Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 2004"
TL;DR: In this paper, the authors show that a metal-insulator-metal geometry is necessary and sufficient condition for subwavelength confinement of the optical mode, and the resulting trade-off between propagation and confinement for surface plasmons is discussed.
Abstract: Plasmonic waveguides can guide light along metal-dielectric interfaces with propagating wave vectors of greater magnitude than are available in free space and hence with propagating wavelengths shorter than those in vacuum. This is a necessary, rather than sufficient, condition for subwavelength confinement of the optical mode. By use of the reflection pole method, the two-dimensional modal solutions for single planar waveguides as well as adjacent waveguide systems are solved. We demonstrate that, to achieve subwavelength pitches, a metal-insulator-metal geometry is required with higher confinement factors and smaller spatial extent than conventional insulator-metal-insulator structures. The resulting trade-off between propagation and confinement for surface plasmons is discussed, and optimization by materials selection is described.
644 citations
TL;DR: A statistical analysis of light propagation in media leads to new relationships between the K-M scattering S and absorbing K coefficients and the intrinsic scattering s and absorbing a coefficients of a material that indicate that the S and K coefficients depend non-linearly on both a and s.
Abstract: Using a statistical analysis of light propagation in media, we propose a revision to Kubelka-Munk (K-M) theory by taking into account the effect of scattering on the path length of light propagation (path variation). This leads to new relationships between the K-M scattering S and absorbing K coefficients and the intrinsic scattering s and absorbing a coefficients of a material that indicate that the S and K coefficients depend non-linearly on both a and s. The additivity law that bridges K-M S and K coefficients of a composite medium, such as dye-dispersed paper (dyed paper) and those of its material components (dye and paper), is also revised. It is further shown that experimental findings on dyed paper that the original K-M theory failed to explain can be clearly understood and accommodated by the new K-M theoretical framework (two-flux approach). Numerical simulations with the revised theory on model ink, paper, and dyed paper have been carried out.
302 citations
TL;DR: A general algorithm for propagating an input field through axially symmetric systems using the generalized method for evaluating the zero-order Hankel transform, particularly suitable for field propagation.
Abstract: The method originally proposed by Yu et al. [Opt. Lett. 23, 409 (1998)] for evaluating the zero-order Hankel transform is generalized to high-order Hankel transforms. Since the method preserves the discrete form of the Parseval theorem, it is particularly suitable for field propagation. A general algorithm for propagating an input field through axially symmetric systems using the generalized method is given. The advantages and the disadvantages of the method with respect to other typical methods are discussed.
254 citations
TL;DR: A new digital two-step reconstruction method for off-axis holograms recorded on a CCD camera that is sufficiently general to be applied to sophisticated optical setups that include a microscope objective.
Abstract: We present a new digital two-step reconstruction method for off-axis holograms recorded on a CCD camera. First, we retrieve the complex object wave in the acquisition plane from the hologram's samples. In a second step, if required, we propagate the wave front by using a digital Fresnel transform to achieve proper focus. This algorithm is sufficiently general to be applied to sophisticated optical setups that include a microscope objective. We characterize and evaluate the algorithm by using simulated data sets and demonstrate its applicability to real-world experimental conditions by reconstructing optically acquired holograms.
217 citations
TL;DR: In this paper, the Ince-Gaussian transition modes (IGM) were introduced, which constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation in elliptic coordinates and that are transverse eigenmodes of stable resonators.
Abstract: We present the Ince-Gaussian modes that constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation in elliptic coordinates and that are transverse eigenmodes of stable resonators. The transverse shape of these modes is described by the Ince polynomials and is structurally stable under propagation. Ince-Gaussian modes constitute the exact and continuous transition modes between Laguerre- and Hermite-Gaussian modes. The expansions between the three families are derived and discussed. As with Laguerre-Gaussian modes, it is possible to construct helical Ince-Gaussian modes that exhibit rotating phase features whose intensity pattern is formed by elliptic rings and whose phase rotates elliptically.
202 citations
TL;DR: An optimal closed-loop control law that accounts for both spatial and temporal statistics is proposed and demonstrated through MCAO numerical simulations representative of astronomical observation on a 8-m-class telescope in the near infrared.
