Fast numerical reconstruction technique for high-resolution hybrid holographic microscopy

A numerical reconstruction method believed to be new is proposed for hybrid holographic microscopy in which the hologram of a microscopic object is recorded by an image sensor and is then reconstructed by a computer. Because the Fresnel-Kirchhoff integral must be used for numerical reconstruction to achieve high resolution, we propose an approximation technique for reducing the calculation time. This approximation technique is suitable for microscopic application. The numerical reconstruction of 1-mum-sized objects was demonstrated with a He-Ne laser (lambda = 0.6328 mum).     

Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements

Optical imaging and localization of objects inside a highly scattering medium, such as a tumor in the breast, is a challenging problem with many practical applications. Conventional imaging methods generally provide only two-dimensional (2-D) images of limited spatial resolution with little diagnostic ability. Here we present an inversion algorithm that uses time-resolved transillumination measurements in the form of a sequence of picosecond-duration intensity patterns of transmitted ultrashort light pulses to reconstruct three-dimensional (3-D) images of an absorbing object located inside a slab of a highly scattering medium. The experimental arrangement used a 3-mm-diameter collimated beam of 800-nm, 150-fs, 1-kHz repetition rate light pulses from a Ti:sapphire laser and amplifier system to illuminate one side of the slab sample. An ultrafast gated intensified camera system that provides a minimum FWHM gate width of 80 ps recorded the 2-D intensity patterns of the light transmitted through the opposite side of the slab. The gate position was varied in steps of 100 ps over a 5-ns range to obtain a sequence of 2-D transmitted light intensity patterns of both less-scattered and multiple-scattered light for image reconstruction. The inversion algorithm is based on the diffusion approximation of the radiative transfer theory for photon transport in a turbid medium. It uses a Green s function perturbative approach under the Rytov approximation and combines a 2-D matrix inversion with a one-dimensional Fourier-transform inversion to achieve speedy 3-D image reconstruction. In addition to the lateral position, the method provides information about the axial position of the object as well, whereas the 2-D reconstruction methods yield only lateral position.     

Superresolved imaging in digital holography by superposition of tilted wavefronts

A technique based on superresolution by digital holographic microscopic imaging is presented. We used a two dimensional (2-D) vertical-cavity self-emitting laser (VCSEL) array as spherical-wave illumination sources. The method is defined in terms of an incoherent superposition of tilted wavefronts. The tilted spherical wave originating from the 2-D VCSEL elements illuminates the target in transmission mode to obtain a hologram in a Mach-Zehnder interferometer configuration. Superresolved images of the input object above the common lens diffraction limit are generated by sequential recording of the individual holograms and numerical reconstruction of the image with the extended spatial frequency range. We have experimentally tested the approach for a microscope objective with an exact 2-D reconstruction image of the input object. The proposed approach has implementation advantages for applications in biological imaging or the microelectronic industry in which structured targets are being inspected.     

Three-dimensional remote sensing by optical scanning holography

A technique is presented by which holograms can be recorded when an object or scene is scanned with an optically heterodyned Fresnel zone pattern. The experimental setup, based on optical scanning holography, is described and experimental results are presented. We apply the scanning holography technique to three-dimensional reflective objects for the first time to our knowledge and address the unique requirements for such a system. We discuss holographic recording and numerical image reconstruction using a system point-spread function (PSF) approach. We demonstrate numerical image reconstruction of experimentally recorded holograms by two techniques: deconvolution with a simulated PSF and an experimentally acquired PSF.     

Simultaneous mapping of absorption and scattering coefficients from a three-dimensional model of time-resolved optical tomography

A Newton-Raphson inversion algorithm has been extended for simultaneous absorption and scattering reconstruction of fully three-dimensional (3D) diffuse optical tomographic imaging from time-resolved measurements. The proposed algorithm is derived from the efficient computation of the Jacobian matrix of the forward model and uses either the algebraic reconstruction technique or truncated singular-value decomposition as the linear inversion tool. Its validation was examined with numerically simulated data from 3-D finite-element discretization models of tissuelike phantoms, with several combinations of geometric and optical properties, as well as two commonly used source-detector configurations. Our results show that the fully 3-D image reconstruction of an object can be achieved with reasonable quality when volumetric light propagation in tissues is considered, and temporal information from the measurements can be effectively employed. Also, we investigated the conditions under which 3-D issues could be approximately addressed with two-dimensional reconstruction algorithms and further demonstrated that these conditions are seldom predictable or attainable in practice. Thus the application of 3-D algorithms to realistic situations is necessary.     

