Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 2007"

Pixelated phase computer holograms for the accurate encoding of scalar complex fields

Abstract: We discuss a class of phase computer-generated holograms for the encoding of arbitrary scalar complex fields. We describe two holograms of this class that allow high quality reconstruction of the encoded field, even if they are implemented with a low-resolution pixelated phase modulator. In addition, we show that one of these holograms can be appropriately implemented with a phase modulator limited by a reduced phase depth.

Maximum permissible exposures for ocular safety (ANSI 2000), with emphasis on ophthalmic devices.

Abstract: After discussing the rationale and assumptions of the ANSI Z136.1-2000 Standard for protection of the human eye from laser exposure, we present the concise formulation of the exposure limits expressed as maximum permissible radiant exposure (in J/cm2) for light overfilling the pupil. We then translate the Standard to a form that is more practical for typical ophthalmic devices or in vision research situations, implementing the special qualifications of the Standard. The safety limits are then expressed as radiant power (watts) entering the pupil of the eye. Exposure by repetitive pulses is also addressed, as this is frequently employed in ophthalmic applications. Examples are given that will familiarize potential users with this format.

Phase unwrapping in three dimensions with application to InSAR time series.

Abstract: The problem of phase unwrapping in two dimensions has been studied extensively in the past two decades, but the three-dimensional (3D) problem has so far received relatively little attention. We develop here a theoretical framework for 3D phase unwrapping and also describe two algorithms for implementation, both of which can be applied to synthetic aperture radar interferometry (InSAR) time series. We test the algorithms on simulated data and find both give more accurate results than a two-dimensional algorithm. When applied to actual InSAR time series, we find good agreement both between the algorithms and with ground truth.

Blind image quality assessment through anisotropy

Abstract: We describe an innovative methodology for determining the quality of digital images. The method is based on measuring the variance of the expected entropy of a given image upon a set of predefined directions. Entropy can be calculated on a local basis by using a spatial/spatial-frequency distribution as an approximation for a probability density function. The generalized Renyi entropy and the normalized pseudo-Wigner distribution (PWD) have been selected for this purpose. As a consequence, a pixel-by-pixel entropy value can be calculated, and therefore entropy histograms can be generated as well. The variance of the expected entropy is measured as a function of the directionality, and it has been taken as an anisotropy indicator. For this purpose, directional selectivity can be attained by using an oriented 1-D PWD implementation. Our main purpose is to show how such an anisotropy measure can be used as a metric to assess both the fidelity and quality of images. Experimental results show that an index such as this presents some desirable features that resemble those from an ideal image quality function, constituting a suitable quality index for natural images. Namely, in-focus, noise-free natural images have shown a maximum of this metric in comparison with other degraded, blurred, or noisy versions. This result provides a way of identifying in-focus, noise-free images from other degraded versions, allowing an automatic and nonreference classification of images according to their relative quality. It is also shown that the new measure is well correlated with classical reference metrics such as the peak signal-to-noise ratio.

Speckle reduction in optical coherence tomography images using digital filtering.

Abstract: Speckle noise is a ubiquitous artifact that limits the interpretation of optical coherence tomography images. Here we apply various speckle-reduction digital filters to optical coherence tomography images and compare their performance. Our results indicate that shift-invariant, nonorthogonal wavelet-transform-based filters together with enhanced Lee and adaptive Wiener filters can significantly reduce speckle and increase the signal-to-noise ratio, while preserving strong edges. The speckle reduction capabilities of these filters are also compared with speckle reduction from incoherent angular compounding. Our results suggest that by using these digital filters, the number of individual angles required to attain a certain level of speckle reduction can be decreased.

Video quality assessment using a statistical model of human visual speed perception.

