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Showing papers in "Applied Optics in 1995"


Journal ArticleDOI
TL;DR: An optical-digital system that delivers near-diffraction-limited imaging performance with a large depth of field that is the standard incoherent optical system modified by a phase mask with digital processing of the resulting intermediate image.
Abstract: We designed an optical‐digital system that delivers near-diffraction-limited imaging performance with a large depth of field. This system is the standard incoherent optical system modified by a phase mask with digital processing of the resulting intermediate image. The phase mask alters or codes the received incoherent wave front in such a way that the point-spread function and the optical transfer function do not change appreciably as a function of misfocus. Focus-independent digital filtering of the intermediate image is used to produce a combined optical‐digital system that has a nearly diffraction limited point-spread function. This high-resolution extended depth of field is obtained through the expense of an increased dynamic range of the incoherent system. We use both the ambiguity function and the stationary-phase method to design these phase masks.

1,344 citations


Journal ArticleDOI
TL;DR: The dispersion of the depolarization factor is shown to affect the Rayleigh phase function slightly, by approximately 1% in the forward, backscattered, and 90° scattering-angle directions.
Abstract: Rayleigh-scattering cross sections and volume-scattering coefficients are computed for standard air; they incorporate the variation of the depolarization factor with wavelength. Rayleigh optical depths are then calculated for the 1962 U.S. Standard Atmosphere and for five supplementary models. Analytic formulas are derived for each of the parameters listed. The new optical depths can be 1.3% lower to 3% higher at midvisible wavelengths and up to 10% higher in the UV region compared with previous calculations, in which a constant or incorrect depolarization factor was used. The dispersion of the depolarization factor is also shown to affect the Rayleigh phase function slightly, by approximately 1% in the forward, backscattered, and 90° scattering-angle directions.

669 citations


Journal ArticleDOI
Yu-lin Xu1
TL;DR: A comprehensive solution to the classical problem of electromagnetic scattering by aggregates of an arbitrary number of arbitrarily configured spheres that are isotropic and homogeneous but may be of different size and composition is presented.
Abstract: We present a comprehensive solution to the classical problem of electromagnetic scattering by aggregates of an arbitrary number of arbitrarily configured spheres that are isotropic and homogeneous but may be of different size and composition. The profile of incident electromagnetic waves is arbitrary. The analysis is based on the framework of the Mie theory for a single sphere and the existing addition theorems for spherical vector wave functions. The classic Mie theory is generalized. Applying the extended Mie theory to all the spherical constituents in an aggregate simultaneously leads to a set of coupled linear equations in the unknown interactive coefficients. We propose an asymptotic iteration technique to solve for these coefficients. The total scattered field of the entire ensemble is constructed with the interactive scattering coefficients by the use of the translational addition theorem a second time. Rigorous analytical expressions are derived for the cross sections in a general case and for all the elements of the amplitude-scattering matrix in a special case of a plane-incident wave propagating along the z axis. As an illustration, we present some of our preliminary numerical results and compare them with previously published laboratory scattering measurements.

621 citations


Journal ArticleDOI
TL;DR: Optical and electron-energy-loss data for evaporated-aluminum films have been critically analyzed and used in an iterative, self-consistent algorithm that represents a combination of the Kramers-Kronig analysis and the semiquantum-model application.
Abstract: Optical and electron-energy-loss data for evaporated-aluminum films have been critically analyzed and used in an iterative, self-consistent algorithm that represents a combination of the Kramers-Kronig analysis and the semiquantum-model application. The novel values of the intrinsic optical functions of aluminum have been determined in a wide spectral range from 200 µm (6.2 meV) to 0.12 nm (10 keV). These functions are in accordance with recent calculations by Lee and Chang [Phys. Rev. B 49, 2362 (1994)], with dc conductivity measurements, and are in good agreement with both peak positions and line widths obtained from electron-energy-loss experiments. The results are examined for internal consistency by inertial and f-sum rules.