Optical image recognition of three-dimensional objects

A three-dimensional (3-D) optical image-recognition technique is proposed and studied. The proposed technique is based on two-pupil optical heterodyne scanning and is capable of performing 3-D image recognition. A hologram of the 3-D reference object is first created and then is used to modulate spatially one of the pupils of the optical system; the other pupil is a point source. A 3-D target object to be recognized is then scanned in two dimensions by optical beams modulated by the two pupils. The result of the two-dimensional scan pattern effectively displays the correlation of the holographic information of the 3-D reference object and that of the 3-D target object. A strong correlation peak results if the two pieces of the holographic information are matched. We analyze the proposed technique and thereby lay a theoretical foundation for optical implementations of the idea. Finally, computer simulations are performed to verify the proposed idea.     

Electrical Capacitance Volume Tomography

A dynamic volume imaging based on the principle of electrical capacitance tomography (ECT), namely, electrical capacitance volume tomography (ECVT), has been developed in this study. The technique generates, from the measured capacitance, a whole volumetric image of the region enclosed by the geometrically three-dimensional capacitance sensor. This development enables a real-time, 3-D imaging of a moving object or a real-time volume imaging (4-D) to be realized. Moreover, it allows total interrogation of the whole volume within the domain (vessel or conduit) of an arbitrary shape or geometry. The development of the ECVT imaging technique primarily encloses the 3-D capacitance sensor design and the volume image reconstruction technique. The electrical field variation in three-dimensional space forms a basis for volume imaging through different shapes and configurations of ECT sensor electrodes. The image reconstruction scheme is established by implementing the neural-network multicriterion optimization image reconstruction (NN-MOIRT), developed earlier by the authors for the 2-D ECT. The image reconstruction technique is modified by introducing into the algorithm a 3-D sensitivity matrix to replace the 2-D sensitivity matrix in conventional 2-D ECT, and providing additional network constraints including 3-to-2-D image matching function. The additional constraints further enhance the accuracy of the image reconstruction algorithm. The technique has been successfully verified over actual objects in the experimental conditions     

Three-dimensional matching by use of phase-only holographic information and the Wigner distribution

Matching of three-dimensional (3-D) objects is achieved by Wigner analysis of the correlation pattern between the phase-only holographic information of a reference object and that of a target object. First, holographic information on the reference object and on the target object is extracted by use of optical scanning holography as a form of electrical signal. This electrical information is then stored in a computer for digital processing. In the digital computer, the correlation between the phase-only information of the hologram of the reference object and that of the target object is calculated and analyzed by use of a Wigner distribution. The Wigner distribution yields a space-frequency map of the correlation pattern that indicates whether the 3-D image of the target object matches that of the reference object. When the 3-D image of the target object matches that of the reference object, the Wigner distribution gives a well-defined line that directly indicates the 3-D location of the matched target object. Optical experiments with digital processing are described to demonstrate the proposed matching technique.     

Automatic threshold technique for holographic particle field characterization

The 3D distribution of a particle field by digital holography is obtained by 3D numerical reconstruction of a 2D hologram. The proper identification of particles from the background during numerical reconstruction influences the overall effectiveness of the technique. The selection of a suitable threshold value to segment particles from the background of reconstructed images during 3D holographic reconstruction process is a critical issue, which influences the accuracy of particle size and number density of reconstructed particles. The object particle field parameters, such as depth of sample volume and density of object particles, influence the optimal threshold value. The present study proposes a novel technique for the determination of the optimal threshold value of a reconstructed image. The effectiveness of the proposed technique is demonstrated using both simulated and experimental data. The proposed technique is robust to variation in optical properties of particle and background, depth of sample volume, and number density of object particle field. The particle diameter obtained from the proposed threshold technique is within 5% of that obtained from the particle size analyzer. There is a maximum ten times increase in reconstruction effectiveness by using the proposed automatic threshold technique in comparison with the fixed manual threshold technique.     

Object recognition using three-dimensional optical quasi-correlation

A novel method of three-dimensional (3-D) object recognition is proposed. Several projections of a 3-D target are recorded under white-light illumination and fused into a single complex two-dimensional function. After proper filtering, the resulting function is coded into a computer-generated hologram. When this hologram is coherently illuminated, a correlation space is reconstructed such that light peaks indicate the existence and locations of true targets in the observed 3-D scene. Experimental results and comparisons with results of another 3-D object recognition technique are presented.     