Abstract: Classical adaptive optics (AO) is now a widespread technique for high-resolution imaging with astronomical ground-based telescopes. It generally uses simple and efficient control algorithms. Multiconjugate adaptive optics (MCAO) is a more recent and very promising technique that should extend the corrected field of view. This technique has not yet been experimentally validated, but simulations already show its high potential. The importance for MCAO of an optimal reconstruction using turbulence spatial statistics has already been demonstrated through open-loop simulations. We propose an optimal closed-loop control law that accounts for both spatial and temporal statistics. The prior information on the turbulence, as well as on the wave-front sensing noise, is expressed in a state-space model. The optimal phase estimation is then given by a Kalman filter. The equations describing the system are given and the underlying assumptions explained. The control law is then derived. The gain brought by this approach is demonstrated through MCAO numerical simulations representative of astronomical observation on a 8-m-class telescope in the near infrared. We also discuss the application of this control approach to classical AO. Even in classical AO, the technique could be relevant especially for future extreme AO systems.
197 citations
TL;DR: A deconvolution method developed in a Bayesian framework in the context of imaging through turbulence with adaptive optics that uses a noise model that accounts for both photonic and detector noises and reckons with an imperfect knowledge of the point-spread function (PSF).
Abstract: Deconvolution is a necessary tool for the exploitation of a number of imaging instruments. We describe a deconvolution method developed in a Bayesian framework in the context of imaging through turbulence with adaptive optics. This method uses a noise model that accounts for both photonic and detector noises. It additionally contains a regularization term that is appropriate for objects that are a mix of sharp edges and smooth areas. Finally, it reckons with an imperfect knowledge of the point-spread function (PSF) by estimating the PSF jointly with the object under soft constraints rather than blindly (i.e., without constraints). These constraints are designed to embody our knowledge of the PSF. The implementation of this method is called Mistral. It is validated by simulations, and its effectiveness is illustrated by deconvolution results on experimental data taken on various adaptive optics systems and telescopes. Some of these deconvolutions have already been used to derive published astrophysical interpretations.
194 citations
TL;DR: The modes are shown to be spatially fully coherent in the sense of a recently introduced spectral degree of electromagnetic coherence and it is proved that the electric cross-spectral density tensor can be rigorously expressed as a correlation tensor averaged over an appropriate ensemble of strictly monochromatic vectorial wave functions.
Abstract: We construct the coherent-mode representation for fluctuating, statistically stationary electromagnetic fields. The modes are shown to be spatially fully coherent in the sense of a recently introduced spectral degree of electromagnetic coherence. We also prove that the electric cross-spectral density tensor can be rigorously expressed as a correlation tensor averaged over an appropriate ensemble of strictly monochromatic vectorial wave functions. The formalism is demonstrated for partially polarized, partially coherent Gaussian Schell-model beams, but the theory applies to arbitrary random electromagnetic fields and can find applications in radiation and propagation and in inverse problems.
180 citations
TL;DR: This work proposes a robust autofocus method for reconstructing digital Fresnel holograms that maximizes a sharpness metric related to the sparsity of the signal's expansion in distance-dependent waveletlike Fresnelet bases.
Abstract: We propose a robust autofocus method for reconstructing digital Fresnel holograms. The numerical reconstruction involves simulating the propagation of a complex wave front to the appropriate distance. Since the latter value is difficult to determine manually, it is desirable to rely on an automatic procedure for finding the optimal distance to achieve high-quality reconstructions. Our algorithm maximizes a sharpness metric related to the sparsity of the signal's expansion in distance-dependent waveletlike Fresnelet bases. We show results from simulations and experimental situations that confirm its applicability.
179 citations
TL;DR: It is shown that, by analyzing highlights, a direct correlation between illumination Chromaticity and image chromaticity can be obtained and this correlation is clearly described in “inverse-intensity chromaticite space,” a novel two-dimensional space that is introduced.
