Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 2009"

Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures

Abstract: Among the most popular approaches used for simulating plasmonic systems, the discrete dipole approximation suffers from poorly scaling volume discretization and limited near-field accuracy. We demonstrate that transformation to a surface integral formulation improves scalability and convergence and provides a flexible geometric approximation allowing, e.g., to investigate the influence of fabrication accuracy. The occurring integrals can be solved quasi-analytically, permitting even rapidly changing fields to be determined arbitrarily close to a scatterer. This insight into the extreme near-field behavior is useful for modeling closely packed particle ensembles and to study "hot spots" in plasmonic nanostructures used for plasmon-enhanced Raman scattering.

Non-line-of-sight underwater optical wireless communication network.

Abstract: The growing need for ocean observation systems has stimulated considerable interest within the research community in advancing the enabling technologies of underwater wireless communication and underwater sensor networks. Sensors and ad hoc sensor networks are the emerging tools for performing extensive data-gathering operations on land, and solutions in the subsea setting are being sought. Efficient communication from the sensors and within the network is critical, but the underwater environment is extremely challenging. Addressing the special features of underwater wireless communication in sensor networks, we propose a novel non-line-of-sight network concept in which the link is implemented by means of back-reflection of the propagating optic signal at the ocean-air interface and derive a mathematical model of the channel. Point-to-multipoint links can be achieved in an energy efficient manner and broadcast broadband communications, such as video transmissions, can be executed. We show achievable bit error rates as a function of sensor node separation and demonstrate the feasibility of this concept using state-of-the-art silicon photomultiplier detectors.

Estimating chromophore distributions from multiwavelength photoacoustic images.

Abstract: Biomedical photoacoustic tomography (PAT) can provide qualitative images of biomedical soft tissue with high spatial resolution. However, whether it is possible to give accurate quantitative estimates of the spatially varying concentrations of the sources of photoacoustic contrast—endogenous or exogenous chromophores—remains an open question. Even if the chromophores' absorption spectra are known, the problem is nonlinear and ill-posed. We describe a framework for obtaining such quantitative estimates. When the optical scattering distribution is known, adjoint and gradient-based optimization techniques can be used to recover the concentration distributions of the individual chromophores that contribute to the overall tissue absorption. When the scattering distribution is unknown, prior knowledge of the wavelength dependence of the scattering is shown to be sufficient to overcome the absorption-scattering nonuniqueness and allow both distributions of chromophore concentrations and scattering to be recovered from multiwavelength photoacoustic images.

Analysis of depolarizing Mueller matrices through a symmetric decomposition.

Abstract: A product decomposition of a depolarizing Mueller matrix consisting in the sequence of five factors—a diagonal depolarizer stacked between two retarder and diattenuator pairs—is proposed. This novel “symmetric” decomposition allows for a straightforward interpretation and parameterization of an experimentally determined Mueller matrix in terms of an arrangement of polarization devices and their characteristic parameters: diattenuations, retardances, and axis azimuths. Its application is illustrated on experimentally determined Mueller matrices.

Spiral phase filtering and orientation-selective edge detection/enhancement

Abstract: A spiral phase plate with an azimuthal structure exp[iϕ](0⩽ϕ<2π) has been used as a filter in a 4f system to achieve edge enhancement. Generally such edge-enhanced effect is isotropic, i.e., each edge of an input pattern is enhanced to the same degree regardless of its orientation. We found that one can achieve anisotropic edge enhancement by breaking down the symmetry of the filtering process. This can be done in two ways: first, by use of a fractional spiral phase filter (SPF) with a fractional topological charge and a controllable orientation of the edge discontinuity, and second, by the lateral shifting of the SPF. We interpret this process as a vortex formation due to the diffraction of the Fourier spectrum of the input pattern by a SPF with an integer and fractional topological charge. Optical experiments using a spatial light modulator were carried out to verify our proposal.

Stochastic variations in sensory awareness are driven by noisy neuronal adaptation: evidence from serial correlations in perceptual bistability

Abstract: When the sensory system is subjected to ambiguous input, perception alternates between interpretations in a seemingly random fashion. Although neuronal noise obviously plays a role, the neural mechanism for the generation of randomness at the slow time scale of the percept durations (multiple seconds) is unresolved. Here significant nonzero serial correlations are reported in series of visual percept durations (to the author's knowledge for the first time accounting for duration impurities caused by reaction time, drift, and incomplete percepts). Serial correlations for perceptual rivalry using structure-from-motion ambiguity were smaller than for binocular rivalry using orthogonal gratings. A spectrum of computational models is considered, and it is concluded that noise in adaptation of percept-related neurons causes the serial correlations. This work bridges, in a physiologically plausible way, widely appreciated deterministic modeling and randomness in experimental observations of visual rivalry.

Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry

Abstract: We use closed-loop deformable mirror telemetry from Altair and Keck adaptive optics (AO) to determine whether atmospheric turbulence follows the frozen flow hypothesis. Using telemetry from AO systems, our algorithms (based on the predictive Fourier control framework) detect frozen flow >94% of the time. Usually one to three layers are detected. Between 20% and 40% of the total controllable phase power is due to frozen flow. Velocity vector RMS variability is less than 0.5 m/s (per axis) on 10-s intervals, indicating that the atmosphere is stable enough for predictive control to measure and adapt to prevailing atmospheric conditions before they change.

Masked fake face detection using radiance measurements

Abstract: This research presents a novel 2D feature space where real faces and masked fake faces can be effectively discriminated. We exploit the reflectance disparity based on albedo between real faces and fake materials. The feature vector used consists of radiance measurements of the forehead region under 850 and 685 nm illuminations. Facial skin and mask material show linearly separable distributions in the feature space proposed. By simply applying Fisher's linear discriminant, we have achieved 97.78% accuracy in fake face detection. Our method can be easily implemented in commercial face verification systems.

Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: spherical aberration.

Abstract: Building off an earlier work on multinodal third-order aberrations [J. Opt. Soc. Am. A22, 1389 (2005)], this is the first in a series of papers that derives and illustrates the characteristic multinodal geometry for each of the fifth-order aberrations. Part I (as this paper will be referred to) will present the spherical aberration family: specifically, W(060), W(240M) and W(242), and W(080) (fifth-order spherical, oblique spherical, and seventh-order spherical). Nodal aberration theory is proving to be very effective as both an optical design tool for fully unobscured off-axis telescopes and as an analysis method, particularly in the context of the response of any imaging optical systems to misalignment. It is important to recognize that this multinodal approach to aberration theory is not restricted to small perturbations. The remaining papers in this series will result in a complete presentation of the intrinsic characteristic multinodal properties of each of the fifth-order aberrations. As such, this series provides a definitive theory of the optical aberrations of (nonanamorphic) imaging systems with a circular aperture stop.

Performance dependence of hybrid x-ray computed tomography/fluorescence molecular tomography on the optical forward problem.

Abstract: Hybrid imaging systems combining x-ray computed tomography (CT) and fluorescence tomography can improve fluorescence imaging performance by incorporating anatomical x-ray CT information into the optical inversion problem. While the use of image priors has been investigated in the past, little is known about the optimal use of forward photon propagation models in hybrid optical systems. In this paper, we explore the impact on reconstruction accuracy of the use of propagation models of varying complexity, specifically in the context of these hybrid imaging systems where significant structural information is known a priori. Our results demonstrate that the use of generically known parameters provides near optimal performance, even when parameter mismatch remains.

Perceptual analysis of distance measures for color constancy algorithms

Abstract: Color constancy algorithms are often evaluated by using a distance measure that is based on mathematical principles, such as the angular error. However, it is unknown whether these distance measures correlate to human vision. Therefore, the main goal of our paper is to analyze the correlation between several performance measures and the quality, obtained by using psychophysical experiments, of the output images generated by various color constancy algorithms. Subsequent issues that are addressed are the distribution of performance measures, suggesting additional and alternative information that can be provided to summarize the performance over a large set of images, and the perceptual significance of obtained improvements, i.e., the improvement that should be obtained before the difference becomes noticeable to a human observer.

Selection of regularization parameter in total variation image restoration.

Abstract: We consider and study total variation (TV) image restoration. In the literature there are several regularization parameter selection methods for Tikhonov regularization problems (e.g., the discrepancy principle and the generalized cross-validation method). However, to our knowledge, these selection methods have not been applied to TV regularization problems. The main aim of this paper is to develop a fast TV image restoration method with an automatic selection of the regularization parameter scheme to restore blurred and noisy images. The method exploits the generalized cross-validation (GCV) technique to determine inexpensively how much regularization to use in each restoration step. By updating the regularization parameter in each iteration, the restored image can be obtained. Our experimental results for testing different kinds of noise show that the visual quality and SNRs of images restored by the proposed method is promising. We also demonstrate that the method is efficient, as it can restore images of size 256 x 256 in approximately 20 s in the MATLAB computing environment.

