Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 2002"

Statistical variation of aberration structure and image quality in a normal population of healthy eyes.

Abstract: A Shack-Hartmann aberrometer was used to measure the monochromatic aberration structure along the primary line of sight of 200 cyclopleged, normal, healthy eyes from 100 individuals. Sphero-cylindrical refractive errors were corrected with ophthalmic spectacle lenses based on the results of a subjective refraction performed immediately prior to experimentation. Zernike expansions of the experimental wave-front aberration functions were used to determine aberration coefficients for a series of pupil diameters. The residual Zernike coefficients for defocus were not zero but varied systematically with pupil diameter and with the Zernike coefficient for spherical aberration in a way that maximizes visual acuity. We infer from these results that subjective best focus occurs when the area of the central, aberration-free region of the pupil is maximized. We found that the population averages of Zernike coefficients were nearly zero for all of the higher-order modes except spherical aberration. This result indicates that a hypothetical average eye representing the central tendency of the population is nearly free of aberrations, suggesting the possible influence of an emmetropization process or evolutionary pressure. However, for any individual eye the aberration coefficients were rarely zero for any Zernike mode. To first approximation, wave-front error fell exponentially with Zernike order and increased linearly with pupil area. On average, the total wave-front variance produced by higher-order aberrations was less than the wave-front variance of residual defocus and astigmatism. For example, the average amount of higher-order aberrations present for a 7.5-mm pupil was equivalent to the wave-front error produced by less than 1/4 diopter (D) of defocus. The largest pupil for which an eye may be considered diffraction-limited was 1.22 mm on average. Correlation of aberrations from the left and right eyes indicated the presence of significant bilateral symmetry. No evidence was found of a universal anatomical feature responsible for third-order optical aberrations. Using the Marechal criterion, we conclude that correction of the 12 largest principal components, or 14 largest Zernike modes, would be required to achieve diffraction-limited performance on average for a 6-mm pupil. Different methods of computing population averages provided upper and lower limits to the mean optical transfer function and mean point-spread function for our population of eyes.

Saturated patterned excitation microscopy: a concept for optical resolution improvement

Abstract: The resolution of optical microscopy is limited by the numerical aperture and the wavelength of light Many strategies for improving resolution such as 4Pi and I5M have focused on an increase of the numerical aperture Other approaches have based resolution improvement in fluorescence microscopy on the establishment of a nonlinear relationship between local excitation light intensity in the sample and in the emitted light However, despite their innovative character, current techniques such as stimulated emission depletion (STED) and ground-state depletion (GSD) microscopy require complex optical configurations and instrumentation to narrow the point-spread function We develop the theory of nonlinear patterned excitation microscopy for achieving a substantial improvement in resolution by deliberate saturation of the fluorophore excited state The postacquisition manipulation of the acquired data is computationally more complex than in STED or GSD, but the experimental requirements are simple Simulations comparing saturated patterned excitation microscopy with linear patterned excitation microscopy (also referred to in the literature as structured illumination or harmonic excitation light microscopy) and ordinary widefield microscopy are presented and discussed The effects of photon noise are included in the simulations

Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization.

Abstract: The phase retrieval problem is of paramount importance in various areas of applied physics and engineering. The state of the art for solving this problem in two dimensions relies heavily on the pioneering work of Gerchberg, Saxton, and Fienup. Despite the widespread use of the algorithms proposed by these three researchers, current mathematical theory cannot explain their remarkable success. Nevertheless, great insight can be gained into the behavior, the shortcomings, and the performance of these algorithms from their possible counterparts in convex optimization theory. An important step in this direction was made two decades ago when the error reduction algorithm was identified as a nonconvex alternating projection algorithm. Our purpose is to formulate the phase retrieval problem with mathematical care and to establish new connections between well-established numerical phase retrieval schemes and classical convex optimization methods. Specifically, it is shown that Fienup’s basic input–output algorithm corresponds to Dykstra’s algorithm and that Fienup’s hybrid input–output algorithm can be viewed as an instance of the Douglas–Rachford algorithm. We provide a theoretical framework to better understand and, potentially, to improve existing phase recovery algorithms.

Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication.

Abstract: A partially coherent quasi-monochromatic Gaussian laser beam propagating in atmospheric turbulence is examined by using a derived analytic expression for the cross-spectral density function. Expressions for average intensity, beam size, phase front radius of curvature, and wave-front coherence length are obtained from the cross-spectral density function. These results provide a model for a free-space laser transmitter with a phase diffuser used to reduce pointing errors.

Contribution of the cornea and internal surfaces to the change of ocular aberrations with age

Abstract: We studied the age dependence of the relative contributions of the aberrations of the cornea and the internal ocular surfaces to the total aberrations of the eye. We measured the wave-front aberration of the eye with a Hartmann-Shack sensor and the aberrations of the anterior corneal surface from the elevation data provided by a corneal topography system. The aberrations of the internal surfaces were obtained by direct subtraction of the ocular and corneal wave-front data. Measurements were obtained for normal healthy subjects with ages ranging from 20 to 70 years. The magnitude of the RMS wave-front aberration (excluding defocus and astigmatism) of the eye increases more than threefold within the age range considered. However, the aberrations of the anterior corneal surface increase only slightly with age. In most of the younger subjects, total ocular aberrations are lower than corneal aberrations, while in the older subjects the reverse condition occurs. Astigmatism, coma, and spherical aberration of the cornea are larger than in the complete eye in younger subjects, whereas the contrary is true for the older subjects. The internal ocular surfaces compensate, at least in part, for the aberrations associated with the cornea in most younger subjects, but this compensation is not present in the older subjects. These results suggest that the degradation of the ocular optics with age can be explained largely by the loss of the balance between the aberrations of the corneal and the internal surfaces.

Tailored freeform optical surfaces

Abstract: Freeform optical surfaces embedded in three-dimensional space, without any symmetry, are tailored so as to solve the archetypal problem of illumination design: redistribute the radiation of a given small light source onto a given reference surface, thus achieving a desired irradiance distribution on that surface. The shape of the optical surface is found by solving a set of partial nonlinear differential equations. For most cases, a few topologically distinct solutions exist, given suitable boundary conditions.

Spreading of partially coherent beams in random media

Abstract: Some published computational work has suggested that partially coherent beams may be less susceptible to distortions caused by propagation through random media than fully coherent beams. In this paper this suggestion is studied quantitatively by examining the mean squared width of partially coherent beams in such media as a function of the propagation distance. The analysis indicates under what conditions, and to what extent, partially coherent beams are less affected by the medium.

Visual performance after correcting the monochromatic and chromatic aberrations of the eye.

Abstract: The development of technology to measure and correct the eye's higher-order aberrations, i.e., those beyond defocus and astigmatism, raises the issue of how much visual benefit can be obtained by providing such correction. We demonstrate improvements in contrast sensitivity and visual acuity in white light and in monochromatic light when adaptive optics corrects the eye's higher-order monochromatic aberrations. In white light, the contrast sensitivity and visual acuity when most monochromatic aberrations are corrected with a deformable mirror are somewhat higher than when defocus and astigmatism alone are corrected. Moreover, viewing conditions in which monochromatic aberrations are corrected and chromatic aberrations are avoided provides an even larger improvement in contrast sensitivity and visual acuity. These results are in reasonable agreement with the theoretical improvement calculated from the eye's optical modulation transfer function.

Peripheral refractive errors in myopic, emmetropic, and hyperopic young subjects.

