Linear astigmatism of confocal off-axis reflective imaging systems and its elimination

Linear astigmatism of a confocal off-axis reflective imaging system when the object plane is tilted and located at a finite distance from the imaging system is derived. We show that linear astigmatism can be eliminated by proper configuration of the parent mirror axes in confocal off-axis two-mirror systems. The tilt angle of the image plane is also derived. The developed theory is verified by ray-tracing analysis of an example system.     

Synthetic aperture superresolution with multiple off-axis holograms

An optical setup to achieve superresolution in microscopy using holographic recording is presented. The technique is based on off-axis illumination of the object and a simple optical image processing stage after the imaging system for the interferometric recording process. The superresolution effect can be obtained either in one step by combining a spatial multiplexing process and an incoherent addition of different holograms or it can be implemented sequentially. Each hologram holds the information of each different frequency bandpass of the object spectrum. We have optically implemented the approach for a low-numerical-aperture commercial microscope objective. The system is simple and robust because the holographic interferometric recording setup is done after the imaging lens.     

Depth Transfer by an Imaging System

In many applications such as three-dimensional (3-D) data acquisition, the scanning of 3-D objects or 3-D display, it is necessary to understand how an imaging system can be used to obtain information on the structure of an object in the direction perpendicular to the image plane, i.e. depth information. In certain cases the formation of a 3-D image can be described by a theory based on optical transfer functions (OTF): the image intensity distribution is given by the 3-D convolution of the object and a 3-D point spread function (PSF); equivalently, in 3-D Fourier space the image spectrum is the product of the object spectrum and a 3-D OTF. This paper investigates the 3-D PSFs and OTFs that are associated with different pupil functions of the imaging system.     

Submicrometer optical tomography by multiple-wavelength digital holographic microscopy

We present a method for submicrometer tomographic imaging using multiple wavelengths in digital holographic microscopy. This method is based on the recording, at different wavelengths equally separated in the k domain, in off-axis geometry, of the interference between a reference wave and an object wave reflected by a microscopic specimen and magnified by a microscope objective. A CCD camera records the holograms consecutively, which are then numerically reconstructed following the convolution formulation to obtain each corresponding complex object wavefront. Their relative phases are adjusted to be equal in a given plane of interest and the resulting complex wavefronts are summed. The result of this operation is a constructive addition of complex waves in the selected plane and destructive addition in the others. Tomography is thus obtained by the attenuation of the amplitude out of the plane of interest. Numerical variation of the plane of interest enables one to scan the object in depth. For the presented simulations and experiments, 20 wavelengths are used in the 480-700 nm range. The result is a sectioning of the object in slices 725 nm thick.     

Optimization method for ultra-wide-angle and panoramic optical systems

To an ultra-wide-angle and panoramic optical system, the aberrations of point object at any field angle are separated into two types: the aperture-ray aberrations of off-axis point object and the chief-ray aberrations. A simple form of the triangular formulae of tracing an oblique-incidence ray is derived to calculate the chief-ray parameters and their aberrations; moreover, the aperture-ray aberrations of an off-axis point object are analyzed with the plane-symmetric aberration theory. Based on the two types of aberrations, we present a merit function for ultra-wide-angle and panoramic optical systems; the optimization program with the differential-evolution algorithm is then developed. To validate the optimization method we finally optimize a fish-eye lens and a catadioptric omnidirectional imaging system.     

Resolution improvement in digital holography by angular and polarization multiplexing

Angular and polarization multiplexing techniques are utilized in both object and reference arms in the digital holographic microscopy system to improve its resolution. The angular multiplexing provides on-axis and off-axis illumination and reference beams with different carrier frequencies. Polarization multiplexing prohibits the occurrence of interference between low and high object spatial frequencies and reference beams. The proposed system does not require special light sources or filtering masks. Experimental results show that the resolution of the synthesized image exceeds the resolution determined by the numerical aperture of the imaging microscope objective.     