Abstract: Motion is one of the most important types of information contained in natural video, but direct use of motion information in the design of video quality assessment algorithms has not been deeply investigated. Here we propose to incorporate a recent model of human visual speed perception [Nat. Neurosci. 9, 578 (2006)] and model visual perception in an information communication framework. This allows us to estimate both the motion information content and the perceptual uncertainty in video signals. Improved video quality assessment algorithms are obtained by incorporating the model as spatiotemporal weighting factors, where the weight increases with the information content and decreases with the perceptual uncertainty. Consistent improvement over existing video quality assessment algorithms is observed in our validation with the video quality experts group Phase I test data set.

Automated identification of cone photoreceptors in adaptive optics retinal images

Abstract: In making noninvasive measurements of the human cone mosaic, the task of labeling each individual cone is unavoidable. Manual labeling is a time-consuming process, setting the motivation for the development of an automated method. An automated algorithm for labeling cones in adaptive optics (AO) retinal images is implemented and tested on real data. The optical fiber properties of cones aided the design of the algorithm. Out of 2153 manually labeled cones from six different images, the automated method correctly identified 94.1% of them. The agreement between the automated and the manual labeling methods varied from 92.7% to 96.2% across the six images. Results between the two methods disagreed for 1.2% to 9.1% of the cones. Voronoi analysis of large montages of AO retinal images confirmed the general hexagonal-packing structure of retinal cones as well as the general cone density variability across portions of the retina. The consistency of our measurements demonstrates the reliability and practicality of having an automated solution to this problem.

Sharper focal spot formed by higher-order radially polarized laser beams

Abstract: The intensity distributions near the focal point for radially polarized laser beams including higher-order transverse modes are calculated based on vector diffraction theory. For higher-order radially polarized mode beams as well as a fundamental mode (R-TEM01*) beam, the strong longitudinal component forms a sharper spot at the focal point under a high-NA focusing condition. In particular, double-ring-shaped radially polarized mode (R-TEM11*) beams can effectively reduce the focal spot size because of destructive interference between the inner and the outer rings with π phase shift. Compared with an R-TEM01* beam focusing in a limit of NA=1, the full width at half-maximum values of the focal spot for an R-TEM11* beam are decreased by 13.6% for the longitudinal component and 25.8% for the total intensity.

Measurement of the relationship between perceived and computed color differences

Abstract: Using simulated data sets, we have analyzed some mathematical properties of different statistical measurements that have been employed in previous literature to test the performance of different color-difference formulas. Specifically, the properties of the combined index PF/3 (performance factor obtained as average of three terms), widely employed in current literature, have been considered. A new index named standardized residual sum of squares (STRESS), employed in multidimensional scaling techniques, is recommended. The main difference between PF/3 and STRESS is that the latter is simpler and allows inferences on the statistical significance of two color-difference formulas with respect to a given set of visual data.

Large-field-of-view, modular, stabilized, adaptive-optics-based scanning laser ophthalmoscope

Abstract: We describe the design and performance of an adaptive optics retinal imager that is optimized for use during dynamic correction for eye movements. The system incorporates a retinal tracker and stabilizer, a wide field line scan Scanning Laser Ophthalmocsope (SLO), and a high resolution MEMS based adaptive optics SLO. The detection system incorporates selection and positioning of confocal apertures, allowing measurement of images arising from different portions of the double pass retinal point spread function (psf). System performance was excellent. The adaptive optics increased the brightness and contrast for small confocal apertures by more than 2x, and decreased the brightness of images obtained with displaced apertures, confirming the ability of the adaptive optics system to improve the pointspread function. The retinal image was stabilized to within 18 microns 90% of the time. Stabilization was sufficient for cross-correlation techniques to automatically align the images.

Normal vector method for convergence improvement using the RCWA for crossed gratings.

Abstract: The rigorous coupled wave analysis (RCWA) is a widely used method for simulating diffraction from periodic structures. Since its recognized formulation by Moharam [J. Opt. Soc. Am. A12, 1068 and 1077 (1995)], there still has been a discussion about convergence problems. Those problems are more or less solved for the diffraction from line gratings, but there remain different concurrent proposals about the convergence improvement for crossed gratings. We propose to combine Popov and Neviere's formulation of the differential method [Light Propagation in Periodic Media (Dekker, 2003) and J. Opt. Soc. Am. A18, 2886 (2001)] with the classical RCWA. With a suitable choice of a normal vector field we obtain a better convergence than for the formulations that are known from the literature.

