Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 2005"
TL;DR: An analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) that imparts an arbitrary-order phase singularity on the light field is deduced and the far-field intensity distribution is derived.
Abstract: We deduce and study an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) that imparts an arbitrary-order phase singularity on the light field. Estimates for the optical vortex radius that depends on the singularity’s integer order n (also termed topological charge, or order of the dislocation) have been derived. The near-zero vortex intensity is shown to be proportional to ρ2n, where ρ is the radial coordinate. Also, an analytical expression for Fresnel diffraction of the Gaussian beam by a SPP with nth-order singularity is analyzed. The far-field intensity distribution is derived. The radius of maximal intensity is shown to depend on the singularity number. The behavior of the Gaussian beam intensity after a SPP with second-order singularity (n=2) is studied in more detail. The parameters of the light beams generated numerically with the Fresnel transform and via analytical formulas are in good agreement. In addition, the light fields with first- and second-order singularities were generated by a 32-level SPP fabricated on the resist by use of the electron-beam lithography technique.
278 citations
TL;DR: It is revealed that in fact there are no new aberrations in imaging optical systems with near-circular aperture stops but otherwise without symmetry, and that the field dependence of an aberration often changes when symmetry is abandoned.
Abstract: Many authors, dating back to at least the 1950s, have presented mathematical expansions of the wave-front aberration function for optical systems without symmetry, typically based on limiting assumptions and simplifications, with some of the most recent work being done by Howard and Stone [Appl. Opt.39, 3232 (2000) ]. This paper reveals that in fact there are no new aberrations in imaging optical systems with near-circular aperture stops but otherwise without symmetry. What does occur is that the field dependence of an aberration often changes when symmetry is abandoned. Each aberration type develops a characteristic field behavior in a system without symmetry. Specifically, for example, astigmatism, develops a binodal field dependence; e.g., there are typically two points in the field with zero astigmatism, and typically neither point is on axis. This construct, nodal aberration theory, for understanding the aberrations in systems without symmetry becomes a direct extension of an optical designer’s knowledge base. Through the use of real ray-based analysis methods, such as Zernike coefficients, it is possible to understand completely the aberrations of optical systems without symmetry in terms of rotationally symmetric aberration theory with the simple addition of the concept of field nodes.
249 citations
TL;DR: A modified formulation of Maxwell's equations is presented that includes a complex and nonlinear coordinate transform along one or two Cartesian coordinates that allows one to map an infinite space to a finite space and to specify graded perfectly matched absorbing boundaries that allow the outgoing wave condition to be satisfied.
Abstract: A modified formulation of Maxwell’s equations is presented that includes a complex and nonlinear coordinate transform along one or two Cartesian coordinates. The added degrees of freedom in the modified Maxwell’s equations allow one to map an infinite space to a finite space and to specify graded perfectly matched absorbing boundaries that allow the outgoing wave condition to be satisfied. The approach is validated by numerical results obtained by using Fourier-modal methods and shows enhanced convergence rate and accuracy.
242 citations
TL;DR: In this article, a detailed study of the propagation of an arbitrary nondiffracting beam whose disturbance in the plane z = 0 is modulated by a Gaussian envelope is presented.
Abstract: A detailed study of the propagation of an arbitrary nondiffracting beam whose disturbance in the plane z=0 is modulated by a Gaussian envelope is presented. We call such a field a Helmholtz–Gauss (HzG) beam. A simple closed-form expression for the paraxial propagation of the HzG beams is written as the product of three factors: a complex amplitude depending on the z coordinate only, a Gaussian beam, and a complex scaled version of the transverse shape of the nondiffracting beam. The general expression for the angular spectrum of the HzG beams is also derived. We introduce for the first time closed-form expressions for the Mathieu–Gauss beams in elliptic coordinates and for the parabolic Gauss beams in parabolic coordinates. The properties of the considered beams are studied both analytically and numerically.
238 citations
TL;DR: In this article, the authors proposed a method to isolate absorption trends confined to the lower layer of a two-layer turbid medium, as is desired in near-infrared spectroscopy (NIRS) of cerebral hemodynamics.