562 citations


Journal ArticleDOI
TL;DR: A new gap-size-analysis theory is presented to quantify the effect of canopy architecture on optical measurements of LAI based on the gap-fraction principle and can be used for any heterogeneous canopies.
Abstract: Optical instruments currently available for measuring the leaf-area index (LAI) of a plant canopy all utilize only the canopy gap-fraction information. These instruments include the Li-Cor LAI-2000 Plant Canopy Analyzer, Decagon, and Demon. The advantages of utilizing both the canopy gap-fraction and gap-size information are shown. For the purpose of measuring the canopy gap size, a prototype sunfleck–LAI instrument named Tracing Radiation and Architecture of Canopies (TRAC), has been developed and tested in two pure conifer plantations, red pine (Pinus resinosa Ait.) and jack pine (Pinus banksiana Lamb). A new gap-size-analysis theory is presented to quantify the effect of canopy architecture on optical measurements of LAI based on the gap-fraction principle. The theory is an improvement on that of Lang and Xiang [Agric. For. Meteorol. 37, 229 (1986)]. In principle, this theory can be used for any heterogeneous canopies.

453 citations


Journal ArticleDOI
TL;DR: The light-scattering properties of dental enamel and dentin were measured at 543, 632, and 1053 nm and their scattering and absorption coefficients and the scattering phase function were deduced by comparing the measured scattering data with angularly resolved Monte Carlo light- scattering simulations.
Abstract: The light-scattering properties of dental enamel and dentin were measured at 543, 632, and 1053 nm. Angularly resolved scattering distributions for these materials were measured from 0° to 180° using a rotating goniometer. Surface scattering was minimized by immersing the samples in an index-matching bath. The scattering and absorption coefficients and the scattering phase function were deduced by comparing the measured scattering data with angularly resolved Monte Carlo light-scattering simulations. Enamel and dentin were best represented by a linear combination of a highly forward-peaked Henyey–Greenstein (HG) phase function and an isotropic phase function. Enamel weakly scatters light between 543 nm and 1.06 μm, with the scattering coefficient (μs) ranging from μs = 15 to 105 cm−1. The phase function is a combination of a HG function with g = 0.96 and a 30–60% isotropic phase function. For enamel, absorption is negligible. Dentin scatters strongly in the visible and near IR (μs ≅ 260 cm−1) and absorbs weakly (μa ≅ 4 cm−1). The scattering phase function for dentin is described by a HG function with g = 0.93 and a very weak isotropic scattering component (~2%).

413 citations


Journal ArticleDOI
TL;DR: A wideband antireflection structure for glass that consists of a diffraction grating with a dielectric overcoat, which leads to an average reflection of less than 0.6% in the wavelength range between 300 and 2100 nm is presented.
Abstract: Diffractive optical structures for increasing the efficiency of crystalline silicon solar cells are discussed. As a consequence of the indirect band gap, light absorption becomes very ineffective near the band edge. This can be remedied by use of optimized diffraction gratings that lead to light trapping. We present blazed gratings that increase the optically effective cell thickness by approximately a factor of 5. In addition we present a wideband antireflection structure for glass that consists of a diffraction grating with a dielectric overcoat, which leads to an average reflection of less than 0.6% in the wavelength range between 300 and 2100 nm.

410 citations


Journal ArticleDOI
TL;DR: Tests of low-volume absorption cells that use mirror rotation, designed for fast-flow atmospheric sampling, show the validity and the usefulness of the techniques that have been developed.
Abstract: A multipass absorption cell, based on an astigmatic variant of the off-axis resonator (Herriott) configuration, has been designed to obtain long path lengths in small volumes. Rotation of the mirror axes is used to obtain an effective adjustability in the two mirror radii. This allows one to compensate for errors in mirror radii that are encountered in manufacture, thereby generating the desired reentrant patterns with less-precise mirrors. Acombination of mirror rotation and separation changes can be used to reach a variety of reentrant patterns and path lengths with a fixed set of astigmatic mirrors. The accessible patterns can be determined from trajectories, as a function of rotation and separation, through a general map of reentrant solutions. Desirable patterns for long-path spectroscopy can be chosen on the basis of path length, distance of the closest beam spot from the coupling hole, and tilt insensitivity. We describe the mathematics and analysis methods for the astigmatic cell with mirror rotation and then describe the design and test of prototype cells with this concept. Two cell designs are presented, a cell with 100-m path length in a volume of 3 L and a cell with 36-m path length in a volume of 0.3 L. Tests of low-volume absorption cells that use mirror rotation, designed for fast-flow atmospheric sampling, show the validity and the usefulness of the techniques that we have developed.