Optical density of the aging human ocular media in the visible and the UV

Abstract: We analyzed the literature on the absorption in the young and aging human eye media. Five templates were derived to provide an adequate description of the spectra from 300 to 700 nm for the lens, cornea, aqueous, and vitreous. Two templates were found in all media. They stand for Rayleigh scatter and the absorbance of tryptophan. Three additional templates for the lens represent absorbance in kynurenine derivatives, such as 3-hydroxykynurenine glucoside (3HKG), and absorbance in two substances found at older age. Except for Rayleigh scatter, all templates have a Gaussian shape. Aging-trend functions were derived that show a linear slope on an age-squared scale. The result can be used to correct for media losses in visual perception tasks, in fundus reflectometry, and in studies on light damage.

Inverse-problem approach for particle digital holography: accurate location based on local optimization.

Abstract: We propose a microparticle localization scheme in digital holography Most conventional digital holography methods are based on Fresnel transform and present several problems such as twin-image noise, border effects, and other effects To avoid these difficulties, we propose an inverse-problem approach, which yields the optimal particle set that best models the observed hologram image We resolve this global optimization problem by conventional particle detection followed by a local refinement for each particle Results for both simulated and real digital holograms show strong improvement in the localization of the particles, particularly along the depth dimension In our simulations, the position precision is > or =1 microm rms Our results also show that the localization precision does not deteriorate for particles near the edge of the field of view

Wide-field schematic eye models with gradient-index lens

Abstract: We propose a wide-field schematic eye model, which provides a more realistic description of the optical system of the eye in relation to its anatomical structure. The wide-field model incorporates a gradient-index (GRIN) lens, which enables it to fulfill properties of two well-known schematic eye models, namely, Navarro's model for off-axis aberrations and Thibos's chromatic on-axis model (the Indiana eye). These two models are based on extensive experimental data, which makes the derived wide-field eye model also consistent with that data. A mathematical method to construct a GRIN lens with its iso-indicial contours following the optical surfaces of given asphericity is presented. The efficiency of the method is demonstrated with three variants related to different age groups. The role of the GRIN structure in relation to the lens paradox is analyzed. The wide-field model with a GRIN lens can be used as a starting design for the eye inverse problem, i.e., reconstructing the optical structure of the eye from off-axis wavefront measurements. Anatomically more accurate age-dependent optical models of the eye could ultimately help an optical designer to improve wide-field retinal imaging.

Orthonormal polynomials in wavefront analysis: analytical solution

Abstract: Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. In recent papers, we derived closed-form polynomials that are orthonormal over a hexagonal pupil, such as the hexagonal segments of a large mirror. We extend our work to elliptical, rectangular, and square pupils. Using the circle polynomials as the basis functions for their orthogonalization over such pupils, we derive closed-form polynomials that are orthonormal over them. These polynomials are unique in that they are not only orthogonal across such pupils, but also represent balanced classical aberrations, just as the Zernike circle polynomials are unique in these respects for circular pupils. The polynomials are given in terms of the circle polynomials as well as in polar and Cartesian coordinates. Relationships between the orthonormal coefficients and the corresponding Zernike coefficients for a given pupil are also obtained. The orthonormal polynomials for a one-dimensional slit pupil are obtained as a limiting case of a rectangular pupil.

