Optical tomographic reconstruction based on multi-slice wave propagation method

Recent Advances and Current Trends in Transmission Tomographic Diffraction Microscopy

Optical microscopy techniques are among the most used methods in biomedical sample characterization. In their more advanced realization, optical microscopes demonstrate resolution down to the nanometric scale. These methods rely on the use of fluorescent sample labeling in order to break the diffraction limit. However, fluorescent molecules' phototoxicity or photobleaching is not always compatible with the investigated samples. To overcome this limitation, quantitative phase imaging techniques have been proposed. Among these, holographic imaging has demonstrated its ability to image living microscopic samples without staining. However, for a 3D assessment of samples, tomographic acquisitions are needed. Tomographic Diffraction Microscopy (TDM) combines holographic acquisitions with tomographic reconstructions. Relying on a 3D synthetic aperture process, TDM allows for 3D quantitative measurements of the complex refractive index of the investigated sample. Since its initial proposition by Emil Wolf in 1969, the concept of TDM has found a lot of applications and has become one of the hot topics in biomedical imaging. This review focuses on recent achievements in TDM development. Current trends and perspectives of the technique are also discussed.

Fast bidirectional vector wave propagation method showcased on targeted noise reduction in imaging fiber bundles using 3D-printed micro optics

In order to extend simulation capabilities for reflective and catadioptric 3D-printed micro optics, we present a fast bidirectional vector wave propagation method (BWPM). Contrary to established fast simulation methods like the wave propagation method (WPM), the BWPM allows for the additional consideration of reflected and backwards propagating electric fields. We study the convergence of the BWPM and investigate relevant simulation examples. Especially, the BWPM is used for evaluation of 3D-printed index matching caps (IMCs) in order to suppress back reflected light in imaging fibers, used for keyhole access endoscopy. Simulations studying the viability of IMCs are followed up with experimental investigations. We demonstrate that 3D-printed IMCs can be used to suppress noise caused by back reflected light, that otherwise would prohibit the use of imaging fibers in an epi-illumination configuration.

Efficient and accurate intensity diffraction tomography of multiple-scattering samples

Optical Diffraction Tomography (ODT) is a label-free method to quantitatively estimate the 3D refractive index (RI) distributions of microscopic samples. Recently, significant efforts were directed towards methods to model multiple-scattering objects. The fidelity of reconstructions rely on accurately modelling light-matter interactions, but the efficient simulation of light propagation through high-RI structures over a large range of illumination angles is still challenging. Here we present a solution dealing with these problems, proposing a method that allows one to efficiently model the tomographic image formation for strongly scattering objects illuminated over a wide range of angles. Instead of propagating tilted plane waves we apply rotations on the illuminated object and optical field and formulate a new and robust multi-slice model suitable for high-RI contrast structures. We test reconstructions made by our approach against simulations and experiments, using rigorous solutions to Maxwell's equations as ground truth. We find the proposed method to produce reconstructions of higher fidelity compared to conventional multi-slice methods, especially for the challenging case of strongly scattering samples where conventional reconstruction methods fail.

Numerical analysis of the effect of reduced temporal coherence in quantitative phase microscopy and tomography

We present the numerical analysis of the effect of the temporarily partially coherent illumination on the phase measurement accuracy in digital holography microscopy (DHM) and optical diffraction tomography (ODT), as reconstruction algorithms tend to assume purely monochromatic conditions. In the regime of reduced temporal coherence, we simulate the hologram formation in two different optical setups, representing classical off-axis two-beam and grating common-path configurations. We consider two ODT variants: with sample rotation and angle-scanning of illumination. Besides the coherence degree of illumination, our simulation considers the influence of the sample normal dispersion, shape of the light spectrum, and optical parameters of the imaging setup. As reconstruction algorithms we employ Fourier hologram method and first-order Rytov approximation with direct inversion and nonnegativity constraints. Quantitative evaluation of the measurement results deviations introduced by the mentioned error sources is comprehensively analyzed, for the first time to the best of our knowledge. Obtained outcomes indicate low final DHM/ODT reconstruction errors for the grating-assisted common-path configuration. Nevertheless, dispersion and asymmetric spectrum introduce non-negligible overestimated refractive index values and noise, and should be thus carefully considered within experimental frameworks.

Non-uniform angular spectrum method in a complex medium based on iteration

The traditional angular spectrum method has an inherent problem that the region of diffraction propagation should be homogeneous. However, in some cases, the medium of the diffraction propagation region is inhomogeneous. In this Letter, based on iteration we proposed the non-uniform angular spectrum method for diffraction propagation calculation in a complex medium. By phase pre-processing in the spatial domain and diffraction calculation in the spatial frequency domain, the diffraction propagation problem of the light field in a complex medium is solved. Theoretical formulation and numerical examples as well as experimental investigation are presented to confirm the validity of the proposed method. The advantages of this method include faster computation, smaller memory requirement, and the ability to compute a larger area compared with the finite element method as well as the ability to compute the non-paraxial case compared with the standard fast Fourier transform beam propagation method.