397 citations


Journal ArticleDOI
TL;DR: The new 5-frame algorithm and two new 6-frame algorithms have smaller phase errors caused by phase-shifter miscalibration than any of the common 3-, 4- or 5- frame algorithms.
Abstract: Phase-shifting interferometry suffers from two main sources of error: phase-shift miscalibration and detector nonlinearity. Algorithms that calculate the phase of a measured wave front require a high degree of tolerance for these error sources. An extended method for deriving such error-compensating algorithms patterned on the sequential application of the averaging technique is proposed here. Two classes of algorithms were derived. One class is based on the popular three-frame technique, and the other class is based on the 4-frame technique. The derivation of algorithms in these classes was calculated for algorithms with up to six frames. The new 5-frame algorithm and two new 6-frame algorithms have smaller phase errors caused by phase-shifter miscalibration than any of the common 3-, 4- or 5-frame algorithms. An analysis of the errors resulting from algorithms in both classes is provided by computer simulation and by an investigation of the spectra of sampling functions.

383 citations


Journal ArticleDOI
TL;DR: An extensive study of the pulling parameter space has revealed a time-dependent functionality between the various pulling parameters dominated by a photon-based heating mechanism.
Abstract: Tip diameter and transmission efficiency of a visible-wavelength near-field optic probe determine both the lateral spatial resolution and experimental utility of the near-field scanning optical microscope. The commonly used tip fabrication technique, laser-heated pulling of fused-silica optical fiber followed by aperture formation through aluminization, is a complex process governed by a large number of parameters. An extensive study of the pulling parameter space has revealed a time-dependent functionality between the various pulling parameters dominated by a photon-based heating mechanism. The photon-based heat source results in a temperature and viscosity dependence that is a complex function of time and fiber diameter. Changing the taper of the optical probe can affect transmission efficiency by an order of magnitude or more.

350 citations


Journal ArticleDOI
TL;DR: An empirical equation for the index of refraction of water as a function of temperature, salinity, and wavelength at atmospheric pressure is determined and reproduces the original data to within its experimental errors.
Abstract: We have determined an empirical equation for the index of refraction of water as a function of temperature, salinity, and wavelength at atmospheric pressure. The experimental data selected by Austin and Halikas ["The index of refraction of seawater," SIO Ref. 76-1 (Scripps Institution of Oceanography, La Jolla, Calif., 1976)] were fitted to power series in the variables. A ten-parameter empirical equation that reproduces the original data to within its experimental errors was obtained.

Journal ArticleDOI
TL;DR: This paper presents a method to calculate photon-measurement density functions (PMDF's), which were introduced in Part 1, for near-infrared imaging and spectroscopy in complex and inhomogeneous objects through the use of a finite-element model.
Abstract: This paper presents a method to calculate photon-measurement density functions (PMDF's), which were introduced in Part 1 [Appl. Opt. 34, 7395-7409 (1995), for near-infrared imaging and spectroscopy in complex and inhomogeneous objects through the use of a finite-element model. PMDF's map the sensitivity of a measurement on the surface of an object to the perturbations of the optical parameters within the object. Data are presented for homogeneous and layered circular objects and for a complex two-dimensional model of a head. In particular the influence of the optical parameters on the shape of the PMDF and the distortions caused by boundary layers and complex inhomogeneties are investigated.

Journal ArticleDOI
TL;DR: The Mie-scattering model predicted an increase in scattering with gestational age on the basis of changes in the collagen-fiber diameters, and this increase was proportional to that measured with the integrating-sphere method.
Abstract: Reduced-scattering coefficients of neonatal skin were deduced in the 450-750-nm range from integrating-sphere measurements of the total reflection and total transmission of 22 skin samples. The reduced-scattering coefficients increased linearly at each wavelength with gestational maturity. The distribution of diameters d and concentration ρ(A) of the skin-sample collagen fibers were measured in histological sections of nine neonatal skin samples of varying gestational ages. An algorithm that calculates Mie scattering by cylinders was used to model the scattering by the collagen fibers in the skin. The fraction of the reduced-scattering coefficient µ(s)' that was attributable to Mie scattering by collagen fibers, as deduced from wavelength-dependent analysis, increased with gestational age and approached that found for adult skin. An assignment of 1.017 for n(rel), the refractive index of the collagen fibers relative to that of the surrounding medium, allowed the values for Mie scattering by collagen fibers, as predicted by the model for each of the nine neonatal skin samples to match the values for Mie scattering by collagen fibers as expected from the measurements of µ(s)'. The Mie-scattering model predicted an increase in scattering with gestational age on the basis of changes in the collagen-fiber diameters, and this increase was proportional to that measured with the integrating-sphere method.