Computer Simulation of Random Sphere Packing in an Arbitrarily Shaped Container

Most simulations of random sphere packing concern a cubic or cylindric container with periodic boundary, containers of other shapes are rarely studied. In this paper, a new relaxation algorithm with pre-expanding procedure for random sphere packing in an arbitrarily shaped container is presented. Boundaries of the container are simulated by overlapping spheres which covers the boundary surface of the container. We find 0.4~0.6 of the overlap rate is a proper value for boundary spheres. The algorithm begins with a random distribution of small internal spheres. Then the expansion and relaxation procedures are performed alternately to increase the packing density. The pre-expanding procedure stops when the packing density of internal spheres reaches a preset value. Following the pre-expanding procedure, the relaxation and shrinking iterations are carried out alternately to reduce the overlaps of internal spheres. The pre-expanding procedure avoids the overflow problem and gives a uniform distribution of initial spheres. Efficiency of the algorithm is increased with the cubic cell background system and double link data structure. Examples show the packing results agree well with both computational and experimental results. Packing density about 0.63 is obtained by the algorithm for random sphere packing in containers of various shapes.     

Experimental Validation of a Monte Carlo Procedure for the Evaluation of the Effect of a Turbid Medium on the Point Spread Function of an Optical System

Abstract

The presence of particulate matter interposed between the object and the receiver affects the quality of the image produced by an optical system. This paper presents the results of measurements pertaining to the effect of a turbid medium on the point spread function of an optical system. The results refer to transmitted received power measurements obtained in controlled laboratory experiments. A random distribution of polystyrene microspheres suspended in water constituted the investigated turbid medium. Measurements were carried out for particulate with diameters of 0·33 μm, 0·995 μm, 15·7 μm at a wavelength of 0·6328 μm and for different values of sphere concentration in water. The measured data are favourably compared with results obtained by means of a Monte Carlo based numerical method. This numerical procedure allows us to obtain the point spread function and the modulation transfer function (MTF) of an optical system when a turbid medium is present. Examples of calculated MTFs that refer to the three kinds of spheres used in the measurements are presented.     

Polychromatic Off-axis Optical Image

The colour specification in the polychromatic point-spread function leads to the integration for each primary colour of the monochromatic point-spread functions, taking account of the spectral emission of the source and the spectral response of the receiver. A numerical technique for the off-axis object point has been programmed. The colour variation on the off-axis image in the presence of the primary aberrations is discussed in terms of the illuminance and the chromaticity, and it is compared with that of the aberration free system. The study has been done for the standard observer (CIE 1931). Different correction types of transverse chromatic aberration, the most influential one on the chromaticity variation of the image, are studied, and the relation between the shape of this residual aberration curve and the quality of the image with respect to the illuminance and the chromaticity are shown. Simultaneously the influence of the spectral distribution of the source is shown.     

Spherical nonlinear correlations for global invariant three-dimensional object recognition

We define a nonlinear filtering based on correlations on unit spheres to obtain both rotation- and scale-invariant three-dimensional (3D) object detection. Tridimensionality is expressed in terms of range images. The phase Fourier transform (PhFT) of a range image provides information about the orientations of the 3D object surfaces. When the object is sequentially rotated, the amplitudes of the different PhFTs form a unit radius sphere. On the other hand, a scale change is equivalent to a multiplication of the amplitude of the PhFT by a constant factor. The effect of both rotation and scale changes for 3D objects means a change in the intensity of the unit radius sphere. We define a 3D filtering based on nonlinear operations between spherical correlations to achieve both scale- and rotation-invariant 3D object recognition.     

Experimental study of an off-axis three mirror anastigmatic system with wavefront coding technology

Wavefront coding (WFC) is a kind of computational imaging technique that controls defocus and defocus related aberrations of optical systems by introducing a specially designed phase distribution to the pupil function. This technology has been applied in many imaging systems to improve performance and/or reduce cost. The application of WFC technology in an off-axis three mirror anastigmatic (TMA) system has been proposed, and the design and optimization of optics, the restoration of degraded images, and the manufacturing of wavefront coded elements have been researched in our previous work. In this paper, we describe the alignment, the imaging experiment, and the image restoration of the off-axis TMA system with WFC technology. The ideal wavefront map is set to be the system error of the interferometer to simplify the assembly, and the coefficients of certain Zernike polynomials are monitored to verify the result in the alignment process. A pinhole of 20 μm diameter and the third plate of WT1005-62 resolution patterns are selected as the targets in the imaging experiment. The comparison of the tail lengths of point spread functions is represented to show the invariance of the image quality in the extended depth of focus. The structure similarity is applied to estimate the relationship among the captured images with varying defocus. We conclude that the experiment results agree with the earlier theoretical analysis.     