High-resolution 3D Fourier ptychographic reconstruction using a hemispherical illumination source with multiplexed-coded strategy

Fourier ptychography is a promising and flexible imaging technique that can achieve 2D quantitative reconstruction with higher resolution beyond the limitation of the system. Meanwhile, by using different imaging models, the same platform can be applied to achieve 3D refractive index reconstruction. To improve the illumination NA as much as possible while reducing the intensity attenuation problem caused by the LED board used in the traditional FP platform, we apply a hemispherical lighting structure and design a new LED arrangement according to 3D Fourier diffraction theory. Therefore, we could obtain the illumination of 0.98NA using 187 LEDs and achieve imaging half-pitch resolutions of ∼174 nm and ∼524 nm for the lateral and axial directions respectively, using a 40×/0.6NA objective lens. Furthermore, to reduce the number of captured images required and realize real-time data collection, we apply the multiplexed-coded illumination strategy and compare several coded patterns through simulation and experiment. Through comparison, we determined a radial-coded illumination pattern that could achieve more similar results as sequential scanning and increase the acquisition speed to above 1 Hz. Therefore, this paper provides the possibility of this technique in real-time 3D observation of in vitro live samples.

GSURE criterion for unsupervised regularized reconstruction in tomographic diffractive microscopy

We propose an unsupervised regularized inversion method for reconstruction of the 3D refractive index map of a sample in tomographic diffractive microscopy. It is based on the minimization of the generalized Stein's unbiased risk estimator (GSURE) to automatically estimate optimal values for the hyperparameters of one or several regularization terms (sparsity, edge-preserving smoothness, total variation). We evaluate the performance of our approach on simulated and experimental limited-view data. Our results show that GSURE is an efficient criterion to find suitable regularization weights, which is a critical task, particularly in the context of reducing the amount of required data to allow faster yet efficient acquisitions and reconstructions.

Optimization-based optical diffraction tomography using iODT initialization

Optical diffraction tomography (ODT) is a label-free and noninvasive technique for biological imaging. However, ODT is only applicable to weakly scattering objects. To extend ODT to the multiple-scattering regime, more advanced inversion algorithms have been developed, including optimization-based ODT (Opti-ODT) and iterative ODT (iODT). In this paper, we propose a combined strategy, namely, an iODT initialization for Opti-ODT, based on the observed complementarity of their individual advantages. This study numerically demonstrates that under this combined strategy, the reconstruction can accurately converge to a better local minimum, especially in the case of multiply scattering objects with large optical path differences.

Common-path intrinsically achromatic optical diffraction tomography

In this work we propose an open-top like common-path intrinsically achromatic optical diffraction tomography system. It operates as a total-shear interferometer and employs Ronchi-type amplitude diffraction grating, positioned in between the camera and the tube lens without an additional 4f system, generating three-beam interferograms with achromatic second harmonic. Such configuration makes the proposed system low cost, compact and immune to vibrations. We present the results of the measurements of 3D-printed cell phantom using laser diode (coherent) and superluminescent diode (partially coherent) light sources. Broadband light sources can be naturally employed without the need for any cumbersome compensation because of the intrinsic achromaticity of the interferometric recording (holograms generated by -1st and +1st conjugated diffraction orders are not affected by the illumination wavelength). The results show that the decreased coherence offers much reduced coherent noise and higher fidelity tomographic reconstruction especially when applied nonnegativity constraint regularization procedure.

Iterative optical diffraction tomography for illumination scanning configuration

Optical diffraction tomography (ODT) is used to reconstruct refractive-index distributions from multiple measurements in the object rotating configuration (ORC) or the illumination scanning configuration (ISC). Because of its fast data acquisition and stability, ISC-based ODT has been widely used for biological imaging. ODT typically fails to reconstruct multiply-scattering samples. The previously developed iterative ODT (iODT) was for the multiply-scattering objects in ORC, and could not be directly applied to ISC. To resolve this mismatch, we developed an ISC update and numerically demonstrated its accuracy. With the same prior knowledge, iODT-ISC outperforms conventional ODT in resolving the missing-angle problem.

Fast multiple-scattering holographic tomography based on the wave propagation method

We develop a time-efficient computation scheme for a holographic tomography reconstruction technique that accounts for multiple scattering by applying the forward model based on the wave propagation method (WPM). The computational efficiency is achieved by employing adjoint equations for calculation of the gradient of the data fidelity term in the gradient descent optimization procedure. In the paper we provide a general computation scheme that is suitable for various forward models that can be represented in the form of an iterative equation. Next, we provide the complete solution for the time-efficient reconstruction utilizing WPM. In the considered reconstruction case, the proposed algorithm enables the 114-fold speed-up of computations with respect to the original tomographic method.

Forward model for propagation-based x-ray phase contrast imaging in parallel- and cone-beam geometry

We demonstrate a fast, flexible, and accurate paraxial wave propagation model to serve as a forward model for propagation-based X-ray phase contrast imaging (XPCI) in parallel-beam or cone-beam geometry. This model incorporates geometric cone-beam effects into the multi-slice beam propagation method. It enables rapid prototyping and is well suited to serve as a forward model for propagation-based X-ray phase contrast tomographic reconstructions. Furthermore, it is capable of modeling arbitrary objects, including those that are strongly or multi-scattering. Simulation studies were conducted to compare our model to other forward models in the X-ray regime, such as the Mie and full-wave Rytov solutions.

Reconstructions of refractive index tomograms via a discrete algebraic reconstruction technique

Optical diffraction tomography (ODT) provides three-dimensional refractive index (RI) tomograms of a transparent microscopic object. However, because of the finite numerical aperture of objective lenses, ODT has a limited access to diffracted light and suffers from poor spatial resolution, particularly along the axial direction. To overcome the limitation of the quality of RI tomography, we present an algorithm that accurately reconstructs RI tomography of a specimen with discrete and uniform RI, using prior information about the RI levels. Through simulations and experiments on various samples, including microspheres, red blood cells, and water droplets, we show that the proposed method can precisely reconstruct RI tomograms of samples which have discrete and homogenous RI distributions in the presence of the missing information and noise.