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Three-dimensional (3D) imaging techniques appeal to a broad range of scientific and industrial applications. Typically, projection slice theorem enables multiple two-dimensional (2D) projections of an object to be combined in the Fourier domain to yield a 3D image. However, traditional techniques require a significant number of projections. The significant number of views required in conventional tomography not only complicates such imaging modalities, but also limits their ability to image samples that are sensitive to radiation dose or are otherwise unstable in time. In this work, we demonstrate through numerical simulations and an eigenvalue analysis that a recently developed technique called ankylography enables 3D image reconstruction using much fewer views than conventional tomography. Such a technique with the ability to obtain the 3D structure information from a few views is expected to find applications in both optical and x-ray imaging fields.
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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.
Coherent diffraction imaging (CDI) is high-resolution lensless microscopy that has been applied to image a wide range of specimens using synchrotron radiation, X-ray free electron lasers, high harmonic generation, soft X-ray laser and electrons. Despite these rapid advances, it remains a challenge to reconstruct fine features in weakly scattering objects such as biological specimens from noisy data. Here we present an effective iterative algorithm, termed oversampling smoothness (OSS), for phase retrieval of noisy diffraction intensities. OSS exploits the correlation information among the pixels or voxels in the region outside of a support in real space. By properly applying spatial frequency filters to the pixels or voxels outside the support at different stage of the iterative process (i.e. a smoothness constraint), OSS finds a balance between the hybrid input-output (HIO) and error reduction (ER) algorithms to search for a global minimum in solution space, while reducing the oscillations in the reconstruction. Both our numerical simulations with Poisson noise and experimental data from a biological cell indicate that OSS consistently outperforms the HIO, ER-HIO and noise robust (NR)-HIO algorithms at all noise levels in terms of accuracy and consistency of the reconstructions. We expect OSS to find application in the rapidly growing CDI field as well as other disciplines where phase retrieval from noisy Fourier magnitudes is needed.
Diffraction unlimited super-resolution imaging critically depends on the switching of fluorophores between at least two states, often induced using intense laser light and special buffers. The high illumination power or UV light required for appropriate blinking kinetics is currently hindering live-cell experiments. Recently, so-called self-blinking dyes that switch spontaneously between an open, fluorescent on-state and a closed colorless off-state were introduced. Here we exploit the synergy between super-resolution optical fluctuation imaging (SOFI) and spontaneously switching fluorophores for 2D functional and for volumetric imaging. SOFI tolerates high labeling densities, on-time ratios, and low signal-to-noise by analyzing higher-order statistics of a few hundred to thousand frames of stochastically blinking fluorophores. We demonstrate 2D imaging of fixed cells with a uniform resolution up to 50-60 nm in 6th order SOFI and characterize changing experimental conditions. We extend multiplane cross-correlation analysis to 4th order using biplane and 8-plane volumetric imaging achieving up to 29 (virtual) planes. The low laser excitation intensities needed for self-blinking SOFI are ideal for live-cell imaging. We show proof-of-principal time-resolved imaging by observing slow membrane movements in cells. Self-blinking SOFI provides a route for easy-to-use 2D and 3D high-resolution functional imaging that is robust against artefacts and suitable for live-cell imaging.
We present a minimally-invasive endoscope based on a multimode fiber that combines photoacoustic and fluorescence sensing. From the measurement of a transmission matrix during a prior calibration step, a focused spot is produced and raster-scanned over a sample at the distal tip of the fiber by use of a fast spatial light modulator. An ultra-sensitive fiber-optic ultrasound sensor for photoacoustic detection placed next to the fiber is combined with a photodetector to obtain both fluorescence and photoacoustic images with a distal imaging tip no larger than 250um. The high signal-to-noise ratio provided by wavefront shaping based focusing and the ultra-sensitive ultrasound sensor enables imaging with a single laser shot per pixel, demonstrating fast two-dimensional hybrid imaging of red blood cells and fluorescent beads.
We present a novel method for Ankylography: three-dimensional structure reconstruction from a single shot diffraction intensity pattern. Our approach allows reconstruction of objects containing many more details than was ever demonstrated, in a faster and more accurate fashion
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