Phase-shift estimation in sinusoidally illuminated images for lateral superresolution

Abstract: Sinusoidally patterned illumination has been used to obtain lateral superresolution and axial sectioning in images. In both of these techniques multiple images are taken with the object illuminated by a sinusoidal pattern, the phase of the sinusoidal illumination being shifted differently in each image. The knowledge of these phase shifts is critical for image reconstruction. We discuss a method to estimate this phase shift with no prior knowledge of the shifts. In postprocessing we estimate randomly introduced, unknown phase shifts and process the images to obtain a superresolved image. Results of computer simulations are shown.

Deconvolution methods for image deblurring in optical coherence tomography

Abstract: Two-dimensional deconvolution methods are proposed to deblur optical coherence tomography images. One employs a two-dimensional deconvolution with a matrix given by the product of the longitudinal and transversal point-spread functions as its kernel, which can be taken as the general point-spread function of an optical coherence tomography system. The other uses two one-dimensional deconvolutions with the longitudinal and transversal point-spread functions successively. It is shown that the two deconvolution methods can deblur the experimentally obtained optical coherence tomography images effectively.

Operational and convolution properties of two-dimensional Fourier transforms in polar coordinates.

Abstract: For functions that are best described in terms of polar coordinates, the two-dimensional Fourier transform can be written in terms of polar coordinates as a combination of Hankel transforms and Fourier series-even if the function does not possess circular symmetry. However, to be as useful as its Cartesian counterpart, a polar version of the Fourier operational toolset is required for the standard operations of shift, multiplication, convolution, etc. This paper derives the requisite polar version of the standard Fourier operations. In particular, convolution-two dimensional, circular, and radial one dimensional-is discussed in detail. It is shown that standard multiplication/convolution rules do apply as long as the correct definition of convolution is applied.

Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry.

Abstract: It has been found that the field dependence of the aberrations of misaligned optical systems made of otherwise rotationally symmetric optical surfaces are often multinodal, including low-order astigmatism and distortion and higher-order coma, astigmatism, oblique spherical, elliptical coma (trifoil), and distortion. The exact location of the nodes in the image is a weighted sum of individual surface contributions. The location of the center of rotational symmetry for the field dependence for all aberrations contributed by a particular rotationally symmetric surface is along the line that connects the center of curvature of the surface with the center of the pupil. Previously, a paraxial ray-trace method was developed to locate the aberration field center for a series of rotationally symmetric surfaces with small tilt and decenter perturbations. The method is based on rotating the coordinate system into the local coordinate system of the surface and then advancing using the conventional paraxial ray-trace equations. This method, developed by Buchroeder [Ph.D. dissertation (University of Arizona, 1976)], heavily constrains how tilts and decenters were implemented in the optical system model, which prevented integration of these equations into an optical design environment. In this paper, a method for locating the aberration field centers using real-ray-trace data that is entirely model independent and, significantly, that is not restricted to small tilts and decenters, is presented. With this new insight, it is now possible to extend any optical design and analysis environment to include multinodal aberration analysis.

Tomographic reconstruction for wide-field adaptive optics systems: Fourier domain analysis and fundamental limitations

Abstract: Several wide-field-of-view adaptive optics (WFAO) concepts such as multi-conjugate AO (MCAO), multi-object AO (MOAO), and ground-layer AO (GLAO) are currently being studied for the next generation of Extremely Large Telescopes (ELTs). All these concepts will use atmospheric tomography to reconstruct the turbulent-phase volume. In this paper, we explore different reconstruction algorithms and their fundamental limitations, conducting this analysis in the Fourier domain. This approach allows us to derive simple analytical formulations for the different configurations and brings a comprehensive view of WFAO limitations. We then investigate model and statistical errors and their effect on the phase reconstruction. Finally, we show some examples of different WFAO systems and their expected performance on a 42 m telescope case.

Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis

Abstract: We present a comprehensive analysis of the linear quadratic Gaussian control approach applied to adaptive optics (AO) and multiconjugated AO (MCAO) based on numerical and experimental validations. The structure of the control law is presented and its main properties discussed. We then propose an extended experimental validation of this control law in AO and a simplified MCAO configuration. Performance is compared with end-to-end numerical simulations. Sensitivity of the performance regarding tuning parameters is tested. Finally, extension to full MCAO and laser tomographic AO (LTAO) through numerical simulation is presented and analyzed.