Abstract: Existing color constancy methods cannot handle both uniformly colored surfaces and highly textured surfaces in a single integrated framework. Statistics-based methods require many surface colors and become error prone when there are only a few surface colors. In contrast, dichromatic-based methods can successfully handle uniformly colored surfaces but cannot be applied to highly textured surfaces, since they require precise color segmentation. We present a single integrated method to estimate illumination chromaticity from single-colored and multicolored surfaces. Unlike existing dichromatic-based methods, the proposed method requires only rough highlight regions without segmenting the colors inside them. We show that, by analyzing highlights, a direct correlation between illumination chromaticity and image chromaticity can be obtained. This correlation is clearly described in "inverse-intensity chromaticity space," a novel two-dimensional space that we introduce. In addition, when Hough transform and histogram analysis is utilized in this space, illumination chromaticity can be estimated robustly, even for a highly textured surface.
159 citations
TL;DR: A fast and accurate method is developed to compute the natural frequencies and scattering characteristics of arbitrary-shape two-dimensional dielectric resonators that is used in the simulation of several optical microcavities for modern dense wavelength-division-multiplexed systems.
Abstract: A fast and accurate method is developed to compute the natural frequencies and scattering characteristics of arbitrary-shape two-dimensional dielectric resonators. The problem is formulated in terms of a uniquely solvable set of second-kind boundary integral equations and discretized by the Galerkin method with angular exponents as global test and trial functions. The log-singular term is extracted from one of the kernels, and closed-form expressions are derived for the main parts of all the integral operators. The resulting discrete scheme has a very high convergence rate. The method is used in the simulation of several optical microcavities for modern dense wavelength-division-multiplexed systems.
TL;DR: The considerable agreement between data obtained with MR and Scheimpflug imaging, two different yet complementary in vivo imaging techniques, validates the Scheim pflug correction algorithms of Cook and Koretz and suggests the capability of directly integrating information from both.
Abstract: High-resolution imaging with a camera system built on the Scheimpflug principle has been used to characterize the geometry of the anterior segment of the adult human eye as a function of aging and accommodative state but is critically dependent on algorithms for correction of distortion. High-resolution magnetic resonance imaging (MRI), in contrast, provides lower-resolution information about the adult eye but is undistorted. To test the accuracy of the Scheimpflug correction methods used by Cook and Koretz [J. Opt. Soc. Am. A 15, 1473 (1998)]; [Appl. Opt. 30, 2088 (1991)], data on anterior chamber and segment lengths, as well as lens thickness and anterior and posterior curvatures, were compared with corresponding MRI data for adults aged 18-50 at 0 diopter accommodation. Excellent statistical agreement was found between the MRI and the Scheimpflug data sets with the exception of the posterior lens radius of curvature, which is less well defined than the other measurements in the Scheimpflug images. The considerable agreement between data obtained with MR and Scheimpflug imaging, two different yet complementary in vivo imaging techniques, validates the Scheimpflug correction algorithms of Cook and Koretz and suggests the capability of directly integrating information from both. A third, equivalent, data set obtained with a Scheimpflug-style camera system differs considerably from both Scheimpflug and MRI results in magnitude and age dependence, with negative implications for this alternative method and its correction procedures.
TL;DR: A new algorithm for calculation of the band structure of photonic crystal slabs is presented that combines the plane-wave expansion method with perfectly matched layers for the termination of the computational region in the direction out of the plane.
Abstract: We present a new algorithm for calculation of the band structure of photonic crystal slabs. This algorithm combines the plane-wave expansion method with perfectly matched layers for the termination of the computational region in the direction out of the plane. In addition, the effective-medium tensor is applied to improve convergence. A general complex eigenvalue problem is then obtained. Two criteria are presented to distinguish the guided modes from the PML modes. As such, this scheme can accurately determine the band structure both above and below the light cone. The convergence of the algorithm presented has been studied. The results obtained by using this algorithm have been compared with those obtained by the finite-difference time-domain method and found to agree very well.
TL;DR: An algorithm for maximum-likelihood image estimation on the basis of the expectation-maximization (EM) formalism is derived by using a new approximate model for depth-varying image formation for optical sectioning microscopy that incorporates spherical aberration that worsens as the microscope is focused deeper under the cover slip.