Journal ArticleDOI
TL;DR: The question of the sensitivity of different measurement schemes on the boundary of an object to perturbations of the optical parameters within the object are addressed and closed-form solutions are given for a number of these functions in infinite space, half-space, and slab geometries.
Abstract: This paper addresses the problem of tomographic reconstruction of absorption and scattering parameters in the optical region from measurements of transilluminated light. Specifically, the question of the sensitivity of different measurement schemes on the boundary of an object to perturbations of the optical parameters within the object are addressed. The concept of a photon-sampling volume [Appl. Opt. 33, 448 (1994)] and a photon-hitting density [Appl. Opt. 32, 448 (1993)] is extended to a photon-measurement density function (PMDF). The PMDF is derived from the Green's function of the diffusion equation and can be expressed for measurements such as the time-varying intensity, integrated intensity, temporal moments, and phase shift, as well as for both absorption and diffusion perturbations. Closed-form solutions are given for a number of these functions in infinite space, half-space, and slab geometries. Example results are given in terms of three-dimensional images.

Journal ArticleDOI
TL;DR: A novel stereocamera has been developed based on the angular-displacement method, wherein the two camera axes are oriented in a nonorthogonal manner toward the object plane, which significantly reduces the radial distortions that arise when imaging through a thick liquid layer.
Abstract: A novel stereocamera has been developed based on the angular-displacement method, wherein the two camera axes are oriented in a nonorthogonal manner toward the object plane. The stereocamera satisfies the Scheimpflug condition such that the image plane, the object plane, and the lens plane are nominally colinear. A unique feature of the stereocamera is the introduction of a liquid prism between the object plane and the recording lens, which significantly reduces the radial distortions that arise when imaging through a thick liquid layer. The design of the camera and its computer optimization with geometric modeling are described. Results indicate that the use of a liquid prism reduces the amount of radial distortion by an order of magnitude. The results have been shown to agree very well with experiments.

Journal ArticleDOI
TL;DR: The correct calculation of the one-dimensional PSD from discrete surface profile data is given, and problems in using fast Fourier-transform routines that are given in some of the standard reference books are flagged.
Abstract: The power spectral density (PSD), in its two-dimensional form, has been designated as the preferred quantity for specifying surface roughness on a draft international drawing standard for surface texture. The correct calculation of the one-dimensional PSD from discrete surface profile data is given, and problems in using fast Fourier-transform routines that are given in some of the standard reference books are flagged. The method given here contains the correct normalizing factors. Two ways to reduce the variance of the PSD estimate are suggested. Examples are shown of the variance reduction possible in the PSD's.

Journal ArticleDOI
TL;DR: A systematic way to derive efficient, error-compensating algorithms for phase-shifting interferometry by integer approximation of well-known data-sampling windows by observing that many of the common sources of phase-estimation error can be related to the frequency-domain characteristics of the sampling window.
Abstract: I propose a systematic way to derive efficient, error-compensating algorithms for phase-shifting interferometry by integer approximation of well-known data-sampling windows. The theoretical basi of the approach is the observation that many of the common sources of phase-estimation error can be related to the frequency-domain characteristics of the sampling window. Improving these characteristics can therefore improve the overall performance of the algorithm. Analysis of a seven-frame example algorithm demonstrates an exceptionally good resistance to first- and second-order distortions in the phase shift and a much reduced sensitivity to low-frequency mechanical vibration.