Abstract: We propose a method to isolate absorption trends confined to the lower layer of a two-layer turbid medium, as is desired in near-infrared spectroscopy (NIRS) of cerebral hemodynamics. Several two-layer Monte Carlo simulations of NIRS time series were generated using a physiologically relevant range of optical properties and varying the absorption coefficients due to bottom-layer, top-layer, and/or global fluctuations. Initial results showed that by measuring absorption trends at two source–detector separations and performing a least-squares fit of one to the other, processed signals strongly resemble the simulated bottom-layer absorption properties. Through this approach, it was demonstrated that fitting coefficients can be estimated within less than ±2% of the ideal value without any a priori knowledge of the optical properties present in the model. An analytical approximation for the least-squares coefficient provides physical insight into the nature of errors and suggests ways to reduce them.
237 citations
TL;DR: The detailed optics of photonic nanojets generated by normal plane-wave incidence on dielectric cylinders, which have a subwavelength beam waist and propagate with little divergence for several wavelengths, are discussed.
Abstract: The detailed optics of photonic nanojets generated by normal plane-wave incidence on dielectric cylinders is discussed. These nanojets have a subwavelength beam waist and propagate with little divergence for several wavelengths. A physical explanation for this peculiar behavior is presented. Characteristic dimensions of the nanojets for a large range of physical parameters are calculated.
214 citations
TL;DR: An analytic formula is proposed that describes the algorithm behavior of Retinex varying the number of paths and its recursive iterations are mathematically analyzed using the formula.
Abstract: We present a detailed mathematical analysis of the original Retinex algorithm due to Land and McCann [J. Opt. Soc. Am.61, 1 (1071) ]. To this end, we propose an analytic formula that describes the algorithm behavior. More than one Retinex version (e.g., with and without threshold) is examined. The behavior of Retinex varying the number of paths is predicted, and its recursive iterations are mathematically analyzed using the formula. The mathematical setting presented serves as a common ground for the various Retinex implementations. Its validity is confirmed by the tests on images that we have performed.
201 citations
TL;DR: In this paper, Cauchy's equation is used to model the chromatic difference in refraction of the Gullstrand number 1 schematic eye with a gradient-index lens.
Abstract: Of the commonly used chromatic dispersion equations, only the Sellmeier and the Cauchy equations seem to be theoretically based. Cauchy's equation is derived from the Sellmeier equation, is simpler to implement, and was found to give an excellent fit to published refractive-index data of the human eye. We used Cauchy's equation to model the chromatic difference in refraction of the Gullstrand number 1 schematic eye with a gradient-index lens. To estimate the dispersion at different refractive-index levels within the lens, a single dispersion equation at one nominal refractive index was linearly scaled. This scaling was justified after exploring the effect of mean refractive index on dispersion by using Sellmeier's equation and finding that a dispersion equation for one wavelength is just a linearly scaled version of the dispersion equation at any other wavlength. Because Cauchy's equation is theoretically based and gives excellent fit to data in the visible spectrum, it can be used to extrapolate results into the near infrared with confidence.
199 citations
TL;DR: The Fast Linear Canonical Transform (FLCT) as mentioned in this paper is derived from the linear canonical transform (LCT) and can be used for FFT, FRT, and FST calculations.
Abstract: The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the area of optical signal processing) to calculate the discrete FT, FRT, and FST. All of these algorithms are based on the use of the fast Fourier transform (FFT). In this paper we develop theory for the discrete linear canonical transform (DLCT), which is to the LCT what the discrete Fourier transform (DFT) is to the FT. We then derive the fast linear canonical transform (FLCT), an NlogN algorithm for its numerical implementation by an approach similar to that used in deriving the FFT from the DFT. Our algorithm is significantly different from the FFT, is based purely on the properties of the LCT, and can be used for FFT, FRT, and FST calculations and, in the most general case, for the rapid calculation of the effect of any QPS.
167 citations
TL;DR: In this article, it is shown how the space-bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadratic phase optical system whose operation is described by the linear canonical transform.
Abstract: By use of matrix-based techniques it is shown how the space–bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadratic-phase optical system whose operation is described by the linear canonical transform. Then, applying the regular uniform sampling criteria imposed by the SBP and linking the criteria explicitly to a decomposition of the optical matrix of the system, it is shown how numerical algorithms (employing interpolation and decimation), which exhibit both invertibility and additivity, can be implemented. Algorithms appearing in the literature for a variety of transforms (Fresnel, fractional Fourier) are shown to be special cases of our general approach. The method is shown to allow the existing algorithms to be optimized and is also shown to permit the invention of many new algorithms.
159 citations
TL;DR: This examination focuses particularly on individual neurons: what are their visual properties, how might these properties arise, what do these properties tell us about visual signal transformations, and how might they be expressed in perception.