Abstract: We derive an algorithm for maximum-likelihood image estimation on the basis of the expectation-maximization (EM) formalism by using a new approximate model for depth-varying image formation for optical sectioning microscopy. This new strata-based model incorporates spherical aberration that worsens as the microscope is focused deeper under the cover slip and is the result of the refractive-index mismatch between the immersion medium and the mounting medium of the specimen. Images of a specimen with known geometry and refractive index show that the model captures the main features of the image. We analyze the performance of the depth-variant EM algorithm with simulations, which show that the algorithm can compensate for image degradation changing with depth.
TL;DR: From diffusing wave spectroscopy measurements, the characteristic depolarization length for linearly polarized light, lp, is deduced and the dependence of this length on the scattering anisotropy parameter g spanning an extended range from -1 (backscattering) to 1 (forward scattering).
Abstract: We formulate a quantitative description of backscattered linearly polarized light with an extended photon diffusion formalism taking explicitly into account the scattering anisotropy parameter g of the medium. From diffusing wave spectroscopy measurements, the characteristic depolarization length for linearly polarized light, lp, is deduced. We investigate the dependence of this length on the scattering anisotropy parameter g spanning an extended range from -1 (backscattering) to 1 (forward scattering). Good agreement is found with Monte Carlo simulations of multiply scattered light.
TL;DR: The spatially filtered wave-front sensor (SFWFS) mitigates this phenomenon by using a field stop at a focal plane before the wave- front sensor to act as a low-pass filter on the phase, significantly reducing the high-spatial-frequency content phase seen by the waveside sensor at moderate to high Strehl ratios.
Abstract: Adaptive optics (AO) systems take sampled measurements of the wave-front phase. Because in the general case the spatial-frequency content of the phase aberration is not band limited, aliasing will occur. This aliasing will cause increased residual error and increased scattered light in the point-spread function (PSF). The spatially filtered wave-front sensor (SFWFS) mitigates this phenomenon by using a field stop at a focal plane before the wave-front sensor. This stop acts as a low-pass filter on the phase, significantly reducing the high-spatial-frequency content phase seen by the wave-front sensor at moderate to high Strehl ratios. We study the properties and performance of the SFWFS for open- and closed-loop correction of atmospheric turbulence, segmented-primary-mirror errors, and sensing with broadband light. In closed loop the filter reduces high-spatial-frequency phase power by a factor of 103 to 108. In a full AO-system simulation, this translates to a reduction by up to 625 times in the residual error power due to aliasing over a specific spatial frequency range. The final PSF (generated with apodization of the pupil) has up to a 100 times reduction in intensity out to λ/2d.
TL;DR: The hollow elliptical Gaussian beam (HEGB) provides a convenient way to describe elliptical dark-hollow laser beams and can be used conveniently to study the motion of atoms in a dark- hollow laser beam.
Abstract: A new mathematical model called hollow elliptical Gaussian beam (HEGB) is proposed to describe a dark-hollow laser beam with noncircular symmetry in terms of a tensor method. The HEGB can be expressed as a superposition of a series of elliptical Hermite–Gaussian modes. By using the generalized diffraction integral formulas for light passing through paraxial optical systems, analytical propagation formulas for HEGBs passing through paraxial aligned and misaligned optical systems are obtained through vector integration. As examples of applications, evolution properties of the intensity distribution of HEGBs in free-space propagation were studied. Propagation properties of HEGBs through a misaligned thin lens were also studied. The HEGB provides a convenient way to describe elliptical dark-hollow laser beams and can be used conveniently to study the motion of atoms in a dark-hollow laser beam.
TL;DR: It is found that the celestial E-vector pattern generally follows the Rayleigh pattern well, which is a fundamental hypothesis in the studies of animal orientation and human navigation with the use of the celestial alpha pattern.