Hydrodynamics of deformable contiguous spherical shapes in an incompressible inviscid fluid

Summary An exact solution to the two-body interaction problem is presented for the case of spherical shapes moving in an incompressible and inviscid fluid. The spheres are assumed to translate in an arbitrary manner and to undergo radial deformation (or pulsation). The problem is formulated in terms of spherical harmonics and the force experienced by the spheres is obtained by employing the Lagally theorem. The expressions for the force are given as an infinite sum of coefficients which are found by solving an infinite set of linear equations. Three main geometries are considered, namely, two spheres exterior to each other, one sphere in the interior of the other and sphere in a rectangular channel. Numerical values for the added-mass coefficients as well as for the hydrodynamic forces are found for the case of rigid sphere moving toward or parallel to a rigid wall or a free surface, and a pulsating sphere in the proximity of these boundaries. Also given are numerical values for the transverse and the longitudinal addedmass coefficients for a sphere moving in a rectangular channel for different channel-blockage ratios.     

软硬交错金属空心球泡沫动力学性能研究

通过控制点阵结构中不同阵点位置空心球的软硬程度建立了交错金属空心球泡沫模型。在此基础上,对比研究了不同冲击条件下,均匀和各种交错金属空心球泡沫的动力学响应特性。重点分析了软硬空心球排布方式对金属空心球泡沫动力学性能的影响。研究结果表明,通过对软硬空心球排布方式的控制,材料可以在一定范围内根据外载条件进行自主调节,以控制金属空心球泡沫内的应力分布,提高了金属空心球泡沫的能量吸收效率。软硬交错空心球模型的建立为实现金属空心球泡沫的自适应设计提供了新的思路。     

Hybrid digital holographic imaging system for three-dimensional dense particle field measurement

To apply digital holography to the measurement of three-dimensional dense particle fields in large facilities, we have developed a hybrid digital holographic particle-imaging system. The technique combines the advantages of off-axis (side) scattering in suppressing speckle noise and on-axis (in-line) recording in lowering the digital sensor resolution requirement. A camera lens is attached to the digital sensor to compensate for the weak object wave from side scattering over a large recording distance. A simple numerical reconstruction algorithm is developed for holograms recorded with a lens without requiring complex and impractical mathematical corrections. We analyze the effect of image sensor resolution and off-axis angle on system performance and quantify the particle positioning accuracy of the system. The holographic system is successfully applied to the study of inertial particle clustering in isotropic turbulence.     

Markov models of integrating spheres for hyperspectral imaging

Theoretical models of the signal detected by a CCD camera during hyperspectral imaging with an integrating sphere are derived using Markov chains with absorbing states. The models provide analytical expressions that describe the real reflectance of the sample as a function of the detected signal at each pixel of the image. Validation of the models was done by using reflectance standards and tissue phantoms. The models provide accurate analytical solutions for samples and spheres that are near-Lambertian reflectors.     

Three-dimensional Linear Transfer by Means of Holographic Depth Selection

The 3D (three-dimensional) refractive index structure of weakly scattering objects can be made visible, without computation, by means of special holographic imaging methods, by which a 3D transfer process is performed. The refractive index may be complex, i.e. the object may weakly absorb. On certain assumptions, the transfer process is linear, and the complex amplitude distribution in the image plane represents the complex refractive index structure in a section through the object resolved three-dimensionally. By shifting the object, any section perpendicular to the axis can be adjusted. The properties of this 3D imaging process are described.     

Light scattering by a coated sphere illuminated with a Gaussian beam

The intensity of light scattered by a coated sphere illuminated with an off-axis Gaussian beam is calculated. Results are shown for different beam positions with respect to the sphere. As the beam is shifted further away from the surface of the sphere, the higher-Q morphology-dependent resonances become increasingly important in the backscatter spectra, and the angular scattering intensity becomes smoother.