Abstract: We review how neurons in the principal pathway connecting the retina to the visual cortex represent information about the chromatic and spatial characteristics of the retinal image. Our examination focuses particularly on individual neurons: what are their visual properties, how might these properties arise, what do these properties tell us about visual signal transformations, and how might these properties be expressed in perception? Our discussion is inclined toward studies on old-world monkeys and where possible emphasizes quantitative work that has led to or illuminates models of visual signal processing.
TL;DR: It is shown that the degree of radial polarization is maximum at a given distance from theinterferometer output port that depends on the diameter of the incident beam at the interferometer input port.
Abstract: We present a theoretical and experimental investigation of an interferometric technique for converting a linearly polarized Gaussian beam into a radially polarized doughnut beam. The experimental setup accomplishes the coherent summation of two orthogonally polarized TEM01 and TEM10 beams that are obtained from the transformation of a TEM00 beam by use of a simple binary diffractive optical element. We have shown that the degree of radial polarization is maximum at a given distance from the interferometer output port that depends on the diameter of the incident beam at the interferometer input port.
TL;DR: A second-order finite-element adaptive strategy with error control for one-dimensional grating problems is developed and is expected to increase significantly the accuracy and efficiency of the discretization as well as reduce the computation cost.
Abstract: A second-order finite-element adaptive strategy with error control for one-dimensional grating problems is developed. The unbounded computational domain is truncated to a bounded one by a perfectly-matched-layer (PML) technique. The PML parameters, such as the thickness of the layer and the medium properties, are determined through sharp a posteriori error estimates. The adaptive finite-element method is expected to increase significantly the accuracy and efficiency of the discretization as well as reduce the computation cost. Numerical experiments are included to illustrate the competitiveness of the proposed adaptive method.
TL;DR: In this article, a method for high-sensitivity birefringence quantification by using enhanced polarization-sensitive optical coherence tomography (EPS-OCT) is presented.
Abstract: Polarization-sensitive optical coherence tomography provides high-resolution cross-sectional characterization of birefringence in turbid media. Weakly birefringent biological tissues such as the retinal nerve fiber layer (RNFL) require advanced speckle noise reduction for high-sensitivity measurement of form birefringence. We present a novel method for high-sensitivity birefringence quantification by using enhanced polarization-sensitive optical coherence tomography (EPS-OCT) and introduce the polarimetric signal-to-noise ratio, a mathematical tool for analyzing speckle noise in polarimetry. Multiple incident polarization states and nonlinear fitting of normalized Stokes vectors allow determination of retardation with ±1° uncertainty with invariance to unknown unitary polarization transformations. Results from a weakly birefringent turbid film and in vivo primate RNFL are presented. In addition, we discuss the potential of EPS-OCT for noninvasive quantification of intracellular filamentous nanostructures, such as neurotubules in the RNFL that are lost during the progression of glaucoma.
TL;DR: It is shown that under certain constraints a minimum data set of three backscatter coefficients and two extinction coefficients is sufficient for a successful inversion, and the quality of the retrieved aerosol parameters depends strongly on the imaginary part owing to the degree of ill-posedness.
Abstract: The hybrid regularization technique developed at the Institute of Mathematics of Potsdam University (IMP) is used to derive microphysical properties such as effective radius, surface-area concentration, and volume concentration, as well as the single-scattering albedo and a mean complex refractive index, from multiwavelength lidar measurements We present the continuation of investigations of the IMP method Theoretical studies of the degree of ill-posedness of the underlying model, simulation results with respect to the analysis of the retrieval error of microphysical particle properties from multiwavelength lidar data, and a comparison of results for different numbers of backscatter and extinction coefficients are presented Our analysis shows that the backscatter operator has a smaller degree of ill-posedness than the operator for extinction This fact underlines the importance of backscatter data Moreover, the degree of ill-posedness increases with increasing particle absorption, ie, depends on the imaginary part of the refractive index and does not depend significantly on the real part Furthermore, an extensive simulation study was carried out for logarithmic-normal size distributions with different median radii, mode widths, and real and imaginary parts of refractive indices The errors of the retrieved particle properties obtained from the inversion of three backscatter (355, 532, and 1064 nm) and two extinction (355 and 532 nm) coefficients were compared with the uncertainties for the case of six backscatter (400, 710, 800 nm, additionally) and the same two extinction coefficients For known complex refractive index and up to 20% normally distributed noise, we found that the retrieval errors for effective radius, surface-area concentration, and volume concentration stay below approximately 15% in both cases Simulations were also made with unknown complex refractive index In that case the integrated parameters stay below approximately 30%, and the imaginary part of the refractive index stays below 35% for input noise up to 10% in both cases In general, the quality of the retrieved aerosol parameters depends strongly on the imaginary part owing to the degree of ill-posedness It is shown that under certain constraints a minimum data set of three backscatter coefficients and two extinction coefficients is sufficient for a successful inversion The IMP algorithm was finally tested for a measurement case
TL;DR: The results of simulations of the spectral dependence of Kubelka-Munk coefficients of absorption and scattering show that they compare very well with those derived from experimental results.