Abstract: To gain more insight into the relationship between foveal and peripheral refractive errors in humans, spheres, cylinders, and their axes were binocularly measured across the visual field in myopic, emmetropic, and hyperopic groups of young subjects. Both automated infrared photorefraction (the “PowerRefractor”; www.plusoptix.de) and a double-pass technique were used because the PowerRefractor provided extensive data from the central 44 deg of the visual field in a very convenient and fast way. Two-dimensional maps for the average cross cylinders and spherical equivalents, as well as for the axes of the power meridians of the cylinders, were created. A small amount of lower-field myopia was detected with a significant vertical gradient in spherical equivalents. In the central visual field there was little difference among the three refractive groups. The established double-pass technique provided complementary data also from the far periphery. At 45 deg eccentricity the double-pass technique revealed relatively more hyperopic spherical equivalents in myopic subjects than in emmetropic subjects [±2.73±2.85 D relative to the fovea, p<0.01 (±standard deviation)] and more myopic spherical equivalents in hyperopic subjects (-3.84±2.86 D relative to the fovea, p<0.01). Owing to the pronounced peripheral astigmatism, spherical equivalents (refractions with respect to the plane of the circle of least confusion) became myopic relative to the fovea in all three groups. The finding of general peripheral myopia was unexpected. Its possible roles in foveal refractive development are discussed.

Spatial frequency, phase, and the contrast of natural images

Abstract: We examined contrast sensitivity and suprathreshold apparent contrast with natural images. The spatial-frequency components within single octaves of the images were removed (notch filtered), their phases were randomized, or the polarity of the images was inverted. Of Michelson contrast, root-mean-square (RMS) contrast, and band-limited contrast, RMS contrast was the best index of detectability. Negative images had lower apparent contrast than their positives. Contrast detection thresholds showed spatial-frequency-dependent elevation following both notch filtering and phase randomization. The peak of the spatial-frequency tuning function was approximately 0.5–2 cycles per degree (c/deg). Suprathreshold contrast matching functions also showed spatial-frequency-dependent contrast loss for both notch-filtered and phase-randomized images. The peak of the spatial-frequency tuning function was approximately 1–3 c/deg. There was no detectable difference between the effects of phase randomization and notch filtering on contrast sensitivity. We argue that these observations are consistent with changes in the activity within spatial-frequency channels caused by the higher-order phase structure of natural images that is responsible for the presence of edges and specularities.

Imaging of the optic disc and retinal nerve fiber layer: the effects of age, optic disc area, refractive error, and gender.

Abstract: We cross-sectionally examined the relationship between age, optic disc area, refraction, and gender and optic disc topography and retinal nerve fiber layer (RNFL) measurements, using optical imaging techniques. One eye from each of 155 Caucasian subjects (age range 23.0-80.8 y) without ocular pathology was included. Measurements were obtained by using the Heidelberg Retina Tomography (HRT), the GDx Nerve Fiber Analyzer, and the Optical Coherence Tomograph (OCT). The effects of age were small (R2 < 17%) and were limited to specific HRT, GDx, and OCT parameters. Disc area was significantly associated with most HRT parameters and isolated GDx and OCT parameters. Refraction and gender were not significantly associated with any optic disc or RNFL parameters. Although effects of age on the optic disc and RNFL are small, they should be considered in monitoring ocular disease. Optic disc area should be considered when cross-sectionally evaluating disc topography and, to a lesser extent, RNFL thickness.

Statistics of Spatial Cone-Excitation Ratios in Natural Scenes

Abstract: For some sets of surfaces, the spatial ratios of cone-photoreceptor excitations produced by light reflected from pairs of surfaces are almost invariant under illuminant changes. These sets include large populations of spectral reflectances, some of which represent individual natural surfaces but not their relative abundances in nature. The aim of this study was to determine whether spatial cone-excitation ratios are preserved under illuminant changes within the natural visual environment. A fast hyperspectral imaging system was used to obtain populations of 640,000 reflectance spectra from each of 30 natural scenes. The statistics of spatial cone-excitation ratios for randomly selected pairs of points in these scenes were determined for two extreme daylights. Almost-invariant ratios were common, suggesting that they represent a reliable property of the natural visual environment and a suitable foundation for visual color constancy.