Journal ArticleDOI
TL;DR: A full-field, time-resolved interferometric method for the characterization of sparse, polydisperse spray systems is reported, which makes use of the angular intensity oscillations in the wide-angle forward-scatter region.
Abstract: A full-field, time-resolved interferometric method for the characterization of sparse, polydisperse spray systems is reported. The method makes use of the angular intensity oscillations in the wide-angle forward-scatter region. A pulsed laser is used to illuminate a planar sheet through the spray, which is imaged, out of focus, from the 45°direction. The image consists of a set of out-of-focus spots, each of which represents an individual droplet, and superimposed on which is a set of fringes corresponding to the angular intensity oscillations of that droplet. Macrophotographic recording with high-resolution digitization for image analysis provides a full-field capability. The spatial frequency of fringes on each spot in the image plane is dependent on the diameter of the corresponding droplet in the object plane, and a simple geometric analysis is shown to be appropriate for the calculation of the spatial frequency of fringes as a function of droplet size. Images are analyzed automatically by a software suite that uses Gaussian blur, Canny edge detection, and Hough transforms to locate individual droplets in the image field. Fringe spatial frequency is then determined by least-squares fitting to a Chirp function. The method is applicable to droplets with diameters in the range of several millimeters to several hundred millimeters and number densities of up to 10(3) to 10(4). The accuracy of the method for droplet-size determination has been evaluated by measurements of monodisperse aerosols of known droplet size, and measurements of droplet-size distribution in a polydisperse aerosol produced by a gasoline fuel injector are also presented. An extension of the method, using high-speed photography to measure two components of velocity in addition to size and position, is discussed. A two-wavelength approach may also offer the capability to measure the concentration of model fuel additives in droplets, and the results of a feasibility study are described.

Journal ArticleDOI
TL;DR: A temporally and spatially nonscanning imaging spectrometer is described in terms of computedtomography concepts, specifically the central-slice theorem and experimental results indicate that the instrument performs well in the case of broadband and narrow-band emitters.
Abstract: A temporally and spatially nonscanning imaging spectrometer is described in terms of computedtomography concepts, specifically the central-slice theorem. A sequence of three transmission sinusoidalphase gratings rotated in 60° increments achieves dispersion in multiple directions and into multiple orders. The dispersed images of the system's field stop are interpreted as two-dimensional projections of a three-dimensional (x, y, λ) object cube. Because of the size of the finite focal-plane array, this imaging spectrometer is an example of a limited-view-angle tomographic system. The imaging spectrometer's point spread function is measured experimentally as a function of wavelength and position in the field of view. Reconstruction of the object cube is then achieved through the maximum-likelihood, expectation-maximization algorithm under the assumption of a Poisson likelihood law. Experimental results indicate that the instrument performs well in the case of broadband and narrow-band emitters.

Journal ArticleDOI
TL;DR: It is shown that blazing the surface-relief diffractive lens for higher diffraction orders enables the design of achromatic and apochromatic singlets and the wavelength-dependent optical transfer function and the associated Strehl ratio are derived for multiorder diffractive lenses.
Abstract: Diffractive lenses have been traditionally designed with the first diffracted order. The spectral characteristics of diffractive lenses operating in higher diffracted orders differ significantly from the first-order case. Multiorder diffractive lenses offer a new degree of freedom in the design of broadband and multispectral optical systems that include diffractive optical elements. It is shown that blazing the surface-relief diffractive lens for higher diffraction orders enables the design of achromatic and apochromatic singlets. The wavelength-dependent optical transfer function and the associated Strehl ratio are derived for multiorder diffractive lenses. Experiments that illustrate lens performance in two spectral bands are described, and the results show excellent agreement with the theoretical predictions.

Journal ArticleDOI
TL;DR: The properties of guided-mode resonance reflection filters constructed with multiple thin- film layers are addressed and it is found that, for a given high modulation index, the double-layer antireflection thin-film approximation fails, whereas for the same modulation in a triple-layer system it holds firmly.
Abstract: The properties of guided-mode resonance reflection filters constructed with multiple thin-film layers are addressed. Greatly improved filter characteristics are shown to follow by the incorporation of multiple homogeneous layers with the spatially modulated layer. Calculated results for single-layer, double-layer, and triple-layer filter structures are presented. Whereas good filter characteristics are obtainable with single layers that are half-resonance-wavelength thick, there remains a residual reflection in the sidebands unless the cover and the substrate permittivities are equal. With double-layer and triple-layer designs, extensive wavelength ranges with low sideband-reflectance values are shown to be possible without requiring equal cover and substrate permittivities. The antireflection properties of the layer stack can be understood if the modulated layer is modeled as a homogeneous layer characterized by its average relative permittivity. However, as the grating-modulation index increases, this approximation deteriorates. In particular it is found that, for a given high modulation index, the double-layer antireflection thin-film approximation fails, whereas for the same modulation in a triple-layer system it holds firmly. Multilayer designs can thus have significantly large filter passbands, as they may contain heavily modulated resonant gratings without corruption of the ideal filter characteristics.