Abstract: We present the first high-resolution maps of Rayleigh behavior in clear and cloudy sky conditions measured by full-sky imaging polarimetry at the wavelengths of 650 nm (red), 550 nm (green), and 450 nm (blue) versus the solar elevation angle θs. Our maps display those celestial areas at which the deviation Δα= |αmeas- αRayleigh| is below the threshold αthres=5°, where αmeas is the angle of polarization of skylight measured by full-sky imaging polarimetry, and αRayleigh is the celestial angle of polarization calculated on the basis of the single-scattering Rayleigh model. From these maps we derived the proportion r of the full sky for which the single-scattering Rayleigh model describes well (with an accuracy of Δα=5°) the E-vector alignment of skylight. Depending on θs,r is high for clear skies, especially for low solar elevations (40%
TL;DR: A method is presented for fluorescence optical diffusion tomography in turbid media using multiple-frequency data that uses a frequency-domain diffusion equation model to reconstruct the fluorescent yield and lifetime by means of a Bayesian framework and an efficient, nonlinear optimizer.
Abstract: A method is presented for fluorescence optical diffusion tomography in turbid media using multiple-frequency data. The method uses a frequency-domain diffusion equation model to reconstruct the fluorescent yield and lifetime by means of a Bayesian framework and an efficient, nonlinear optimizer. The method is demonstrated by using simulations and laboratory experiments to show that reconstruction quality can be improved in certain problems through the use of more than one frequency. A broadly applicable mutual information performance metric is also presented and used to investigate the advantages of using multiple modulation frequencies compared with using only one.
TL;DR: It is shown that for noncorrelated noise, the Bhattacharyya distance can be an efficient candidate for contrast definition when one uses statistical algorithms for detection, location, or segmentation.
Abstract: In many imaging applications, the measured optical images are perturbed by strong fluctuations or noise. This can be the case, for example, for coherent-active or low-flux imagery. In such cases, the noise is not Gaussian additive and the definition of a contrast parameter between two regions in the image is not always a straightforward task. We show that for noncorrelated noise, the Bhattacharyya distance can be an efficient candidate for contrast definition when one uses statistical algorithms for detection, location, or segmentation. We demonstrate with numerical simulations that different images with the same Bhattacharyya distance lead to equivalent values of the performance criterion for a large number of probability laws. The Bhattacharyya distance can thus be used to compare different noisy situations and to simplify the analysis and the specification of optical imaging systems.
TL;DR: Singular-value analysis of the fluorescence tomographic problem was applied to determine optimal source and detector distributions that result in data sets that are balanced between information content and size and demonstrated the utility of SVA as a simple and efficient means of optimizing experimental parameters in problems for which a forward model of the data collection process is available.
Abstract: The advent of specific molecular markers and probes employing optical reporters has encouraged the application of in vivo diffuse tomographic imaging at greater spatial resolutions and hence data-set volumes. This study applied singular-value analysis (SVA) of the fluorescence tomographic problem to determine optimal source and detector distributions that result in data sets that are balanced between information content and size. Weight matrices describing the tomographic forward problem were constructed for a range of source and detector distributions and fields of view and were decomposed into their associated singular values. These singular-value spectra were then compared so that we could observe the effects of each parameter on imaging performance. The findings of the SVA were then confirmed by examining reconstructions of simulated and experimental data acquired with the same optode distributions as examined by SVA. It was seen that for a 20-mm target width, which is relevant to the small-animal imaging situation, the source and detector fields of view should be set at approximately 30 mm. Equal numbers of sources and detectors result in the best imaging performance in the parallel-plate geometry and should be employed when logistically feasible. These data provide guidelines for the design of small-animal diffuse optical tomographic imaging systems and demonstrate the utility of SVA as a simple and efficient means of optimizing experimental parameters in problems for which a forward model of the data collection process is available.
TL;DR: This work presents a texture camera that can conveniently capture spatially varying reflectance on a surface, and eliminates the need for complex mechanical apparatus to move the light source and the camera over a hemisphere of possible directions.
Abstract: Capturing surface appearance is a challenging task because reflectance varies as a function of viewing and illumination direction. In addition, most real-world surfaces have a textured appearance, so reflectance also varies spatially. We present a texture camera that can conveniently capture spatially varying reflectance on a surface. Unlike other bidirectional imaging devices, the design eliminates the need for complex mechanical apparatus to move the light source and the camera over a hemisphere of possible directions. To facilitate fast and convenient measurement, the device uses a curved mirror so that multiple views of the same surface point are captured simultaneously. Simple planar motions of the imaging components also permit change of illumination direction and region imaging. We present the current prototype of this device, imaging results, and an analysis of the important imaging properties.
