This research presents the WUTScope, a novel interferometric microscope developed by the Quantitative Computational Imaging group at Warsaw University of Technology. This system, leveraging Quantitative Phase Microscopy and Optical Diffraction Tomography, provides insightful three-dimensional reconstructions of the refractive index distribution in semi-transparent objects. The WUTScope is distinguished by its compact design and capability to operate under partially coherent illumination, using polarization diffraction gratings for beam splitting and recombination. This approach allows for efficient phase shifting and reduces speckle noise, enhancing image signal-to-noise ratio. The system's achromatic nature, due to the identical optical paths of the diffraction orders, facilitates the use of less coherent light sources, a distinct advantage over traditional holographic methods. Its effectiveness is demonstrated through tomographic reconstruction of a 3D-printed brain sample and analysis of refractive index changes in HeLa cells' lipid droplets, revealing the impact of cholesterol accumulation.
Quantitative phase microscopy (QPM) is pivotal for revealing phase distributions, and optical diffraction tomography (ODT) effectively showcases 3D refractive index (RI) structures across diverse technical and biological entities. Our novel polarization grating-based system, integrated with Hilbert spiral transform (HST) phase demodulation, stands out for its streamlined design, adaptability with partially coherent light, and efficient beam interference through diffraction gratings. In scenarios involving high numerical aperture (NA) paired with low magnification, standard sampling frequently falls short for proficient phase demodulation via Fourier transform. Kramers–Kronig relations enhance phase estimation but face challenges in on-axis configurations as it requires full separation of cross-correlation terms. Our solution, HST with fast iterative filtering, bypasses the need for full term separation enabling phase and amplitude estimation from holographic projections for tomographic reconstruction. Results are validated by 3D RI reconstruction of phase targets 3D printed via 2-photon polymerization and fixed neuron imaging.
We discuss implementations of a straightforward common-path interferometric system within the microscope setup to allow for quantitative phase contrast imaging. Fringe pattern generation is based on the interference between +1 and -1 diffraction grating orders. Limited angle optical diffraction tomography is realized upon illuminating the sample under varying angles and reconstructing a 3D refractive index distribution via filtered back-projection. Due to equalized optical path of both conjugate +1/-1 beams temporal coherence alteration can be easily implemented with benefits of coherent noise minimization (reducing speckles and parasitic interferences). Presented setups employ single microscope objective in an open-top configuration allowing for comfortable sample operation. Proposed 2D/3D grating-based common-path quantitative phase imaging systems are limited to sparse samples, as +1/-1 interference needs to superimpose object replica and object-free area, however.
Holographic tomography (HT) enables measurement of three-dimensional refractive index distribution of transparent micro-objects by merging information from multiple transmitted waves corresponding to various illumination directions. HT has proven its great potential in technical inspection and biomedical studies; nonetheless, its further progress is hindered by inability of the standard reconstruction algorithms to account for multiple scattering. This limitation has been recently addressed with a few novel reconstruction approaches. In those techniques the tomographic reconstruction is iteratively improved by minimizing discrepancy between the experimentally acquired transmitted fields uE(x,y) and the analogical data uq(x,y) obtained via numerical propagation of the incident beams through the current refractive index estimate nq(x,y,z). The accuracy of these multiple-scattering reconstruction methods depends primarily on two features: (1) the forward model that allows computing the transmitted fields uq; (2) the feedback mechanism that converts uE - uq discrepancy into the reconstruction upgrade nq+1=nq+Δnq+1. In our work, we address the first issue with the wave propagation method that represents a reasonable trade-off between accuracy and time of computation. The paper focuses primary on the second issue, i.e. the feedback mechanism, that considerably influences the performance of the multiple-scattering reconstruction methods. In our work, we cross-analyze two feedback solutions, i.e. the gradient descent and the forward backward method. The performance of these solutions is tested via numerical simulations on different types of samples: step-objects representing technical samples and gradient structures emulating biological specimens. Our study investigates accuracy of the reconstruction, time of computation as well as stability and flexibility of the feedback method.
The aim of this work is to develop a holographic method that provides the shape reconstruction with an extended measurement range and preserved high accuracy. The method requires recording of series of fully-coherent holograms generated with varying tilt of plane wave illumination. The captured holograms are numerically processed to obtain the corresponding complex fields. The complex fields are used to produce a new set of holograms, which are used for calculating the longitudinal coherence function. This function allows observing fringes of high contrast at specific heights similar to white light interferometry, and thus, shape reconstruction of the three-dimensional object is carried out. The conclusions of this work are supported with results of numerical simulations.