Scaling Zernike expansion coefficients to different pupil sizes

Abstract: Recent developments in technologies to correct aberrations in the eye have fostered extensive research in wave-front sensing of the eye, resulting in many reports of Zernike expansions of wave-front errors of the eye. For different reports of Zernike expansions, to be compared, the same pupil diameter is required. Since no standard pupil size has been established for reporting these results, a technique for converting Zernike expansion coefficients from one pupil size to another is needed. This investigation derives relationships between the Zernike expansion coefficients for two different pupil sizes.

Bit-error rate for free-space adaptive optics laser communications.

Abstract: An analysis of adaptive optics compensation for atmospheric-turbulence-induced scintillation is presented with the figure of merit being the laser communications bit-error rate. The formulation covers weak, moderate, and strong turbulence; on-off keying; and amplitude-shift keying, over horizontal propagation paths or on a ground-to-space uplink or downlink. The theory shows that under some circumstances the bit-error rate can be improved by a few orders of magnitude with the addition of adaptive optics to compensate for the scintillation. Low-order compensation (less than 40 Zernike modes) appears to be feasible as well as beneficial for reducing the bit-error rate and increasing the throughput of the communication link.

Theory of quantitative phase-contrast computed tomography.

Abstract: Phase-contrast x-ray computed tomography (CT) is an emerging imaging technique that can be implemented at third-generation synchrotron radiation sources or by using a microfocus x-ray source Promising results have recently been obtained in materials science and medicine At the same time, the lack of a mathematical theory comparable with that of conventional CT limits the progress in this field Such a theory is now suggested, establishing a fundamental relation between the three-dimensional Radon transform of the object function and the two-dimensional Radon transform of the phase-contrast projection A reconstruction algorithm is derived in the form of a filtered backprojection The filter function is given in the space and spatial-frequency domains The theory suggested enables one to quantitatively determine the refractive index of a weakly absorbing medium from x-ray intensity data measured in the near-field region The results of computer simulations are discussed

Estimating the scene illumination chromaticity by using a neural network

Abstract: A neural network can learn color constancy, defined here as the ability to estimate the chromaticity of a scene's overall illumination. We describe a multilayer neural network that is able to recover the illumination chromaticity given only an image of the scene. The network is previously trained by being presented with a set of images of scenes and the chromaticities of the corresponding scene illuminants. Experiments with real images show that the network performs better than previous color constancy methods. In particular, the performance is better for images with a relatively small number of distinct colors. The method has application to machine vision problems such as object recognition, where illumination-independent color descriptors are required, and in digital photography, where uncontrolled scene illumination can create an unwanted color cast in a photograph.

Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques.

Abstract: The complexity of computing conventional matrix multiply wave-front reconstructors scales as O(n3) for most adaptive optical (AO) systems, where n is the number of deformable mirror (DM) actuators. This is impractical for proposed systems with extremely large n. It is known that sparse matrix methods improve this scaling for least-squares reconstructors, but sparse techniques are not immediately applicable to the minimum-variance reconstructors now favored for multiconjugate adaptive optical (MCAO) systems with multiple wave-front sensors (WFSs) and DMs. Complications arise from the nonsparse statistics of atmospheric turbulence, and the global tip/tilt WFS measurement errors associated with laser guide star (LGS) position uncertainty. A description is given of how sparse matrix methods can still be applied by use of a sparse approximation for turbulence statistics and by recognizing that the nonsparse matrix terms arising from LGS position uncertainty are low-rank adjustments that can be evaluated by using the matrix inversion lemma. Sample numerical results for AO and MCAO systems illustrate that the approximation made to turbulence statistics has negligible effect on estimation accuracy, the time to compute the sparse minimum-variance reconstructor for a conventional natural guide star AO system scales as O(n3/2) and is only a few seconds for n = 3500, and sparse techniques reduce the reconstructor computations by a factor of 8 for sample MCAO systems with 2417 DM actuators and 4280 WFS subapertures. With extrapolation to 9700 actuators and 17,120 subapertures, a reduction by a factor of approximately 30 or 40 to 1 is predicted.

Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform.

Abstract: Wave-front reconstruction with the use of the fast Fourier transform (FFT) and spatial filtering is shown to be computationally tractable and sufficiently accurate for use in large Shack–Hartmann-based adaptive optics systems (up to at least 10,000 actuators). This method is significantly faster than, and can have noise propagation comparable with that of, traditional vector–matrix-multiply reconstructors. The boundary problem that prevented the accurate reconstruction of phase in circular apertures by means of square-grid Fourier transforms (FTs) is identified and solved. The methods are adapted for use on the Fried geometry. Detailed performance analysis of mean squared error and noise propagation for FT methods is presented with the use of both theory and simulation.

Image description with Chebyshev–Fourier moments

Abstract: Chebyshev-Fourier moments for describing images were proposed. After definition of the moments, the multidistortion invariance of the moments was verified. The performance of the moments in describing images was investigated in terms of the normalized image-reconstruction error and the results of the experiments on the noise sensitivity are given.

Multiple multipole method with automatic multipole setting applied to the simulation of surface plasmons in metallic nanostructures

Abstract: Highly accurate computations of surface plasmons in metallic nanostructures with various geometries are presented. Calculations for cylinders with irregular cross section, coupled structures, and periodic gratings are shown. These systems exhibit a resonant behavior with complex field distribution and strong field enhancement, and therefore their computation requires a very accurate numerical method. It is shown that the multiple multipole (MMP) method, together with an automatic multipole setting (AMS) procedure, is well suited for these computations. An AMS technique for the two-dimensional MMP method is presented. It relies on the global topology of each domain boundary to generate a distribution of numerically independent multipole expansions. This technique greatly facilitates the MMP modeling.

Calculated impact of higher-order monochromatic aberrations on retinal image quality in a population of human eyes.

Abstract: We calculated the impact of higher-order aberrations on retinal image quality and the magnitude of the visual benefit expected from their correction in a large population of human eyes. Wave aberrations for both eyes of 109 normal subjects and 4 keratoconic patients were measured for 3-, 4-, and 5.7-mm pupils with a Shack-Hartmann sensor. Retinal image quality was estimated by means of the modulation transfer function (MTF) in white light. The visual benefit was calculated as the ratio of the MTF when the monochromatic higher-order aberrations are corrected to the MTF corresponding to the best correction of defocus and astigmatism. On average, the impact of the higher-order aberrations for a 5.7-mm pupil in normal eyes is similar to an equivalent defocus of approximately 0.3 D. The average visual benefit for normal eyes at 16 c/deg is approximately 2.5 for a 5.7-mm pupil and is negligible for small pupils (1.25 for a 3-mm pupil). The benefit varies greatly among eyes, with some normal eyes showing almost no benefit and others a benefit higher than 4 at 16 c/deg across a 5.7-mm pupil. The benefit for keratoconic eyes is much larger. The benefit at 16 c/deg is 12 and 3 for 5.7- and 3-mm pupils, respectively, averaged across four keratoconics. These theoretical benefits could be realized in normal viewing conditions but only under specific conditions.

Extended Nijboer-Zernike approach for the computation of optical point-spread functions

Abstract: New Bessel-series representations for the calculation of the diffraction integral are presented yielding the point-spread function of the optical system, as occurs in the Nijboer-Zernike theory of aberrations. In this analysis one can allow an arbitrary aberration and a defocus part. The representations are presented in full detail for the cases of coma and astigmatism. The analysis leads to stably converging results in the case of large aberration or defocus values, while the applicability of the original Nijboer-Zernike theory is limited mainly to wave-front deviations well below the value of one wavelength. Because of its intrinsic speed, the analysis is well suited to supplement or to replace numerical calculations that are currently used in the fields of (scanning) microscopy, lithography, and astronomy. In a companion paper [J. Opt. Soc. Am. A 19, 860 (2002)], physical interpretations and applications in a lithographic context are presented, a convergence analysis is given, and a comparison is made with results obtained by using a numerical package.