Three-dimensional relationship between high-order root-mean-square wavefront error, pupil diameter, and aging

Abstract: We report root-mean-square (RMS) wavefront error (WFE) for individual aberrations and cumulative highorder (HO) RMS WFE for the normal human eye as a function of age by decade and pupil diameter in 1 mm steps from 3 to 7 mm and determine the relationship among HO RMS WFE, mean age for each decade of life, and luminance for physiologic pupil diameters. Subjects included 146 healthy individuals from 20 to 80 years of age. Ocular aberration was measured on the preferred eye of each subject (for a total of 146 eyes through dilated pupils; computed for 3, 4, 5, 6, and 7 mm pupils; and described with a tenth-radial-order normalized Zernike expansion. We found that HO RMS WFE increases faster with increasing pupil diameter for any given age and pupil diameter than it does with increasing age alone. A planar function accounts for 99% of the variance in the 3-D space defined by mean log HO RMS WFE, mean age for each decade of life, and pupil diameter. When physiologic pupil diameters are used to estimate HO RMS WFE as a function of luminance and age, at low luminance 9c d/m 2 HO RMS WFE decreases with increasing age. This normative data set details (1) the 3-D relationship between HO RMS WFE and age for fixed pupil diameters and (2) the 3-D relationship among HO RMS WFE, age, and luminance for physiologic pupil diameters. © 2007 Optical Society of America OCIS codes: 170.4460, 330.5510.

Reduced-illuminance autofluorescence imaging in ABCA4-associated retinal degenerations

Abstract: The health of the retinal pigment epithelium (RPE) can be estimated with autofluorescence (AF) imaging of lipofuscin, which accumulates as a byproduct of retinal exposure to light. Lipofuscin may be toxic to the RPE, and its toxicity may be enhanced by short-wavelength (SW) illumination. The high-intensity and SW excitation light used in conventional AF imaging could, at least in principle, increase the rate of lipofuscin accumulation and/or increase its toxicity. We considered two reduced-illuminance AF imaging (RAFI) methods as alternatives to conventional AF imaging. RAFI methods use either near-infrared (NIR) light or reduced-radiance SW illumination for excitation of fluorophores. We quantified the distribution of RAFI signals in relation to retinal structure and function in patients with the prototypical lipofuscin accumulation disease caused by mutations in ABCA4. There was evidence for two subclinical stages of macular ABCA4 disease involving hyperautofluorescence of both SW- and NIR-RAFI with and without associated loss of visual function. Use of RAFI methods and microperimetry in future clinical trials involving lipofuscinopathies should allow quantification of subclinical disease expression and progression without subjecting the diseased retina/RPE to undue light exposure.

Experimental implementation of the gyrator transform

Abstract: The gyrator transform (GT) promises to be a useful tool in image processing, holography, beam characterization, mode transformation, and quantum information. We introduce what we believe to be the first flexible optical experimental setup that performs the GT for a wide range of transformation parameters. The feasibility of the proposed scheme is demonstrated on the gyrator transformation of Hermite-Gaussian modes. For certain parameters the output mode corresponds to the Laguerre-Gaussian one.

Reduction of speckle in digital holography by discrete Fourier filtering.

Abstract: We present a digital signal processing technique that reduces the speckle content in reconstructed digital holograms. The method is based on sequential sampling of the discrete Fourier transform of the reconstructed image field. Speckle reduction is achieved at the expense of a reduced intensity and resolution, but this trade-off is shown to be greatly superior to that imposed by the traditional mean and median filtering techniques. In particular, we show that the speckle can be reduced by half with no loss of resolution (according to standard definitions of both metrics).

Calibration and precompensation of noncommon path aberrations for extreme adaptive optics.

Abstract: Noncommon path aberrations (NCPAs) are one of the main limitations of an extreme adaptive optics (AO) system. NCPAs prevent extreme AO systems from achieving their ultimate performance. These static aberrations are unseen by the wavefront sensor and therefore are not corrected in closed loop. We present experimental results validating what we believe to be new procedures of measurement and precompensation of the NCPAs on the AO bench at ONERA (Office National d'Etudes et de Recherches Aerospatiales). The measurement procedure is based on refined algorithms of phase diversity. The precompensation procedure makes use of a pseudo-closed-loop scheme to overcome the AO wavefront-sensor-model uncertainties. Strehl ratio obtained in the images reaches 98.7% at 632.8 nm. This result allows us to be confident of achieving the challenging performance required for direct observation of extrasolar planets.