Abstract: A generally applicable theoretical model describing light propagating through turbid media is proposed. The theory is a generalization of the revised Kubelka-Munk theory, extending its applicability to accommodate a wider range of absorption influences. A general expression for a factor taking into account the effect of scattering on the total photon path traversed in a turbid medium is derived. The extended model is applied to systems of ink-dyed paper sheets-mixtures of wood fibers with dyes-which represent examples of systems that have thus far eluded the original Kubelka-Munk model. The results of simulations of the spectral dependence of Kubelka-Munk coefficients of absorption and scattering show that they compare very well with those derived from experimental results.
TL;DR: It is shown that both the cross-spectral density and the mutual coherence function of partially coherent pulses can be expressed as a sum of spatially and spectrally and temporally completely coherent modes.
Abstract: A coherent-mode representation for spatially and spectrally partially coherent pulses is derived both in the space–frequency domain and in the space–time domain. It is shown that both the cross-spectral density and the mutual coherence function of partially coherent pulses can be expressed as a sum of spatially and spectrally and temporally completely coherent modes. The concept of the effective degree of coherence for nonstationary fields is introduced. As an application of the theory, the propagation of Gaussian Schell-model pulsed beams in the space–frequency domain is considered and their coherent-mode representation is presented.
TL;DR: A new mathematical model called "controllable dark-hollow beams" is introduced to describe hollow beams, and the central dark size of this beam can be controlled easily by the beam order N and parameter epsilon.
Abstract: A new mathematical model called “controllable dark-hollow beams” is introduced to describe hollow beams. The central dark size of this beam can be controlled easily by the beam order N and parameter ϵ. An analytical formula is derived for the propagation of a controllable dark-hollow beam through a paraxial optical system, and some numerical calculations are carried out. Some important propagation characteristics of this beam, such as the beam propagation factor and the kurtosis parameter, are studied in detail, and their variation rules versus the beam order N and parameter ϵ are presented and plotted.
TL;DR: It is shown that a modification of an initial assumption in one of the formulations leads to equivalent results in the two previously reported calculations of the amplitude distribution of speckles in optical coherence tomography.
Abstract: The two previously reported calculations of the amplitude distribution of speckles in optical coherence tomography, each based on a different mathematical formulation, yield different results. We show that a modification of an initial assumption in one of the formulations leads to equivalent results.
TL;DR: The modal basis is the real Fourier basis, which allows direct control of specific regions of the point-spread function and is computationally efficient enough to be implemented with off-the-shelf technology for a 2.5 kHz, 64 x 64 adaptive optics system.
Abstract: Optimal modal Fourier-transform wavefront control combines the speed of Fourier-transform reconstruction (FTR) with real-time optimization of modal gains to form a fast, adaptive wavefront control scheme. Our modal basis is the real Fourier basis, which allows direct control of specific regions of the point-spread function. We formulate FTR as modal control and show how to measure custom filters. Because the Fourier basis is a tight frame, we can use it on a circular aperture for modal control even though it is not an orthonormal basis. The modal coefficients are available during reconstruction, greatly reducing computational overhead for gain optimization. Simulation results show significant improvements in performance in low-signal-to-noise-ratio situations compared with nonadaptive control. This scheme is computationally efficient enough to be implemented with off-the-shelf technology for a 2.5 kHz, 64×64 adaptive optics system.
TL;DR: A novel method for reflectance recovery is introduced that finds the smoothest spectrum consistent with both the colorimetric data and a linear model of reflectance.
