Propagation-based phase-contrast tomography is a coherent imaging method that seeks to reconstruct the
three-dimensional complex-valued refractive index distribution of an object. Measurements of the transmitted
wavefield intensities on two parallel detector-planes at each tomographic view angle are utilized to determine
the wavefield's complex amplitude, which represent the projection data utilized for tomographic reconstruction.
The mathematical formulas employed to determine the complex amplitude contain Fourier domain singularities
that can result in greatly amplified noise levels in the reconstructed images. In this article, statistically optimal
reconstruction methods that employ multiple (>2) detector-planes are developed that mitigate the noise
amplification effects due to singularities in the reconstruction formulas. These reconstruction methods permit
exploitation of statistically complementary information in a collection of in-line holographic measurement data,
resulting in images that can have dramatically reduced noise levels. Computer-simulation studies are conducted
to demonstrate and investigate quantitatively the developed reconstruction methods.
Intensity diffraction tomography (I-DT) is an in-line holographic imaging method for reconstructing the three-dimensional
complex refractive index distribution of a weakly scattering object. Because it circumvents the
phase retrieval problem of diffraction tomography, I-DT reconstruction methods may benefit a range of imaging
problems involving optical and coherent X-ray radiation. In this work, we investigate the use of statistically
complementary data, provided by multiple (> 2) in-line intensity measurements, for effective suppression of
image noise in I-DT. The noise properties of the reconstructed images are demonstrated to depend strongly
on the specification of measurement geometry. The effects of experimental uncertainties on the performance
of I-DT is investigated also. Computer-simulation studies that are representative of a tomographic microscopy
implementation of I-DT are presented.
Diffraction tomography (DT) is an established imaging technique for reconstructing the complex-valued refractive index distribution of a weakly scattering 3D sample. Due to experimental difficulties associated with the direct measurement of the phase of an optical wavefield, the effectiveness of DT for optical imaging applications
has been limited. A theory of intensity diffraction tomography (I-DT) has been proposed to circumvent this phase retrieval problem. In this work, we review the features of I-DT reconstruction theory that are relevant to optical microscopy. Computer-simulation studies are conducted to investigate the performance of reconstruction
algorithms for a proposed I-DT microscope. The effects of data noise are assessed, and statistically optimal reconstruction strategies that employ multiple detector planes are proposed.
In this work we investigate the phase-contrast tomography reconstruction problem assuming an incident (paraxial) spherical-wave. Starting from linearized inverse scattering theory, we develop an intensity diffraction tomography (I-DT) reconstruction algorithm that is relevant to scanning geometries that have a fixed source-to-object distance. This reconstruction algorithm accounts for first-order scattering effects introduced by the object and provides a
relationship between the intensity measurements made on two parallel detector planes and the desired complex refractive index distribution. A preliminary numerical investigation of the developed
reconstruction algorithm is presented.
In this work, we examine the application of intensity diffraction tomography (I-DT) 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. We demonstrate that the numerical and noise propagation properties of the two reconstruction algorithms differ considerably.
A reconstruction theory for intensity diffraction tomography (I-DT) has been proposed that permits for the reconstruction of a weakly-scattering object without explicity knowledge of phase information. In this work, we examine the noise properties of I-DT. An explicit expression for the variance of the estimated object function as a function of spatial frequency is derived and employed for understanding the noise properties of images reconstruction in I-DT. It is demonstrated analytically and numerically that the noise properties of I-DT are significantly different from those of conventional diffraction tomography (DT).