Bronnikov-aided correction for x-ray computed tomography

Abstract: When a very-low-absorbing sample is scanned at an x-ray computed tomography setup with a microfocus x-ray tube and a high-resolution detector, the obtained projection images contain not only absorption contrast but also phase contrast. While images without a phase signal can be reconstructed very well, such mixed phase and absorption images give rise to severe artifacts in the reconstructed slices. A method is described that applies a correction to these mixed projections to remove the phase signal. These corrected images can then be processed using a standard filtered backprojection algorithm to obtain reconstructions with only few or no phase artifacts. This new method, which we call the Bronnikov-aided correction (BAC), can be used in a broad variety of applications and without much additional effort. It is tested on a biological and a pharmaceutical sample, and results are evaluated and discussed by comparing them with those of conventional reconstruction methods.

Application of signal-subspace and optimization methods in reconstructing extended scatterers

Abstract: A signal-subspace approach to reconstruct the permittivities of extended scatterers in two-dimensional settings is proposed. A portion of the scatterers' information is retrieved by the signal-subspace method, and the remaining part is obtained by solving a nonlinear least-squares problem. The method exhibits several strengths, including robustness against noise, fast convergence, less scattering data, high resolution, and the ability to deal with scatterers of special shapes.

Early-photon fluorescence tomography: spatial resolution improvements and noise stability considerations.

Abstract: In vivo tissue imaging using near-infrared light suffers from low spatial resolution and poor contrast recovery because of highly scattered photon transport. For diffuse optical tomography (DOT) and fluorescence molecular tomography (FMT), the resolution is limited to about 5-10% of the diameter of the tissue being imaged, which puts it in the range of performance seen in nuclear medicine. This paper introduces the mathematical formalism explaining why the resolution of FMT can be significantly improved when using instruments acquiring fast time-domain optical signals. This is achieved through singular-value analysis of the time-gated inverse problem based on weakly diffused photons. Simulations relevant to mouse imaging are presented showing that, in stark contrast to steady-state imaging, early time-gated intensities (within 200 ps or 400 ps) can in principle be used to resolve small fluorescent targets (radii from 1.5 to 2.5 mm) separated by less than 1.5 mm.

Fractional Fourier transform of Lorentz-Gauss beams

Abstract: Lorentz-Gauss beams are introduced to describe certain laser sources that produce highly divergent beams. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz-Gauss beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz-Gauss beam passing through an FRFT system has been derived. By using the derived expression, the properties of a Lorentz-Gauss beam in the FRFT plane are graphically illustrated with numerical examples.

Quasi-physical phase compensation in digital holographic microscopy

Abstract: In digital holographic microscopy, if an optical setup is well aligned, the phase curvature introduced by the microscope objective (MO) together with the illuminating wave to the object wave is a spherical phase curvature. It can be physically compensated by introducing the same spherical phase curvature in the reference beam. Digital holographic microscopy setups based on the Michelson interferometric configuration with MO and an adjustable lens are presented, which can well perform the quasi-physical phase compensation during the hologram recording. In the reflection mode, the adjustable lens serves as both the condensing lens and the compensation lens. When the spatial frequency spectra of the hologram become a point spectrum, one can see that the phase curvature introduced by imaging is quasi-physically compensated. A simple plane numerical reference wavefront used for the reconstruction can give the correct quantitative phase map of the test object. A theoretical analysis and experimental demonstration are given. The simplicity of the presented setup makes it easy to align it well at lower cost.

Hollow vortex beams

Abstract: Hollow beam formation of radially and azimuthally polarized vortex beams, which has arbitrary topological charge, is analytically discussed under the strong focusing condition. The expressions for the electric fields of the focused vector-vortex beams are obtained based on a vector diffraction theory. The order of the Bessel function of the first kind appearing in the expressions indicates the ability to form hollow beams. Similar discussion is applied for different vortex beams, which are expressed by linear combination of radially and azimuthally polarized beams. Calculations of intensity profiles across the focus are also presented.

Optimal method for exoplanet detection by angular differential imaging

Abstract: We propose a novel method for the efficient direct detection of exoplanets from the ground using angular differential imaging. The method combines images appropriately, then uses the combined images jointly in a maximum-likelihood framework to estimate the position and intensity of potential planets orbiting the observed star. It takes into account the mixture of photon and detector noises and a positivity constraint on the planet's intensity. A reasonable detection criterion is also proposed based on the computation of the noise propagation from the images to the estimated intensity of the potential planet. The implementation of this method is tested on simulated data that take into account static aberrations before and after the coronagraph, residual turbulence after adaptive optics correction, and noise.