Adaptive optics-optical coherence tomography: optimizing visualization of microscopic retinal structures in three dimensions.

Abstract: Adaptive optics-optical coherence tomography (AO-OCT) permits improved imaging of microscopic retinal structures by combining the high lateral resolution of AO with the high axial resolution of OCT, resulting in the narrowest three-dimensional (3D) point-spread function (PSF) of all in vivo retinal imaging techniques. Owing to the high volumetric resolution of AO-OCT systems, it is now possible, for the first time, to acquire images of 3D cellular structures in the living retina. Thus, with AO-OCT, those retinal structures that are not visible with AO or OCT alone (e.g., bundles of retinal nerve fiber layers, 3D mosaic of photoreceptors, 3D structure of microvasculature, and detailed structure of retinal disruptions) can be visualized. Our current AO-OCT instrumentation uses spectrometer-based Fourier-domain OCT technology and two-deformable-mirror-based AO wavefront correction. We describe image processing methods that help to remove motion artifacts observed in volumetric data, followed by innovative data visualization techniques [including two-dimensional (2D) and 3D representations]. Finally, examples of microscopic retinal structures that are acquired with the University of California Davis AO-OCT system are presented.

Transformation of Zernike coefficients: scaled, translated, and rotated wavefronts with circular and elliptical pupils.

Abstract: Zernike polynomials and their associated coefficients are commonly used to quantify the wavefront aberrations of the eye. When the aberrations of different eyes, pupil sizes, or corrections are compared or averaged, it is important that the Zernike coefficients have been calculated for the correct size, position, orientation, and shape of the pupil. We present the first complete theory to transform Zernike coefficients analytically with regard to concentric scaling, translation of pupil center, and rotation. The transformations are described both for circular and elliptical pupils. The algorithm has been implemented in MATLAB, for which the code is given in an appendix.

Fourier transform wavefront control with adaptive prediction of the atmosphere

Abstract: Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48×48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2×109 floating-point operations/s.

Adaptive optics retinal imaging reveals S-cone dystrophy in tritan color-vision deficiency.

Abstract: Tritan color-vision deficiency is an autosomal dominant disorder associated with mutations in the short-wavelength-sensitive- (S-) cone-pigment gene. An unexplained feature of the disorder is that individuals with the same mutation manifest different degrees of deficiency. To date, it has not been possible to examine whether any loss of S-cone function is accompanied by physical disruption in the cone mosaic. Two related tritan subjects with the same novel mutation in their S-cone-opsin gene, but different degrees of deficiency, were examined. Adaptive optics was used to obtain high-resolution retinal images, which revealed distinctly different S-cone mosaics consistent with their discrepant phenotypes. In addition, a significant disruption in the regularity of the overall cone mosaic was observed in the subject completely lacking S-cone function. These results taken together with other recent findings from molecular genetics indicate that, with rare exceptions, tritan deficiency is progressive in nature.

Model of retinal local adaptation for the tone mapping of color filter array images

Abstract: We present a tone mapping algorithm that is derived from a model of retinal processing. Our approach has two major improvements over existing methods. First, tone mapping is applied directly on the mosaic image captured by the sensor, analogous to the human visual system that applies a nonlinearity to the chromatic responses captured by the cone mosaic. This reduces the number of necessary operations by a factor 3. Second, we introduce a variation of the center/surround class of local tone mapping algorithms, which are known to increase the local contrast of images but tend to create artifacts. Our method gives a good improvement in contrast while avoiding halos and maintaining good global appearance. Like traditional center/surround algorithms, our method uses a weighted average of surrounding pixel values. Instead of being used directly, the weighted average serves as a variable in the Naka-Rushton equation, which models the photoreceptors' nonlinearity. Our algorithm provides pleasing results on various images with different scene content and dynamic range.

