Half-scan and single-plane intensity diffraction tomography for phase objects (original) (raw)
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A reconstruction theory for intensity diffraction tomography (I-DT) has been proposed that permits reconstruction of a weakly scattering object without explicit knowledge of phase information. In this work, we examine the application of I-DT, using either planar-or spherical-wave incident wavefields, for imaging three-dimensional (3D) phase objects. We develop and investigate two algorithms for reconstructing phase objects that utilize only half of the measurements that would be needed to reconstruct a complex-valued object function. Each reconstruction algorithm reconstructs the phase object by use of different sets of intensity measurements. Although the developed reconstruction algorithms are equivalent mathematically, we demonstrate that their numerical and noise propagation properties differ considerably. We implement numerically the reconstruction algorithms and present reconstructed images to demonstrate their use and to corroborate our theoretical assertions.
Image reconstruction in spherical-wave intensity diffraction tomography
Journal of the Optical Society of America A, 2005
A reconstruction theory for intensity diffraction tomography (I-DT) has been proposed that permits reconstruction of a weakly scattering object without explicit knowledge of phase information. We investigate the I-DT reconstruction problem assuming an incident (paraxial) spherical wave and scanning geometries that employ fixed source-to-object distances. Novel reconstruction methods are derived by identifying and exploiting tomographic symmetries and the rotational invariance of the problem. An underlying theme is that symmetries in tomographic imaging systems can facilitate solutions for phase-retrieval problems. A preliminary numerical investigation of the developed reconstruction methods is presented.
A reconstruction theory for intensity diffraction tomography (I-DT) has been proposed that permits reconstruction of a weakly scattering object without explicit knowledge of phase information. We investigate the I-DT reconstruction problem assuming an incident (paraxial) spherical wave and scanning geometries that employ fixed source-to-object distances. Novel reconstruction methods are derived by identifying and exploiting tomographic symmetries and the rotational invariance of the problem. An underlying theme is that symmetries in tomographic imaging systems can facilitate solutions for phase-retrieval problems. A preliminary numerical investigation of the developed reconstruction methods is presented.
Physical Review A, 2019
We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample's refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known phase-retrieval problem in ptychography in a tomographic framework which allows for simultaneous reconstruction of the illumination function and the sample's refractive indices in three dimensions. Our iterative reconstruction algorithm is based on the Levenberg-Marquardt algorithm and we demonstrate the performance of our proposed method with simulated and real datasets.
QUANTITATIVE EVALUATION OF PHASE RETRIEVAL ALGORITHMS IN PROPAGATION BASED PHASE TOMOGRAPHY
Phase contrast provides new possibilities in X-ray imaging, offering up to 1000 times higher sensitivity than standard absorption contrast. In propagation based phase contrast imaging, a quantitative relationship exists between intensity in the image plane and the phase shift induced by the object. Inversion of this relationship is called phase retrieval. Used as input to a 3D tomographic reconstruction algorithm this gives a reconstruction of the refractive index. Several methods for phase retrieval have been described, but few quantitative studies have been performed. In this paper we describe three phase retrieval methods, respectively based on the Transport of Intensity Equation (TIE), Contrast Transfer Function (CTF) and a Mixed approach recently developed at the ESRF. The methods are evaluated using simulated and experimental data in the case of mixed absorption and phase objects. Using the TIE on simulated data we obtain a reconstruction with a mean error of 10 %, but fail to achieve a qualitatively acceptable reconstruction of experimental data. The CTF approach yields qualitative reconstructions both using simulated and experimental data. Using the Mixed approach, we obtain reconstructions with close correspondence to expected values with an average errors of 3.8 % for the simulated and 5.9 % for the experimental data.
Direct quantitative tomographic reconstruction for weakly absorbing homogeneous phase objects
Review of Scientific Instruments, 2007
We examine a direct filtered back projection approach that is suitable for the reconstruction of weakly absorbing homogeneous phase objects. Like recent similar approaches this method needs only one intensity image in each projection without the requirement for an intermediate step of phase retrieval. We tested the method using simulation and experimental results. Simulation results show good quantitative reconstruction which includes the correct refractive index value and distribution of the sample. However, experimental result still indicates the presence of artifacts.
Improved phase imaging from intensity measurements in multiple planes
Applied Optics, 2007
Problems stemming from quantitative phase imaging from intensity measurements play a key role in many fields of physics. Techniques based on the transport of intensity equation require an estimate of the axial derivative of the intensity to invert the problem. Derivation formulas in two adjacent planes are commonly used to experimentally compute the derivative of the irradiance. Here we propose a formula that improves the estimate of the derivative by using a higher number of planes and taking the noisy nature of the measurements into account. We also establish an upper and lower limit for the estimate error and provide the distance between planes that optimizes the estimate of the derivative.
Three-Dimensional Phase Imaging with the Intensity Transport Equation
Applied Optics, 2002
Phase can be retrieved from intensity measurements with the intensity transport equation. Three-dimensional image formation of weak phase objects based on this method is investigated. It is shown that, although the refractive index of a thin object can be measured, the three-dimensional variation of refractive index of an arbitrary object cannot, in general, be reconstructed, as spatial frequencies with a zero-axial component are not detected. However, this may not be a problem if regions with known refractive index are present in the sample.
High-resolution 3D phase imaging using a partitioned detection aperture: a wave-optic analysis
Journal of the Optical Society of America A, 2015
An optically transparent thin sample is characterized by a distribution of pathlengths and a weak attenuation parameter. The phase shifts imparted by the sample can be measured using a partitioned detection aperture [Opt. Lett. 37, 4062 (2012)]. In this work, we analyze the system using paraxial wave optics and derive three-dimensional spread functions for phase and intensity. Using these functions we discuss methods of phase reconstruction for in-and out-of-focus samples, insensitive to weak attenuations of light. Our approach provides a strategy for detection-limited lateral resolution with extended depth of field, and is applicable to imaging smooth and rough samples.
We introduce a hybrid tomographic method, based on recent investigations concerning the connection between computed tomography and diffraction tomography, that allows direct reconstruction of scattering objects from intensity measurements. This technique is noniterative and is intuitively easier to understand and easier to implement than some other methods described in the literature. The manner in which the new method reduces to computed tomography at short wavelengths is discussed. Numerical examples of reconstructions are presented.