Holographic tomography (HT) enables nondestructive, quantitative measurement of three-dimensional refractive index distribution of transparent, weakly-scattering micro-samples. The method has been successfully applied for inspection of technical objects, as well as biomedical specimens. The key element of the HT measurement is acquisition of multiple holograms corresponding to various projection directions. In the conventional configuration of HT, this is achieved by rotating a sample, which provides high and almost isotropic resolution of tomographic imaging. However, the major disadvantages of this configuration is degradation of the reconstruction quality due to inaccuracies of the sample rotation. In this paper, we propose a novel autofocusing solution, which enables compensation of the rotation errors in HT. The method utilizes cross-analysis of two optical fields that were registered for special combination of the illumination and rotation angles. The proper selection of these parameters ensures redundancy of information in the fields, which here is used for quantitative evaluation of the misalignment error. Notably, the proposed solution is fundamentally different than other alignment methods for HT. Those methods utilize autofocusing algorithms that assume a single in-focus plane of a sample. Contrarily, our solution does not disregard the 3D character of a sample and thus is compatible with tomographic measurements. The utility of the proposed alignment method is validated with numerical simulations using two examples of complex samples with large axial thickness: a set of beads and Shepp-Logan phantom.
The aim of this work is to develop a holographic method that provides the shape reconstruction with high, interferometric accuracy and an extended measurement range. The method requires recording of a set of n holograms obtained for selected combination of illumination angles θ𝑛. The difference between the optical phases corresponding to on-axis φ0 and offaxis φ𝑛 fields allows calculating the object height. To maintain high-accuracy evaluation of height the dedicated shape reconstruction algorithm is proposed. The algorithm consists of n steps, each with several substeps. Each substep is divided into: (1) calculation of the height from φ0 and φ𝑛 ; (2) propagation of the optical fields. In this paper, the proposed algorithm is numerically validated using three types of objects.
KEYWORDS: Holograms, Optical spheres, Spherical lenses, Digital holography, Reconstruction algorithms, 3D image processing, Signal to noise ratio, Denoising, Holography, Microscopy
This paper proposes an improvement of the measurement method of focusing high gradient microobjects of small and large radius of curvature. The measurement process is carried out in a Fourier digital holographic microscope with spherical illumination, which ensures maximum usage of numerical aperture of the optical system. The interference pattern is the result of interference between the deformed, quasi-spherical object and spherical reference waves. The noise influence on the phase measurement is analyzed and minimized with block-matching 3-D (BM3D) filtering method. The accurate shape reconstruction of the object and localization of the imaging reference plane are provided by (1) the aberration compensation procedure, and (2) the calibration procedure. To obtain the final shape, the Local Ray Approximation approach is used. In this work an effective BM3D method was applied in the process of the reconstruction of the object beam, improving accuracy of the measurement method. The validation of our approach is presented for spherical objects of large radius of curvature and high gradient of shape.
Holographic tomography (HT) allows noninvasive, quantitative, 3D imaging of transparent microobjects, such as living
biological cells and fiber optics elements. The technique is based on acquisition of multiple scattered fields for various
sample perspectives using digital holographic microscopy. Then, the captured data is processed with one of the
tomographic reconstruction algorithms, which enables 3D reconstruction of refractive index distribution.
In our recent works we addressed the issue of spatially variant accuracy of the HT reconstructions, which results from
the insufficient model of diffraction that is applied in the widely-used tomographic reconstruction algorithms basing on
the Rytov approximation. In the present study, we continue investigating the spatially variant properties of the HT
imaging, however, we are now focusing on the limited spatial size of holograms as a source of this problem. Using the
Wigner distribution representation and the Ewald sphere approach, we show that the limited size of the holograms results
in a decreased quality of tomographic imaging in off-center regions of the HT reconstructions. This is because the finite
detector extent becomes a limiting aperture that prohibits acquisition of full information about diffracted fields coming
from the out-of-focus structures of a sample. The incompleteness of the data results in an effective truncation of the
tomographic transfer function for the out-of-center regions of the tomographic image. In this paper, the described effect
is quantitatively characterized for three types of the tomographic systems: the configuration with 1) object rotation, 2)
scanning of the illumination direction, 3) the hybrid HT solution combing both previous approaches.