Pseudopolar decomposition of the Jones and Mueller-Jones exponential polarization matrices.

Abstract: We propose a new algorithm, the pseudopolar decomposition, to decompose a Jones or a Mueller-Jones matrix into a sequence of matrix factors: J≅JRJDJ1CJ2C or M≅MRMDM1CM2C. The matrices JR(MR) and JD(MD) parameterize, respectively, the retardation and dichroic properties of J(M) in a good approximation, while JiC(MiC) are correction factors that arise from the noncommutativity of the polarization properties. The exponential versions of the general Jones matrix are used to demonstrate the pseudopolar decomposition and to calculate each one of the matrix factors. The decomposition preserves all the polarization properties of the system on the factorized JR(MR) and JD(MD) matrix terms. The algorithm that calculates the pseudopolar decomposition for experimentally determined Mueller matrices is presented.

Optical angular momentum transfer by Laguerre-Gaussian beams.

Abstract: It is well known that Laguerre-Gaussian beams carry angular momentum and that this angular momentum has a mechanical effect when such beams are incident on particles whose refractive indices differ from those of the background medium. Under conditions of tight focusing, intensity gradients arise that are sufficiently large to trap micrometer-sized particles, permitting these mechanical effects to be observed directly. In particular, when the particles are spherical and absorbing, they rotate steadily at a rate that is directly proportional to the theoretical angular momentum flux of the incident beam. We note that this behavior is peculiar to absorbing spheres. For arbitrary, axially placed particles the induced torque for rotation angle ζ is shown to be Γz=Asin(2ζ+δ)+B, where A, B, and δ are constants that are determined by the mechanisms coupling optical and mechanical angular momentum. The resulting behavior need not be directly related to the total angular momentum in the beam but can, nonetheless, be understood in terms of an appropriate torque density. This observation is illustrated by calculations of the torque induced in optically and geometrically anisotropic particles using a T-matrix approach.

Population distribution of wavefront aberrations in the peripheral human eye

Abstract: We present a population study of peripheral wavefront aberrations in large off-axis angles in terms of Zernike coefficients. A laboratory Hartmann-Shack sensor was used to assess the aberrations in 0 degrees, 20 degrees, and 30 degrees in the nasal visual field of 43 normal eyes. The elliptical pupil meant that the quantification could be done in different ways. The three approaches used were (1) over a circular aperture encircling the pupil, (2) over a stretched version of the elliptical pupil, and (3) over a circular aperture within the pupil (MATLAB conversion code given). Astigmatism (c(2)(2)) increased quadratically and coma (c(3)(1)) linearly with the horizontal viewing angle, whereas spherical aberration (c(4)(0)) decreased slightly toward the periphery. There was no correlation between defocus and angle, although some trends were found when the subjects were divided into groups depending on refractive error. When comparing results of different studies it has to be kept in mind that the coefficients differ depending on how the elliptical pupil is taken into consideration.

Euclidean color-difference formula for small-medium color differences in log-compressed OSA-UCS space.

Abstract: This work continues previous research by the same authors [J. Opt. Soc. Am. A23, 2077 (2006)], where empirical small-medium color differences were represented by an ellipsoidal equation ΔEGP in the Uniform Color System of the Optical Society of America. Now logarithmic compressions on chroma and lightness are introduced to produce a new space with Euclidean color-difference formulas ΔEE. The CIEDE2000, ΔEGP, and ΔEE formulas are found statistically equivalent in the prediction of many available empirical datasets. However, ΔEE is the simplest formula providing relationships with visual processing. These analyses hold true for CIE 1964 Supplementary Standard Observer and D65 illuminant.

Effect of target localization on the sensitivity of a localized surface plasmon resonance biosensor based on subwavelength metallic nanostructures

Abstract: A localized surface plasmon resonance (LSPR) biosensor using surface relief nanostructures was investigated to evaluate the importance of target localization on the sensitivity enhancement. The LSPR device was modeled as periodic metallic nanowires with a square profile on a gold film and the target as a self-assembled monolayer in buffer solution. The numerical results using rigorous coupled-wave analysis and the finite-difference time domain method demonstrated localized plasmonic fields induced by the surface nanostructure from which the effect of target localization on the sensitivity was quantitatively analyzed. Interestingly, it was found that target localization on nanowire sidewalls improves sensitivity significantly because of strong overlap with localized plasmonic fields. An LSPR structure optimized for a localized target on sidewalls provides sensitivity enhancement per unit target volume by more than 20 times in water ambience.