Abstract: We investigate methods for the recovery of reflectance spectra from the responses of trichromatic camera systems and the application of these methods to the problem of camera characterization. The recovery of reflectance from colorimetric data is an ill-posed problem, and a unique solution requires additional constraints. We introduce a novel method for reflectance recovery that finds the smoothest spectrum consistent with both the colorimetric data and a linear model of reflectance. Four multispectral methods were tested using data from a real trichromatic camera system. The new method gave the lowest maximum colorimetric error in terms of camera characterization with test data that were independent of the training data. However, the average colorimetric performances of the four multispectral methods were statistically indistinguishable from each other but were significantly worse than conventional methods for camera characterization such as polynomial transforms.
TL;DR: In this paper, the authors developed a theoretical and experimental methodology to obtain localized stationary wave fields (with high transverse localization) whose longitudinal intensity pattern can approximately assume any desired shape within a chosen interval 0�z⩽L of the propagation axis z.
Abstract: In this work, starting by suitable superpositions of equal-frequency Bessel beams, we develop a theoretical and experimental methodology to obtain localized stationary wave fields (with high transverse localization) whose longitudinal intensity pattern can approximately assume any desired shape within a chosen interval 0⩽z⩽L of the propagation axis z. Their intensity envelope remains static, i.e., with velocity v=0, so we have named “frozen waves” (FWs) these new solutions to the wave equations (and, in particular, to the Maxwell equation). Inside the envelope of a FW, only the carrier wave propagates. The longitudinal shape, within the interval 0⩽z⩽L, can be chosen in such a way that no nonnegligible field exists outside the predetermined region (consisting, e.g., in one or more high-intensity peaks). Our solutions are notable also for the different and interesting applications they can have—especially in electromagnetism and acoustics—such as optical tweezers, atom guides, optical or acoustic bistouries, and various important medical apparatuses.
TL;DR: An automated reflectometry system is constructed for accurate measurement of coherent reflectance curves of turbid samples and analyzed the presence of coherent and diffuse reflection near the specular reflection angle to determine complex refractive indices of fresh porcine skin epidermis and dermis tissues and Intralipid solutions.
Abstract: We constructed an automated reflectometry system for accurate measurement of coherent
reflectance curves of turbid samples and analyzed the presence of coherent and
diffuse reflection near the specular reflection angle. An existing method has been
validated to determine the complex refractive indices of turbid samples on the basis
of nonlinear regression of the coherent reflectance curves by Fresnel’s
equations. The complex refractive indices of fresh porcine skin epidermis and dermis
tissues and Intralipid solutions were determined at eight wavelengths: 325, 442, 532,
633, 850, 1064, 1310, and 1557 nm.
TL;DR: A full-vectorial three-dimensional nonlinear inversion scheme to retrieve the map of the permittivity of the object from the scattered far-field data and analyzes the role of the solid angle of illumination, the incident polarization, and the position of the prism interface on the resolution of the images.
Abstract: We simulate a total internal reflection tomography experiment in which an unknown object is illuminated by evanescent waves and the scattered field is detected along several directions. We propose a full-vectorial three-dimensional nonlinear inversion scheme to retrieve the map of the permittivity of the object from the scattered far-field data. We study the role of the solid angle of illumination, the incident polarization, and the position of the prism interface on the resolution of the images. We compare our algorithm with a linear inversion scheme based on the renormalized Born approximation and stress the importance of multiple scattering in this particular configuration. We analyze the sensitivity to noise and point out that using incident propagative waves together with evanescent waves improves the robustness of the reconstruction.
TL;DR: This work fabricated the highest-numerical-aperture photon sieves reported to date and experimentally verified their focusing characteristics and proposes two new designs of the photon sieve that have the potential to significantly increase focusing efficiency.
Abstract: We present the first lithography results that use high-numerical-aperture photon sieves as focusing elements in a scanning-optical-beam-lithography system [J. Vac. Sci. Technol. B21, 2810 (2003)]. Photon sieves are novel optical elements that offer the advantages of higher resolution and improved image contrast compared with traditional diffractive optics such as zone plates [Nature414, 184 (2001)]. We fabricated the highest-numerical-aperture photon sieves reported to date and experimentally verified their focusing characteristics. We propose two new designs of the photon sieve that have the potential to significantly increase focusing efficiency.
TL;DR: A theoretical analysis and experimental investigation reveals that in OCT, despite multiple scattering, the field backscattered from the sample is generally spatially coherent and that the resulting interference signal with the reference field is stationary relative to measurement time.