In this contribution, we propose a method of digital holographic microscopy (DHM) that enables measurement of high
numerical aperture spherical and aspherical microstructures of both concave and convex shapes. The proposed method
utilizes reflection of the spherical illumination beam from the object surface and the interference with a spherical
reference beam of the similar curvature. In this case, the NA of DHM is fully utilized for illumination and imaging of the
reflected object beam. Thus, the system allows capturing the phase coming from larger areas of the quasi-spherical
object and, therefore, offers possibility of high accuracy characterization of its surface even in the areas of high
inclination. The proposed measurement procedure allows determining all parameters required for the accurate shape
recovery: the location of the object focus point and the positions of the illumination and reference point sources. The
utility of the method is demonstrated with characterization of surface of high NA focusing objects. The accuracy is
firstly verified by characterization of a known reference sphere with low error of sphericity. Then, the method is applied
for shape measurement of spherical and aspheric microlenses. The results provide a full-field reconstruction of high NA
topography with resolution in the nanometer range. The surface sphericity is evaluated by the deviation from the best
fitted sphere or asphere, and the important parameters of the measured microlens: e.g.: radius of curvature and conic
constant.
Filtered back propagation (FBPP) is a well-established reconstruction technique that is used in diffractive holographic tomography. The great advantage of the algorithm is the space-domain implementation, which enables avoiding the error-prone interpolation in the spectral domain that is an inherent part of the main counterpart of FBPP - the direct inversion tomographic reconstruction method. However, the fundamental flaw of FBPP is lack of generality, i.e. the method can be applied solely for the classical tomographic systems, where alternation of the measurement views is achieved by rotating a sample. At the same time, majority of the nowadays tomographic setups apply an alternative measurement concept, which is based on scanning of an illumination beam. The aim of this paper is to remove the mentioned limitation of the FBPP and enable its application in the systems utilizing scanning of illumination. This is achieved by introducing a new method of accounting for uneven cover of the sampled object frequencies, which applies normalization of the object spectrum with coherent transfer function of a considered tomographic system. The feasibility of the proposed, modified filtered back propagation algorithm is demonstrated with numerical simulations, which mimic tomographic measurement of a complex sample, i.e. the Shepp-Logan phantom.
Optical diffraction tomography (ODT) is a non-invasive method for quantitative measurement of micrometre-sized samples. In ODT a series of multiple holograms captured for various illumination directions with respect to a sample is processed using a tomographic reconstruction algorithm. The result of tomographic evaluation is 3D distribution of refractive index. Data acquisition in ODT is commonly realized in two ways, either by rotating a sample under fixed illumination and observation directions (object rotation configuration - ORC), or by scanning the illumination direction of a fixed sample (illumination scanning configuration - ISC). From the purely theoretical standpoint, the ORC configuration is superior to ISC due to larger (in terms of volume) and more isotropic optical transfer function. However, the theoretical maximal resolution achievable with ORC is lower than that provided with ISC. Moreover, the quality of tomographic reconstructions in ORC is significantly degraded due to experimental difficulties, including problematic determination of location of the rotation axis. This applies particularly to displacement of the rotation axis from the infocus plane that is either disregarded or detected with object-dependent autofocusing algorithms, which do not provide sufficient accuracy. In this paper we propose a new ODT approach, which provides solution to the both mentioned problems of ORC – the resolution limit and the rotation axis misalignment problem. The proposed tomographic method, besides rotating a sample in a full angle of 360°, uses simultaneous illumination from two fixed, highly off-axis directions. This modification enables enlarging the ORC optical transfer function up to the ISC limit. Moreover, the system enables implementation of an accurate, efficient and object-independent autofocusing method, which takes advantage of the off-axis illumination. The autofocusing method provides accurate and reliable detection of axial location of the rotation axis, enabling precise alignment of the tomographic data.
We present a study on spatial changes in the accuracy of tomographic reconstructions obtained with two of the most popular tomographic reconstruction algorithms for diffraction tomography—filtered backprojection (FBPJ) and Rytov-based filtered backpropagation (FBPP). We find out that not only FBPJ but also FBPP suffers from a significant loss of accuracy in the off-axis regions of a tomographic reconstruction and this effect is stronger for objects with a high refractive index contrast. Moreover, we propose some modifications to FBPP which allow for significant improvement of the off-axis performance of the algorithm. In the modified algorithm, called the extended depth of focus filtered backpropagation (EDOF-FBPP), scattered waves are backpropagated using a rigorous propagation algorithm, and then the Rytov approximation is applied on extended EDOF images. This modification (1) prevents violation of the Rytov validity condition due to the defocus of scattered waves and (2) suppresses unwrapping errors. The tomographic reconstruction algorithms FBPJ, FBPP, and EDOF-FBPP are extensively tested with numerical simulations supported with rigorous wave scattering methods. The experimental evaluation of the performance of the tomographic algorithms is provided with a tomographic measurement of an optical microtip located 21 μm from the central axis of the reconstruction.