An Algebraic Algorithm for Nonuniformity Correction in Focal-Plane Arrays

Abstract: A scene-based algorithm is developed to compensate for bias nonuniformity in focal-plane arrays. Nonuniformity can be extremely problematic, especially for mid- to far-infrared imaging systems. The technique is based on use of estimates of interframe subpixel shifts in an image sequence, in conjunction with a linear-interpolation model for the motion, to extract information on the bias nonuniformity algebraically. The performance of the proposed algorithm is analyzed by using real infrared and simulated data. One advantage of this technique is its simplicity; it requires relatively few frames to generate an effective correction matrix, thereby permitting the execution of frequent on-the-fly nonuniformity correction as drift occurs. Additionally, the performance is shown to exhibit considerable robustness with respect to lack of the common types of temporal and spatial irradiance diversity that are typically required by statistical scene-based nonuniformity correction techniques.

Staircase approximation validity for arbitrary-shaped gratings.

Abstract: An electromagnetic study of the staircase approximation of arbitrary shaped gratings is conducted with three different grating theories. Numerical results on a deep aluminum sinusoidal grating show that the staircase approximation introduces sharp maxima in the local field map close to the edges of the profile. These maxima are especially pronounced in TM polarization and do not exist with the original sinusoidal profile. Their existence is not an algorithmic artifact, since they are found with different grating theories and numerical implementations. Since the number of the maxima increases with the number of the slices, a greater number of Fourier components is required to correctly represent the electromagnetic field, and thus a worsening of the convergence rate is observed. The study of the local field map provides an understanding of why methods that do not use the staircase approximation (e.g., the differential theory) converge faster than methods that use it. As a consequence, a 1% accuracy in the efficiencies of a deep sinusoidal metallic grating is obtained 30 times faster when the differential theory is used in comparison with the use of the rigorous coupled-wave theory. A theoretical analysis is proposed in the limit when the number of slices tends to infinity, which shows that even in that case the staircase approximation is not well suited to describe the real profile.

In vivo resonant Raman measurement of macular carotenoid pigments in the young and the aging human retina.

Abstract: We have used resonant Raman scattering spectroscopy as a novel, noninvasive, in vivo optical technique to measure the concentration of the macular carotenoid pigments lutein and zeaxanthin in the living human retina of young and elderly adults. Using a backscattering geometry and resonant molecular excitation in the visible wavelength range, we measure the Raman signals originating from the single- and double-bond stretch vibrations of the p-conjugated molecule’s carbon backbone. The Raman signals scale linearly with carotenoid content, and the required laser excitation is well below safety limits for macular exposure. Furthermore, the signals decline significantly with increasing age in normal eyes. The Raman technique is objective and quantitative and may lead to a new method for rapid screening of carotenoid pigment levels in large populations at risk for vision loss from age-related macular degeneration, the leading cause of blindness in the elderly in the United States. © 2002 Optical Society of America OCIS codes: 170.0170, 170.4470, 170.4580, 170.1610, 300.6450, 330.4300.

Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths

Abstract: Techniques for modeling an object through observation are very important in object recognition and virtual reality. A wide variety of techniques have been developed for modeling objects with opaque surfaces, whereas less attention has been paid to objects with transparent surfaces. A transparent surface has only surface reflection; it has little body reflection. We present a new method for obtaining surface orientations of transparent surfaces through analysis of the degree of polarization in surface reflection and emission in visible and far-infrared wavelengths, respectively. This parameter, the polarization degree of reflected light at the visible wavelengths, is used for determining the surface orientation at a surface point. The polarization degree at visible wavelengths provides two possible solutions, and the proposed method uses the polarization degree at far-infrared wavelengths to resolve this ambiguity.