Abstract: We present a new model of optical coherence tomography (OCT) taking into account multiple scattering. A theoretical analysis and experimental investigation reveals that in OCT, despite multiple scattering, the field backscattered from the sample is generally spatially coherent and that the resulting interference signal with the reference field is stationary relative to measurement time. On the basis of this result, we model an OCT signal as a sum of spatially coherent fields with random-phase arguments--constant during measurement time--caused by multiple scattering. We calculate the mean of such a random signal from classical results of statistical optics and a Monte Carlo simulation. OCT signals predicted by our model are in very good agreement with a depth scan measurement of a sample consisting of a mirror covered with an aqueous suspension of microspheres. We discuss other comprehensive OCT models based on the extended Huygens-Fresnel principle, which rest on the assumption of partially coherent interfering fields.
TL;DR: The developed theory and algorithms are directly applicable to reconstructing images exactly from data acquired with these trajectories, and the proposed algorithms become the algorithms that were proposed previously for image reconstruction on PI-line segments.
Abstract: We introduce a formula for image reconstruction on a chord of a general source trajectory. We subsequently develop three algorithms for exact image reconstruction on a chord from data acquired with the general trajectory. Interestingly, two of the developed algorithms can accommodate data containing transverse truncations. The widely used helical trajectory and other trajectories discussed in literature can be interpreted as special cases of the general trajectory, and the developed theory and algorithms are thus directly applicable to reconstructing images exactly from data acquired with these trajectories. For instance, chords on a helical trajectory are equivalent to the n-PI-line segments. In this situation, the proposed algorithms become the algorithms that we proposed previously for image reconstruction on PI-line segments. We have performed preliminary numerical studies, which include the study on image reconstruction on chords of two-circle trajectory, which is nonsmooth, and on n-PI lines of a helical trajectory, which is smooth. Quantitative results of these studies verify and demonstrate the proposed theory and algorithms.
TL;DR: This work shows how to increase the angular tolerance up to the divergence of standard beams without modifying the spectral bandwidth under oblique angle of incidence, using a multimode planar waveguide and a bi-atom grating.
Abstract: Resonant grating filters have been proposed as a promising alternative to multilayer stacks for narrowband free-space filtering. The efficiency of such filters under normal incidence has been demonstrated. Unfortunately, under oblique incidence, the limited angular tolerance of the resonance forbids any filtering applications with use of standard collimated incident beams. Using a multimode planar waveguide and a bi-atom grating, we show how to increase the angular tolerance up to the divergence of standard beams (0.2 deg) without modifying the spectral bandwidth (0.1 nm), under any oblique angle of incidence.
TL;DR: In this article, the average receiver intensity of the HcosG beam was analyzed for the case of propagation in turbulent atmosphere and its dependence on the source parameters was examined by application of the Fresnel diffraction integral.
Abstract: Hermite-cosine-Gaussian (HcosG) laser beams are studied. The source plane intensity of the HcosG beam is introduced and its dependence on the source parameters is examined. By application of the Fresnel diffraction integral, the average receiver intensity of HcosG beam is formulated for the case of propagation in turbulent atmosphere. The average receiver intensity is seen to reduce appropriately to various special cases. When traveling in turbulence, the HcosG beam initially experiences the merging of neighboring beam lobes, and then a TEM-type cosh-Gaussian beam is formed, temporarily leading to a plain cosh-Gaussian beam. Eventually a pure Gaussian beam results. The numerical evaluation of the normalized beam size along the propagation axis at selected mode indices indicates that relative spreading of higher-order HcosG beam modes is less than that of the lower-order counterparts. Consequently, it is possible at some propagation distances to capture more power by using higher-mode-indexed HcosG beams.
TL;DR: A significant and systematic increase in the response accommodation time, and a reduction in the peak velocity, is found in both subjects when the aberrations were corrected in real time, which may indicate that the monochromaticAberrations play a role in driving the accommodation response.
Abstract: The effect of asymmetric monochromatic aberrations in the accommodation response was studied by using an adaptive optics (AO) system. This approach permits the precise modification of ocular aberrations during accommodation. The AO system is composed of a real-time Hartmann-Shack wavefront sensor and a membrane deformable mirror with 37 independent actuators. The accommodation response was measured in two subjects with their normal aberrations and with the asymmetric aberrations terms corrected. We found a significant and systematic increase in the response accommodation time, and a reduction in the peak velocity, in both subjects when the aberrations were corrected in real time. However, neither the latency time nor the precision of the accommodation were affected. These results may indicate that the monochromatic aberrations play a role in driving the accommodation response.