TL;DR: It is shown that, given the required bit-error rate (BER) and the rms random pointing jitter, an optimal transceiver gain exists that minimizes transmitted power.
Abstract: We derive a model that optimizes the performance of a laser satellite communication link with an optical preamplifier in the presence of random jitter in the transmitter–receiver line of sight. The system utilizes a transceiver containing a single telescope with a circulator. The telescope is used for both transmitting and receiving and thus reduces communication terminal dimensions and weight. The optimization model was derived under the assumption that the dominant noise source was amplifier spontaneous-emission noise. It is shown that, given the required bit-error rate (BER) and the rms random pointing jitter, an optimal transceiver gain exists that minimizes transmitted power. We investigate the effect of the amplifier spontaneous-emission noise on the optimal transmitted power and gain by performing an optimization procedure for various combinations of amplifier gain and noise figure. We demonstrate that the amplifier noise figure determines the optimal transmitted power needed to achieve the desired BER but does not affect the optimal transceiver telescope gain. Our numerical example shows that for a BER of 10-9, doubling the amplifier noise figure results in an 80% increase in minimal transmitted power for a rms pointing jitter of 0.44 μrad.
TL;DR: A very simple theoretical demonstration that a homogeneous material with both relative permittivity and permeability equal to -1 cannot exist, even for a unique frequency, and concludes that a material able to focus the light more efficiently than the current devices (but not perfectly) could exist.
Abstract: In a recent paper, Pendry [Phys. Rev. Lett.86, 3966 (2000)] mentioned the possibility of making perfect lenses by using a slab of left-handed material with relative permeability and permittivity equal to -1, a property first stated by Veselago [Sov. Phys. Usp.10, 509 (1968)]. Pendry gave a demonstration of the vital effect of the evanescent waves in this process, arguing that these waves are amplified inside the slab. We present first a very simple theoretical demonstration that a homogeneous material with both relative permittivity and permeability equal to -1 cannot exist, even for a unique frequency. This demonstration shows that the perfect lens proposed by Pendry can be interpreted as a means to move in real space the virtual perfect image of a point source given by a plane mirror. We show that, owing to evanescent waves, the concept of effective medium for heterogeneous materials is questionable, even when the wavelength of the incident light is much larger than the size of the heterogeneities. The effect of heterogeneities is compared with that of absorption. We conclude that a material able to focus the light more efficiently than the current devices (but not perfectly) could exist.
TL;DR: This work presents a new prescription-the surface-corrected-lattice-dispersion relation (SCLDR)--for assigning the dipole polarizabilities while taking into account both target geometry and finite wavelength.
Abstract: The discrete-dipole approximation (DDA) is a powerful method for calculating absorption and scattering by targets that have sizes smaller than or comparable with the wavelength of the incident radiation. We present a new prescription—the surface-corrected-lattice-dispersion relation (SCLDR)—for assigning the dipole polarizabilities while taking into account both target geometry and finite wavelength. We test the SCLDR in DDA calculations for spherical and ellipsoidal targets and show that for a fixed number of dipoles, the SCLDR prescription results in increased accuracy in the calculated cross sections for absorption and scattering. We discuss extension of the SCLDR prescription to irregular targets.
TL;DR: In this paper, the authors studied light propagation in biological tissue using the radiative transport equation and showed that the Green's function is the fundamental solution to the transport equation from which all other solutions can be computed.
Abstract: We study light propagation in biological tissue using the radiative transport equation. The Green’s function is the fundamental solution to the radiative transport equation from which all other solutions can be computed. We compute the Green’s function as an expansion in plane-wave modes. We calculate these plane-wave modes numerically using the discrete-ordinate method. When scattering is sharply peaked, calculating the plane-wave modes for the transport equation is difficult. For that case we replace it with the Fokker–Planck equation since the latter gives a good approximation to the transport equation and requires less work to solve. We calculate the plane-wave modes for the Fokker–Planck equation numerically using a finite-difference approximation. The method of computing the Green’s function for it is the same as for the transport equation. We demonstrate the use of the Green’s function for the transport and Fokker–Planck equations by computing the point-spread function in a half-space composed of a uniform scattering and absorbing medium.
