 491$ voxels with a diffraction angle of 32.3°.Reuse & Permissions
Figure 3
Supports from loose (a) to tight (c) used for the ankylographic reconstructions. (a) Initial loose support. (b) Updated support. (c) Final tight support.Reuse & Permissions
Figure 4
(a)–(c) Three projections of the final reconstruction along the $X$ , $Y$ , and $Z$ (beam) axes. Based on the achieved resolution of ∼1.0 μm along the $X$ and $Y$ axes and ∼3.5 μm along the $Z$ axis, the projection length of the object in the $X$ , $Y$ , and $Z$ axes was estimated to be ∼19 μm, ∼23 μm, and ∼23 μm, respectively. (d)–(f) Three central slices of the final reconstruction along the $X$ , $Y$ , and $Z$ axes.Reuse & Permissions
Figure 5
(a) Isosurface rendering of the ankylographic reconstruction of the phase object where the relative orientation of the incident beam to the object position is illustrated. (b) The reconstruction is tilted to the same orientation as the DIC image [Fig. 2a]. Although the resolution of the reconstruction is lower than the DIC image, the two images are in good agreement. (c) Line scans across the reconstruction and the DIC image. The two curves agree reasonably well. The discrepancy in ankylography produces a quantitative reconstruction of the phase object, but not the DIC image.Reuse & Permissions

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