Microscopic phase-shifting profilometry based on digital micromirror device technology

A microscopic three-dimensional (3-D) shape measurement system based on digital fringe projection has been developed and experimentally investigated. A Digital Micromirror Device along with its illumination optics is integrated into a stereomicroscope, which projects computer-generated fringe patterns with a sinusoidal intensity profile through the microscope objective onto the object surface being measured. The fringe patterns deformed by the object surface are recorded by a CCD camera. The microscopic 3-D shape of the object surface is measured and reconstructed by use of a phase-shifting technique. We discuss design considerations and error analysis of the system. Experimental results successfully demonstrate the capability of this technique for surface profile measurement of rough surfaces at the micrometer level.     

Three-dimensional reconstruction of fracture surfaces

An original method is presented to improve fracture surface characterization through an accurate three-dimensional (3-D) reconstruction. The method, based on digital image-processing techniques, was developed under the Khoros system. The reconstruction technique is based upon the stereoscopic principle to extract the surface local elevations from the stereo-pair images. The fractographs that compose the stereo pair are obtained by scanning electron microscopy from two points of view by tilting the object at two observation angles. The first step of image processing is the alignment of the two images. Next, an iterative processing based on the cross-correlation operation builds a very dependable high resolution elevation map of the fracture surface. Finally, the elevation map can be used to provide a 3-D perspective view of the surface by using various visualization tools. Also, profiles and horizontal sections are generated by sectioning the 3-D reconstructed surface.     

Three-dimensional surface contouring of macroscopic objects by means of phase-difference images

We report a technique to determine the 3D contour of objects with dimensions of at least 4 orders of magnitude larger than the illumination optical wavelength. Our proposal is based on the numerical reconstruction of the optical wave field of digitally recorded holograms. The required modulo 2pi phase map in any contouring process is obtained by means of the direct subtraction of two phase-contrast images under different illumination angles to create a phase-difference image of a still object. Obtaining the phase-difference images is only possible by using the capability of numerical reconstruction of the complex optical field provided by digital holography. This unique characteristic leads us to a robust, reliable, and fast procedure that requires only two images. A theoretical analysis of the contouring system is shown, with verification by means of numerical and experimental results.     

Ultrasound imaging through time-domain diffraction tomography

Time-domain diffraction tomography, a technique for imaging with acoustic (and other) fields in which a medium parameter, such as density, can be mapped from scatter data collected from one pulse, is discussed. When Born approximations hold, the technique provides an exact inversion of the acoustical scattering equations. Computer simulation of the time-domain diffraction tomography equations indicates that under ideal conditions, and when the Born approximation is valid, the method can reconstruct maps of parameter variations. However, when data are collected from an incident pulse whose bandwidth is limited, the reconstruction is no longer perfect. A simple question is derived that characterizes the performance of time-domain diffraction tomography, and the limitations are explained as the effect of a spatial filter that eliminates some of the spatial frequencies. Relations between the object parameters, pulse bandwidth, and reconstruction accuracy are investigated with numerical experiments.     

Usefulness of ultrasonic strain measurement-based shear modulus reconstruction for diagnosis and thermal treatment

We previously reported an ultrasonic strain measurement-based one-dimensional (1-D) shear modulus reconstruction technique using a regularization method for differential diagnosis of malignancies on human superficial tissues (e.g., breast tissues). Here, ultrasonic strain measurement-based 2-D and 3-D shear modulus reconstruction techniques are described, and the 1-D technique is reviewed and subsequently applied to various human in vivo tissues, including deeply situated tissues (e.g., liver). Because soft tissues are deformed in 3-D space by externally situated arbitrary mechanical sources, the accuracy of the low-dimensional (i.e., 1-D or 2-D) reconstructions is lower to that of 3-D reconstruction due to occurrence of erroneous reconstruction artifacts (i.e., the reconstructed modulus is different than reality). These artifacts are confirmed on simulated inhomogeneous cubic phantoms containing a spherical homogenous inclusion using numerically calculated deformation data. The superiority of quasi-real-time imaging of the shear modulus is then demonstrated by comparing it with conventional B-mode imaging and strain imaging from the standpoints of monitoring the effectiveness of minimally invasive thermal therapy as well as differential diagnosis. Because the 2-D and 3-D techniques require special ultrasonic (US) equipment, the 1-D technique using conventional US imaging equipment is used, even though erroneous artifacts will occur. Specifically, the 1-D technique is applied as a diagnostic tool for differentiating malignancies in human in vivo liver and breast tissue, and a monitoring technique for determining the effectiveness of interstitial electromagnetic wave (micro and rf) thermal therapy on human in vivo liver and calf in vitro liver. Even when using the 1-D technique, reconstructed shear moduli were confirmed to be a suitable measure for monitoring thermal treatment as well as differential diagnosis. These results are encouraging in that they will promote use of 2-D and 3-D reconstruction techniques.     