Polarization patterns of thick clouds: overcast skies have distribution of the angle of polarization similar to that of clear skies

Abstract: The distribution of polarization in the overcast sky has been practically unknown. Earlier the polarization of light from heavily overcast skies (when the Sun's disc was invisible) has been measured only sporadically in some celestial points by point-source polarimetry. What kind of patterns of the degree p and angle α of linear polarization of light could develop after transmission through a thick layer of ice or water clouds? To answer this question, we measured the p and α patterns of numerous totally overcast skies on the Arctic Ocean and in Hungary by full-sky imaging polarimetry. We present here our finding that depending on the optical thickness of the cloud layer, the pattern of α of light transmitted through the ice or water clouds of totally overcast skies is qualitatively the same as the α pattern of the clear sky. Under overcast conditions the value of α is determined predominantly by scattering on cloud particles themselves. Nevertheless, the degrees of linear polarization of light from overcast skies were rather low (p≤16%). Our results obtained under overcast conditions complete the earlier findings that the α pattern of the clear sky also appears in partly cloudy, foggy, and smoky skies. Our results show that the celestial distribution of the direction of polarization is a very robust pattern being qualitatively always the same under all possible sky conditions. This is of great importance for the orientation of polarization-sensitive animals based on sky polarization under conditions when the Sun is not visible.

Mechanism of compensation of aberrations in the human eye

Abstract: We studied the mechanism of compensation of aberrations within the young human eye by using experimental data and advanced ray-tracing modeling. Corneal and ocular aberrations along with the alignment properties (angle kappa, lens tilt, and decentration) were measured in eyes with different refractive errors. Predictions from individualized ray-tracing optical models were compared with the actual measurements. Ocular spherical aberration was, in general, smaller than corneal spherical aberration without relation to refractive error. However, horizontal coma compensation was found to be significantly larger for hyperopic eyes where angle kappa tended to also be larger. We propose a simple analytical model of the relationship between the corneal coma compensation effect with the field angle and corneal and crystalline shape factors. The actual shape factors corresponded approximately to the optimum shapes that automatically provide this coma compensation. We showed that the eye behaves as an aplanatic optical system, an optimized design solution rendering stable retinal image quality for different ocular geometries.

High-resolution adaptive optics scanning laser ophthalmoscope with multiple deformable mirrors

Abstract: An adaptive optics scanning laser ophthalmoscopes is introduced to produce non-invasive views of the human retina. The use of dual deformable mirrors improved the dynamic range for correction of the wavefront aberrations compared with the use of the MEMS mirror alone, and improved the quality of the wavefront correction compared with the use of the bimorph mirror alone. The large-stroke bimorph deformable mirror improved the capability for axial sectioning with the confocal imaging system by providing an easier way to move the focus axially through different layers of the retina.

Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics.

Abstract: We report the experimental observation of the fractional Fourier transform (FRT) for a partially coherent optical beam with Gaussian statistics [i.e., partially coherent Gaussian Schell-model (GSM) beam]. The intensity distribution (or beam width) and the modulus of the square of the spectral degree of coherence (or coherence width) of a partially coherent GSM beam in the FRT plane are measured, and the experimental results are analyzed and agree well with the theoretical results. The FRT optical system provides a convenient way to control the properties, e.g., the intensity distribution, beam width, spectral degree of coherence, and coherence width, of a partially coherent beam.

Optical trapping of spheroidal particles in Gaussian beams.

Abstract: The T matrix method is used to compute equilibrium positions and orientations for spheroidal particles trapped in Gaussian light beams. It is observed that there is a qualitative difference between the behavior of prolate and oblate ellipsoids in linearly polarized Gaussian beams; the former generally orient with the symmetry axis parallel to the beam except at very small particle sizes, while the latter orient with the symmetry axis perpendicular to the beam. In the presence of a circularly polarized beam, it is demonstrated that oblate ellipsoids will experience a torque about the beam axis. However, for a limited range of particle sizes, where the particle dimensions are comparable with the beam waist, the particles are predicted to rotate in a sense counter to the sense of rotation of the circular polarization. This unusual prediction is discussed in some detail.