The scattered intensity depends on the beam position, the refractive indices of the core and coat, the radius of the core, and the thickness of the coat. As the beam is moved further away from the sphere, the effect of the core on the scattering intensity decreases. When the incident Gaussian beam is focused outside of a particle with a relatively small core, the scattering spectra and angular scattering patterns become similar to those of a homogeneous sphere having the refractive index of the coat. These calculated results suggest that measurements of spectral scattering and angular scattering patterns for several Gaussian beam positions could be useful for the characterization of coated spheres.

     

SEPARATION AND BEHAVIOR OF NONSPHERICAL PARTICLES IN SEDIMENTATION/STERIC FIELD-FLOW FRACTIONATION

Sedimentation/steric field-flow fractionation (Sd/StFFF) is an elution separation technique capable of measuring the size distribution of 0.3-100 µm spherical and near-spherical particles with advantages including high resolution, fast analysis, and the ready collection of narrow size fractions. In this study we investigate the applicability of Sd/StFFF to various nonspherical particles including the doublets of spheres, rod-shaped glass fibers, compressed latex discs, and quartz particles (BCR 67 and 70) with complex mixed shapes. Some fractionation, retention, and selectivity features of these particles are defined and measured in relationship to those of spheres (latex beads), which are better understood. While the relative behavior of these two particle types depends on many factors, especially the distance of the particle from the Sd/StFFF channel wall, in most cases the nonspherical particles are eluted before spheres of equal volume and they often display higher selectivity than spherical particles. However, when retention of nonspherical particles is compared with that for spheres whose diameter is equal to the particle length, elongated particles (doublets and rods) eluted after the sphere while flattened particles (discs) eluted earlier than spheres, an observation that might assist in shape discrimination by Sd/StFFF. Thus, when latex microspheres are used for calibration to obtain size distribution curves, the diameter obtained for any given subpopulation will be less than the length of rods but greater than the diameter of discs. For complex particles such as the quartz particles, the diameter of a particle provided by classical sedimentation using spherical calibration is less than the equivalent spherical diameter of the particle in question whereas Sd/StFFF yields a diameter somewhat greater than the particle length. Thus, these two techniques will yield size distribution curves displaced from one another along the diameter axis. The difference in diameters can be eliminated by using a diameter correction factor of 2.7, which brings the distribution curves for quartz obtained by these two techniques into concurrence.     

Anechoic sphere phantoms for estimating 3-D resolution of very-high-frequency ultrasound scanners

Two phantoms have been constructed for assessing performance of high-frequency ultrasound imagers. They also allow for periodic quality assurance tests and training technicians in the use of higher-frequency scanners. The phantoms contain eight blocks of tissue-mimicking material; each block contains a spatially random distribution of suitably small anechoic spheres having a small distribution of diameters. The eight mean sphere diameters are distributed from 0.10 to 1.09 mm. The two phantoms differ primarily in terms of the frequency dependence of the backscatter coefficient of the background material. Because spheres have no preferred orientation, all three (spatial) dimensions of resolution contribute to sphere detection on an equal basis; thus, the resolution is termed 3-D. Two high-frequency scanners are compared. One employs single-element (fixed focus) transducers (25 and 55 MHz), and the other employs variable focus linear arrays (20, 30, and 40 MHz). The depth range for detection of spheres of each size is determined corresponding to determination of 3-D resolution as a function of depth. As expected, the single-element transducers are severely limited in useful imaging depth ranges compared with the linear arrays. In this preliminary report, only one human observer analyzed images.     

An application of splines to maximum likelihood radar imaging

Recent results in radar imaging using estimation theoretic techniques are applied to forming images from data from a compact radar range. Nonparametric maximum likelihood methods based on spline approximations are used. The object imaged is a one meter diameter sphere covered with wrinkled aluminum foil. This rough sphere approximately fits the diffuse model and the ideal scattering function for a rough rotating sphere is known. The results shown demonstrate that the proposed algorithm is realizable and that the image are comparable to simulations.©1993 John Wiley & Sons Inc