Three-dimensional shape measurement of non-full-field reflective surfaces

We describe a technique for the measurement of non-full-field reflective surfaces by using phase-stepping profilometry. We explain the principles of phase demodulation and discuss three-dimensional (3-D) height reconstruction in the case of measuring surfaces with reflective properties such as plain glass and mirrored glass. A number of required calibration algorithms are described to obtain surface slopes and reconstructed 3-D heights of the whole surface. Masking for non-full-field objects and the surface reconstruction procedure are demonstrated mathematically and algorithmically. Several experimental results are given for glass with different shapes and defects. Measurement of a spherical mirror with a known radius has also allowed us to show the performance of the proposed technique. This allows for the possibility to compare 3-D data from the known object with data taken from the measurement system.     

Digital recording and reconstruction of holograms in hologram interferometry and shearography

The fundamentals of digital recording and mathematical reconstruction of Fresnel holograms are described. The object is recorded in two different states, and the holograms are stored electronically with a charge-coupled-device detector. In the process of reconstruction the digitally sampled holograms are applied to the different coherent optical methods as hologram interferometry and shearography. If the holograms are superimposed and reconstructed jointly, a holographic interferogram results. If a shearing is introduced in the reconstruction process, a shearogram results. This means that the evaluation technique, e.g., hologram interferometry or shearography, can be influenced by numerical methods.     

Improving the quality of phase maps in phase object digital holographic interferometry by finding the right reconstruction distance

Improved quality of phase maps in pulsed digital holographic interferometry is demonstrated by finding the right reconstruction distance. The objective is to improve the optical phase information when the object under study is a phase object and when it is out of focus, leading to low contrast fringes in the phase map. A numerical refocusing is performed by introducing an ideal lens as a multiplication by a phase field in the Fourier domain, and then a region of maximum speckle correlation is found by comparing undisturbed and disturbed subimages in different refocused imaging planes. After finding the right reconstruction distance, a phase map of high visibility is constructed. By this technique a 30% reduction of the phase error for a flow of helium gas and a 50% reduction of the phase error for a weak thin lens were obtained, which resulted in a significant improvement of the visual appearance of the phase maps.     

3-D FDTD simulation of shear waves for evaluation of complex modulus imaging

The Navier equation describing shear wave propagation in 3-D viscoelastic media is solved numerically with a finite differences time domain (FDTD) method. Solutions are formed in terms of transverse scatterer velocity waves and then verified via comparison to measured wave fields in heterogeneous hydrogel phantoms. The numerical algorithm is used as a tool to study the effects on complex shear modulus estimation from wave propagation in heterogeneous viscoelastic media. We used an algebraic Helmholtz inversion (AHI) technique to solve for the complex shear modulus from simulated and experimental velocity data acquired in 2-D and 3-D. Although 3-D velocity estimates are required in general, there are object geometries for which 2-D inversions provide accurate estimations of the material properties. Through simulations and experiments, we explored artifacts generated in elastic and dynamic-viscous shear modulus images related to the shear wavelength and average viscosity.     

低能电子投射全息的计算机模拟和数值重现研究

点源发出的低能量电子波经过样品的散射后,带有物体原子结构信息的散射波(物波)和未被散射的电子波(参考波)在收集平面上相互干涉形成的电子全息图即为低能电子投射全息图.本文在合理的物理模型下,以石墨的晶体结构为试样,通过计算机模拟的方法,首次对低能电子投射全息进行了研究,讨论了一些关键参数对晶体结构电子全息的重现像和分辨率的影响,并且实现了晶体结构三维数值重现,讨论了三维重现的效果.