Assessment of an extended Nijboer–Zernike approach for the computation of optical point-spread functions

Abstract: We assess the validity of an extended Nijboer–Zernike approach [J. Opt. Soc. Am. A19, 849 (2002)], based on recently found Bessel-series representations of diffraction integrals comprising an arbitrary aberration and a defocus part, for the computation of optical point-spread functions of circular, aberrated optical systems. These new series representations yield a flexible means to compute optical point-spread functions, both accurately and efficiently, under defocus and aberration conditions that seem to cover almost all cases of practical interest. Because of the analytical nature of the formulas, there are no discretization effects limiting the accuracy, as opposed to the more commonly used numerical packages based on strictly numerical integration methods. Instead, we have an easily managed criterion, expressed in the number of terms to be included in the Bessel-series representations, guaranteeing the desired accuracy. For this reason, the analytical method can also serve as a calibration tool for the numerically based methods. The analysis is not limited to pointlike objects but can also be used for extended objects under various illumination conditions. The calculation schemes are simple and permit one to trace the relative strength of the various interfering complex-amplitude terms that contribute to the final image intensity function.

Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations.

Abstract: The analysis of many systems in optical communications and metrology utilizing Gaussian beams, such as free-space propagation from single-mode fibers, point diffraction interferometers, and interference lithography, would benefit from an accurate analytical model of Gaussian beam propagation. We present a full vector analysis of Gaussian beam propagation by using the well-known method of the angular spectrum of plane waves. A Gaussian beam is assumed to traverse a charge-free, homogeneous, isotropic, linear, and nonmagnetic dielectric medium. The angular spectrum representation, in its vector form, is applied to a problem with a Gaussian intensity boundary condition. After some mathematical manipulation, each nonzero propagating electric field component is expressed in terms of a power-series expansion. Previous analytical work derived a power series for the transverse field, where the first term (zero order) in the expansion corresponds to the usual scalar paraxial approximation. We confirm this result and derive a corresponding longitudinal power series. We show that the leading longitudinal term is comparable in magnitude with the first transverse term above the scalar paraxial term, thus indicating that a full vector theory is required when going beyond the scalar paraxial approximation. In spite of the advantages of a compact analytical formalism, enabling rapid and accurate modeling of Gaussian beam systems, this approach has a notable drawback. The higher-order terms diverge at locations that are sufficiently far from the initial boundary, yielding unphysical results. Hence any meaningful use of the expansion approach calls for a careful study of its range of applicability. By considering the transition of a Gaussian wave from the paraxial to the spherical regime, we are able to derive a simple expression for the range within which the series produce numerically satisfying answers.

Monochromatic Aberrations of Human Eyes in the Horizontal Visual Field

Abstract: We measured the monochromatic aberrations of five subjects' right eyes both temporally and nasally out to 40 degrees from fixation. We used a Hartmann-Shack sensor with modifications to equipment and software to enable off-axis measurements. Results were standardized for 6-mm pupils. There was considerable variation among subjects in the pattern of aberrations. Aberrations were generally greater in the nasal visual field than in the temporal visual field; in the case of third-order aberrations, this was true for all subjects. The contribution of third-order Zernike aberrations to the root-mean-square aberration increased up to four times from the center to the edge of the field, but the contribution of fourth- to sixth-order Zernike aberrations varied little across the visual field. Results were similar to those of a previous investigation using laser ray tracing and were of the order of those predicted by Navarro's finite schematic eye.

Phenomenon of spectral switches as a new effect in singular optics with polychromatic light

Abstract: It is shown that the recently discovered phenomenon of so-called spectral switches has a natural interpretation in the framework of singular optics with polychromatic light and that it should be regarded as being primarily a manifestation of diffraction-induced spectral changes rather than correlation-induced spectral changes as was suggested in the original papers [the first one appearing in Opt. Commun. 162, 57 (1999)] reporting this effect.