TL;DR: In this article, a fast and accurate direct Fourier method for reconstructing a function f of three variables from a number of its parallel beam projections is described, where the main application is to reconstruct the mass density of a biological macromolecule.
Abstract: We describe a fast and accurate direct Fourier method for reconstructing a function f of three variables from a number of its parallel beam projections. The main application of our method is in single particle analysis, where the goal is to reconstruct the mass density of a biological macromolecule. Typically, the number of projections is extremely large, and each projection is extremely noisy. The projection directions are random and initially unknown. However, it is possible to determine both the directions and f by an iterative procedure; during each stage of the iteration, one has to solve a reconstruction problem of the type considered here. Our reconstruction algorithm is distinguished from other direct Fourier methods by the use of gridding techniques that provide an efficient means to compute a uniformly sampled version of a function g from a nonuniformly sampled version of Fg, the Fourier transform of g, or vice versa. We apply the two-dimensional reverse gridding method to each available projection of f, the function to be reconstructed, in order to obtain Ff on a special spherical grid. Then we use the three-dimensional gridding method to reconstruct f from this sampled version of Ff. This stage requires a proper weighting of the samples of Ff to compensate for their nonuniform distribution. We use a fast method for computing appropriate weights that exploits the special properties of the spherical sampling grid for Ff and involves the computation of a Voronoi diagram on the unit sphere. We demonstrate the excellent speed and accuracy of our method by using simulated data.
TL;DR: In this article, the defocused weak-object transfer function of a partially coherent bright-field microscope is calculated for weak defocus, and the use of this transfer function for phase restoration from images of weak mixed phase-amplitude objects is discussed.
Abstract: The defocused weak-object transfer function of a partially coherent bright-field microscope is calculated. For weak defocus, this can be expressed analytically. Use of this transfer function for phase restoration (quantitative phase retrieval) from images of weak mixed phase-amplitude objects is discussed.
TL;DR: It is shown that by using the plane-wave representation of the fundamental Gaussian mode as a seed function, all higher-order beam modes can be derived by acting with differential operators on this fundamental solution.
Abstract: A unified operator approach is described for deriving Hermite–Gaussian and Laguerre–Gaussian laser beams by using as a starting point a plane-wave-spectrum representation of the electromagnetic field. We show that by using the plane-wave representation of the fundamental Gaussian mode as a seed function, all higher-order beam modes can be derived by acting with differential operators on this fundamental solution. The approach presented can be easily generalized to nonparaxial situations and to include vector effects of the electromagnetic field.
TL;DR: Two alternatives, based on a change of independent variables and on Dirichlet-to-interior-derivative operators, respectively, successfully resolve the cancellations and thus allow for very-high-order calculations that can significantly expand the domain of applicability of shape-perturbation approaches.
Abstract: We present new, stabilized shape-perturbation methods for calculations of scattering from rough surfaces. For practical purposes, we present new algorithms for both low- (first- and second-) and high-order implementations. The new schemes are designed with guidance from our previous results that uncovered the basic mechanism behind the instabilities that can arise in methods based on shape perturbations [ D. P. Nicholls F. Reitich , J. Opt. Soc. Am. A21, 590 (2004)]. As was shown there, these instabilities stem from significant cancellations that are inevitably present in the recursions underlying these methods. This clear identification of the source of instabilities resulted also in a collection of guiding principles, which we now test and confirm. As predicted, improved low-order algorithms can be attained from an explicit consideration of the recurrence. At high orders, on the other hand, the complexity of the formulas precludes an explicit account of cancellations. In this case, however, the theory suggests a number of alternatives to implicitly mollify them. We show that two such alternatives, based on a change of independent variables and on Dirichlet-to-interior-derivative operators, respectively, successfully resolve the cancellations and thus allow for very-high-order calculations that can significantly expand the domain of applicability of shape-perturbation approaches.