Journal ArticleDOI
TL;DR: An electrostatically controlled flexible mirror has been fabricated on a silicon chip by means of bulk micromachining and the possibility of electrostatic control of the reflecting surface make the on-chip mirror useful for various electro-optical applications.
Abstract: An electrostatically controlled flexible mirror has been fabricated on a silicon chip by means of bulk micromachining. The mirror has a 10.5 mm × 10.5 mm square aperture and consists of a 0.5-µm-thick tensile-stressed silicon-nitride diaphragm coated with a 0.2-µm-thick reflective aluminum layer. The reflecting surface is initially plane with a mean-square deviation of ~λ/8 for λ = 633 nm. The shape of the reflecting surface is controlled electrostatically by an array of integrated actuators. Good initial optical quality and the possibility of electrostatic control of the reflecting surface make the on-chip mirror useful for various electro-optical applications.

Journal ArticleDOI
TL;DR: The numerical solutions of binary-phase (0, π) gratings for one-dimensional array illuminators up to 32 are presented and some fabrication errors are calculated to show that even-number array illumnators are superior to odd-numberarray illuminator when these fabrication errorsare considered.
Abstract: The numerical solutions of binary-phase (0, π) gratings for one-dimensional array illuminators up to 32 are presented. Some fabrication errors, which are due to position-quantization errors, phase errors, dilation (or erosion) errors, and the side-slope error, are calculated and show that even-number array illuminators are superior to odd-number array illuminators when these fabrication errors are considered. One (0, π) binary-phase, 8 × 16 array illuminator made with the wet-chemical-etching method is given in this paper.

Journal ArticleDOI
TL;DR: The harmonic diffractive lens is a diffractive imaging lens for which the optical path-length transition between adjacent facets is an integer multiple m of the design wavelength λ(o).
Abstract: The harmonic diffractive lens is a diffractive imaging lens for which the optical path-length transition between adjacent facets is an integer multiple m of the design wavelength λ(o). The total lens thickness in air is mλ(o)/(n - 1), which is m times thicker than the so-called modulo 2π diffractive lens. Lenses constructed in this way have hybrid properties of both refractive and diffractive lenses. Such a lens will have a diffraction-limited, common focus for a number of discrete wavelengths across the visible spectrum. A 34.75-diopter, 6-mm-diameter lens is diamond turned in aluminum and replicated in optical materials. The sag of the lens is 23 µm. Modulation transfer function measurements in both monochromatic and white light verify the performance of the lens. The lens approaches the diffraction limit for 10 discrete wavelengths across the visible spectrum.

Journal ArticleDOI
TL;DR: An analytical perturbation analysis is presented for studying the sensitivity of diffusive photon flux to the addition of a small spherical defect object in multiple-scattering media such as human tissues.
Abstract: We present an analytical perturbation analysis for studying the sensitivity of diffusive photon flux to the addition of a small spherical defect object in multiple-scattering media such as human tissues. As a first simple application of our perturbation method, we derive analytically the photon migration path distributions and the shapes of the so-called banana regions in which the photon migration paths are concentrated. We then derive analytically the sensitivity of detected photon flux densities to the inclusion of small spherical defects in the multiple-scattering medium for both single-source and two-source configurations, at both steady-state (dc) and frequency-modulation conditions, and compare the results with Monte Carlo simulations.

