Arkadiusz Kuś

Tomographic phase microscopy of living three-dimensional cell cultures

Abstract. A successful application of self-interference digital holographic microscopy in combination with a sample-rotation-based tomography module for three-dimensional (3-D) label-free quantitative live cell imaging with subcellular resolution is demonstrated. By means of implementation of a hollow optical fiber as the sample cuvette, the observation of living cells in different 3-D matrices is enabled. The fiber delivers a stable and accurate rotation of a cell or cell cluster, providing quantitative phase data for tomographic reconstruction of the 3-D refractive index distribution with an isotropic spatial resolution. We demonstrate that it is possible to clearly distinguish and quantitatively analyze several cells grouped in a “3-D cluster” as well as subcellular organelles like the nucleoli and local internal refractive index changes.

Generalized total variation iterative constraint strategy in limited angle optical diffraction tomography

Due to incompleteness of input data inherent to Limited Angle Tomography (LAT), specific additional constraints are usually employed to suppress image artifacts. In this work we demonstrate a new two-stage regularization strategy, named Generalized Total Variation Iterative Constraint (GTVIC), dedicated to semi-piecewise-constant objects. It has been successfully applied as a supplementary module for two different reconstruction algorithms: an X-ray type solver and a diffraction-wise solver. Numerical tests performed on a detailed phantom of a biological cell under conical illumination pattern show significant reduction of axial blurring in the reconstructed refractive index distribution after GTVIC is added. Analogous results were obtained with experimental data.

Accurate approach to capillary-supported optical diffraction tomography.

A new holographic data processing path for accurate quantitative tomographic reconstruction of 3D samples placed in a cylindrical capillary is proposed. The method considers strong unintentional focusing effects induced by the inner cylindrical boundary of the vessel: 1) introduction of cylindrical wave illumination of a sample, and 2) object wave deformation. The first issue is addressed by developing an arbitrary illumination tomographic reconstruction algorithm based on filtered backpropagation, while the second by a novel correction algorithm utilizing the optical rays analysis. Moreover, the processing path includes a novel holographic method for correction of spherical aberration related to refraction at a planar surface. Utility of the developed data processing path is proven with numerical simulations and experimental measurement of a specially prepared test sample.

Holographic tomography with scanning of illumination: space-domain reconstruction for spatially invariant accuracy

The paper presents two novel, space-domain reconstruction algorithms for holographic tomography utilizing scanning of illumination and a fixed detector that is highly suitable for imaging of living biomedical specimens. The first proposed algorithm is an adaptation of the filtered backpropagation to the scanning illumination tomography. Its space-domain implementation enables avoiding the error-prone interpolation in the Fourier domain, which is a significant problem of the state-of-the-art tomographic algorithm. The second proposed algorithm is a modified version of the former, which ensures the spatially invariant reconstruction accuracy. The utility of the proposed algorithms is demonstrated with numerical simulations and experimental measurement of a cancer cell.

Limited-angle holographic tomography with optically controlled projection generation

In the paper we demonstrate a holographic tomography system with limited angle of projections, realized by optical– only, diffraction-based beam steering. The system created for this purpose is a Mach-Zehnder interferometer modified to serve as a digital holographic microscope with high Numerical Aperture illumination module and a Spatial Light Modulator. Such solution is fast and robust. Apart from providing an elegant solution to the viewing angle shifting, it also adds new capabilities of the holographic microscope system. SLM, being an active optical element, allows wavefront correction in order to improve measurement accuracy. Integrated phase data captured with different scenarios within a highly limited angular range are processed by a new tomographic reconstruction algorithm based on the compressed sensing technique: total variation minimization, which is applied to non-piecewise constant samples. Finally, the accuracy of full measurement and processing path proposed is tested for a calibrated 3D microobject.