This paper presents the study on the accuracy of topography measurement of high numerical aperture focusing
microobjects in digital holographic microscope setup. The system works in reflective configuration with spherical wave
illumination. For numerical reconstruction of topography of high NA focusing microobjects we are using two algorithms:
Thin Element Approximation (TEA) and Spherical Local Ray Approximation (SLRA). In this paper we show comparison
of the accuracy of topography reconstruction results using these algorithms. We show superiority of SLRA method.
However, to obtain accurate results two experimental conditions have to be determined: the position of point source (PS)
and imaging reference plane (IRP).Therefore we simulate the effect of point source (PS) and imaging reference plane (IRP)
position on the accuracy of shape calculation. Moreover we evaluate accuracy of determination of location of PS and IRP
and finally present measurement result of microlens object.
Optical diffraction tomography is an increasingly popular method that allows for reconstruction of three-dimensional refractive index distribution of semi-transparent samples using multiple measurements of an optical field transmitted through the sample for various illumination directions. The process of assembly of the angular measurements is usually performed with one of two methods: filtered backprojection (FBPJ) or filtered backpropagation (FBPP) tomographic reconstruction algorithm. The former approach, although conceptually very simple, provides an accurate reconstruction for the object regions located close to the plane of focus. However, since FBPJ ignores diffraction, its use for spatially extended structures is arguable. According to the theory of scattering, more precise restoration of a 3D structure shall be achieved with the FBPP algorithm, which unlike the former approach incorporates diffraction. It is believed that with this method one is allowed to obtain a high accuracy reconstruction in a large measurement volume exceeding depth of focus of an imaging system. However, some studies have suggested that a considerable improvement of the FBPP results can be achieved with prior propagation of the transmitted fields back to the centre of the object. This, supposedly, enables reduction of errors due to approximated diffraction formulas used in FBPP. In our view this finding casts doubt on quality of the FBPP reconstruction in the regions far from the rotation axis. The objective of this paper is to investigate limitation of the FBPP algorithm in terms of an off-axis reconstruction and compare its performance with the FBPJ approach. Moreover, in this work we propose some modifications to the FBPP algorithm that allow for more precise restoration of a sample structure in off-axis locations. The research is based on extensive numerical simulations supported with wave-propagation method.
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.
The most suited techniques for quantitative and accurate determination of the phase distribution in a phase photonic
microstructures are based on the interferometry, especially the digital holography (DH) in microscopic configuration.
However there is well known limitation of the coherent full- field interferometric measurements: the phase difference
between the neighboring samples cannot be larger than 2π, or objects shape have to generate light that can be collected
by used optical system. This limitation might be overcame by use of a well-known technique called low-coherence
interferometry (LCI) which allows for absolute shape measurements with a nanometer resolution and does not have 2π
limitation of coherent interferometric techniques. In this work a dual channel measurement system for characterization of
a high numerical aperture objects is presented. The system combines functionalities of the LCI system based on
Twyman-Green configuration and the DHM system based on Mach-Zehnder configuration. The DHM allows to measure
sample in transmission while LCI setup provides reflective measurement data and, therefore, provides a more complete
tool for topography characterization. In presented paper we focus on the measurement of high gradient objects were both methods fail if applied independently: the LCI gives measurement only in the object area of low NA while the DHM cannot provide absolute shape characterization due to limited NA of imaging system. The dual channel system extends
capabilities of both methods. In our paper we present experimental results for topography measurement of high NA
microlenses. The accuracy of the development method is discussed and both simulation and experimental data are
provided.
The paper is devoted to characterization of topography of micro optical elements with very high numerical aperture
using digital holographic microscope. For very high numerical aperture we mean the one larger than numerical aperture
of optical system conjugating the object plane with the detector plane. In this case the optical system is not capable of
capturing any information about micro element areas with high numerical aperture (high shape gradients). In the paper
we are presenting method that can be used for recovering high numerical aperture shape from few measurements with
digital holographic microscope working in transmission and reflective configuration. We are focusing on metrology of
microlenses of high numerical aperture. Within the presented method measurement of tilted object is necessary. When
the element is tilted then some of optical field is coming from "new high gradient element area", when the element is
tangential the area of high gradient is producing field with numerical aperture larger that numerical aperture of the
measurement optical system. In our paper we therefore use data captured for tilted sample in order to reconstruct micro
element topography within a region of high numerical aperture. Such data are then defocused to tilted plane and only
then can be used for topography reconstruction.
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