Journal ArticleDOI
TL;DR: A modified nearest neighbor approach is found to be the most successful and can reliably unwrap unfiltered speckle-interferometry phase maps with discontinuity source densities of 0.05 sources pixel(-1).
Abstract: An algorithm for unwrapping noisy phase maps has recently been proposed, based on the identification of discontinuity sources that mark the start or end of a 2π phase discontinuity Branch cuts between sources act as barriers to unwrapping, resulting in a unique phase map that is independent of the unwrapping route We investigate four methods for optimizing the placement of the cuts A modified nearest neighbor approach is found to be the most successful and can reliably unwrap unfiltered speckle-interferometry phase maps with discontinuity source densities of 005 sources pixel(-1)

Journal ArticleDOI
TL;DR: A simple and quick approach is used to measure the reduced scattering coefficient (µ(s)') of a semi-infinite turbid medium having a much smaller absorption coefficient than µ(s')'.
Abstract: A simple and quick approach is used to measure the reduced scattering coefficient (μs′) of a semi-infinite turbid medium having a much smaller absorption coefficient than μs′. A laser beam with an oblique angle of incidence to the medium causes the center of the diffuse reflectance that is several transport mean-free paths away from the incident point to shift away from the point of incidence by an amount Δx. This amount is used to compute μs′ by μs′ = sin(αi)/(nΔx), where n is the refractive index of the turbid medium divided by that of the incident medium and αi is the angle of incidence measured from the surface normal. For a turbid medium having an absorption coefficient comparable with μs′, a revision to the above formula is made. This method is tested theoretically by Monte Carlo simulations and experimentally by a video reflectometer.

Journal ArticleDOI
TL;DR: The nonpolar perylene dyes had better performance in partially organic hosts, and the ionic rhodamine and pyrromethene dyes performed best in the inorganic sol-gel glass host.
Abstract: Laser performance is described for Rhodamine 590, Pyrromethene 567, Perylene red, and Perylene orange in inorganic porous sol-gel glass, poly (methyl methacrylate) (PMMA), a composite of porous sol-gel glass with PMMA and organically modified silicate ormosil glass. Lasers were excited with a flash-lamp-pumped dye laser in the long-pulse-length regime (3 μs, 506 nm, 300 mJ) and a second-harmonic Nd:YAG laser in the short-pulse-length regime (6 or 15 ns, 532 nm, 60 mJ). The feasibility of long-pulse-length operation is demonstrated, detailed characteristics of short-pulse operation are described, and laser damage measurements are given. The nonpolar perylene dyes had better performance in partially organic hosts, and the ionic rhodamine and pyrromethene dyes performed best in the inorganic sol-gel glass host.

Journal ArticleDOI
TL;DR: It is shown that although the reflection characteristics can be accurately modeled with the second-order EMT, the phase difference created by form birefringence for TE- and TM-polarized waves requires the use of a more rigorous, RCWA approach.
Abstract: Diffraction characteristics of high-spatial-frequency (HSF) gratings are evaluated for application to polarization-selective computer-generated holograms by the use of two different approaches: second-order effective-medium theory (EMT) and rigorous coupled-wave analysis (RCWA). The reflectivities and the phase differences for TE- and TM-polarized waves are investigated in terms of various input parameters, and results obtained with second-order EMT and RCWA are compared. It is shown that although the reflection characteristics can be accurately modeled with the second-order EMT, the phase difference created by form birefringence for TE- and TM-polarized waves requires the use of a more rigorous, RCWA approach. The design of HSF gratings in terms of their form birefringence and reflectivity properties is discussed in conjunction with polarization-selective computer-generated holograms. A specific design optimization example furnishes a grating profile that provides a trade-off between the largest form birefringence and the lowest reflectivities.

Journal ArticleDOI
TL;DR: The novel powder-intube method, or a single-draw rod-in-tube method, was used to make silica-clad optical fibers with a high terbium oxide content aluminosilicate core, which could lead to all-fiber isolators of dramatically lower cost and ease of fabrication compared with their crystalline competitors.
Abstract: The Faraday effect provides a mechanism for achieving unidirectional light propagation in optical isolators; however, miniaturization requires large Verdet constants. High rare-earth content glasses produce suitably large Verdet values, but intrinsic fabrication problems remain. The novel powder-intube method, or a single-draw rod-in-tube method, obviates these difficulties. The powder-in-tube method was used to make silica-clad optical fibers with a high terbium oxide content aluminosilicate core. Core diameters of 2.4 µm were achieved in 125-µm-diameter fibers, with a numerical aperture of 0.35 and a Verdet constant of -20.0 rad/(T m) at 1.06 µm. This value is greater than 50% for crystals found in current isolator systems. This development could lead to all-fiber isolators of dramatically lower cost and ease of fabrication compared with their crystalline competitors.