Holographic method for capillary induced aberration compensation for 3D tomographic measurements of living cells

In this paper we present a method for numerical correction of phase images captured in a digital holographic microscopy (DHM) setup adapted to tomographic measurement of biological objects. The purpose of the correction is a removal of the object wave deformation associated with a fluid filled fiber capillary, which is used in DHM system to enable manipulation of a specimen. The proposed correction procedure is based on a simple concept of the phase subtraction, preceded by an estimation of the aberration profile using areas of a hologram that have not been affected by the object. The phase subtraction methodology, developed on the ground of the thin element approximation, is very effective in the visual enhancement of phase images; however, its application to quantitative measurement of micro-objects is questionable. Therefore, in this paper we verify the possible use of the phase subtraction methodology in DHM by performing a numerical experiment, supported with the finite difference time domain method (FDTD), which allows us to identify the residual error of the correction. The FDTD computation reveals that the phase subtraction methodology is insufficient to properly remove the influence of a capillary, in particular to compensate for two effects associated with the focusing properties of the aberration: a transversal shift of the image and the change of its magnification. Nevertheless, the possibility of the visual improvement of holographic images of a living human leukemia cell using the outlined method is demonstrated.

Limited-angle hybrid optical diffraction tomography system with total-variation-minimization-based reconstruction

Abstract. The case of diffraction tomography with limited angle of projections is discussed from the algorithmic and experimental points of view. To reconstruct a three-dimensional distribution of refractive index of a micro-object under study, we use a hybrid approach based on the simultaneous algebraic reconstruction technique (SART) enhanced by a compressed sensing reconstruction technique. It enables us to apply the standard computed tomography algorithms (which assume that the rays are traveling in straight lines through the object) for phase data obtained by means of digital holography. We present the results of analysis of a phantom and real objects obtained by applying SART with anisotropic total variation (ATV) minimization. The real data are acquired from an experimental setup based on a Mach–Zehnder interferometer configuration. Also, it is proven that in the case of simulated data, the limited number of projections captured in a limited angular range can be compensated by a higher number of iterations of the algorithm. We also show that the SART + ATV method applied for experimental data gives better results than the data replenishment algorithm.

Focus-tunable lens in limited-angle holographic tomography

In this paper a new, hardware-based solution for extending the depth of field in holographic tomography is presented. The solution is based on a 4f system and an electric, focus-tunable lens, which provides fast, motion-free defocusing of the plane conjugate with the camera, which acquires holograms. The optimum parameters for the required axial scanning are provided for a specific model of a commercially available tunable lens. Then, the quality of the system equipped with the designed module is analyzed and the reconstruction of a standard object (microsphere) scanned by the 4f-based defocusing system is presented. Finally, the result of the increased depth of field in the measurement domain is demonstrated with a reconstruction of a mouse fibroblast cell.

Reconstruction method for extended depth-of-field optical diffraction tomography

In the paper we present a novel method of extended depth-of-field limited-angle optical diffraction tomography, in which the change of a focal plane position is performed with a liquid focus-tunable lens. One sinogram is acquired for each state of a focus-tunable lens. After acquisition process is complete, all sinograms are independently reconstructed and stitched to form the final tomographic reconstruction. The presented solution effectively extends the applicability of the Rytov approximation to relatively thick samples and provides uniform resolution of 3D tomographic reconstructions. The method is also combined with Generalized Total Variation Iterative Constraint algorithm, which minimizes distortion of the results due to the limited angular range of acquired projections. The combined solution is dedicated to investigation of transparent and semi-transparent biological micro-structures, like cells and tissue slices.

Illumination-related errors in limited-angle optical diffraction tomography

In the paper, the design and tolerances of optical systems and scanning components used in limited-angle optical diffraction tomography are analyzed in order to improve the performance of the measurement systems and to encourage the application of tomography as a standard method for quantitative analysis of 3D refractive index distribution in biological microstructures. The first part of the presented analysis consists of component selection for the scanning device and optical system in the illumination part of the setup and the influence of the illumination wavefront on reconstruction quality. In the second part, the sensitivity of the tomographic reconstruction quality to three representative measurement-related errors based on synthetic data is demonstrated. Finally, a configuration of the system, selected to minimize reconstruction errors, is proposed and alignment tolerances simulated using the Monte Carlo method are provided.