Marginal Ray Research Articles

Fabrication and Characterization of Sub-100 µm Diameter Gallium Phosphide Solid Immersion Lens Arrays

Fabrication and testing of a sub-100 µm gallium phosphide solid immersion lens is described with suitable sphericity (<160 nm deviation) to a marginal ray angle of 42° for NA up to 2.2 inside the material.

Occurrence of radial sieve elements in the secondary phloem rays of some tropical species

Solitary or groups of two to three sieve elements were found in the rays of the secondary phloem of Tamarindus indica L., Melia azedarach L., Gmelina arborea Roxb., Bombax ceiba L., Pongamia pinnata (L.) Pierre, Sterculia urens Roxb., and Thespesia populnea (L.) Correa trees. These elements were similar in length while slightly larger in diameter than ray parenchyma cells, and possessed a simple plate on their transverse to slightly oblique end walls. Like axial sieve elements, the ray sieve elements were associated with single companion cells at their corners. When functional, they also exhibited slime plugs and cytoplasmic strands, like axial sieve elements. Non-functional ray sieve elements exhibited massive accumulation of callose on sieve plates, followed by collapse and obliteration. The distribution pattern of the elements differed among the species studied. Usually they developed from the marginal ray parenchyma cells, but they were also found in the central part of the rays. Structural details and their possible significance are discussed.

Effect of Pectoral Fin Ray Removal on Station‐Holding Ability of Shovelnose Sturgeon

The effect of fin ray removal on swimming performance was evaluated for shovelnose sturgeon Scaphirhynchus platorynchus from the lower Mississippi River. Immediately upon collection, the marginal pectoral fin ray was removed from some fish, and others were left unclipped as a control group. Fish were promptly returned to the laboratory and held in 1,300-L recirculating tanks at 21-26°C. After a minimum recovery time of 48 h, individual fish were placed in a 1,000-L, Brett-type swim tunnel, and their ability to maintain station in flowing water by swimming, skimming, or substrate appression was tested by subjecting fish to increasing speeds beginning at 10 cm/s. After a 60-min swimming bout, speed was increased by 10 cm/s. This was repeated until the fish could no longer maintain station. Fin ray removal had no significant effect on critical station-holding speed (CSHS). The CSHS (mean ± SE) of fin-ray clipped fish was 60.1 ± 4.2 cm/s, and that of unclipped fish was 59.2 ± 3.0 cm/s. Correlation analysis and analysis of variance indicated that collection method, water temperature, size of fish, and time spent in the laboratory had no significant effects on CSHS. Tail beat frequency increased with water velocity, but clipped and unclipped fish were not significantly different. Results indicate that removal of the pectoral fin ray has little or no effect on station-holding ability in shovelnose sturgeon.

Raman spectroscopy for a micrometric and tensorial analysis of stress in silicon

This letter presents a method to measure stress by a Raman spectroscopic technique that combines high spatial resolution with tensorial analysis. The experiment is based on separating the contributions to the Raman spectrum from the marginal and paraxial rays of the collection cone of the objective. The stress tensor was measured over a 20 μm line scan with a resolution of 1 μm on a highly strained (001) silicon surface in proximity to a micrometric scratch by observing the different frequency shifts of three orthogonal crystal vibrations.

Phase and amplitude apodization induced by focusing through an evanescent gap in a solid immersion lens microscope

We characterize phase and amplitude apodization induced when a converging beam passes through an evanescent gap. The apodization is caused by vector transmission and reflection properties. General characteristics are described for solid immersion lens indices from nSIL51.5 to 3.1, gap heights from h50 to 300 nm, and marginal ray angles a m50.7 or 0.84, where a m is the direction cosine of the marginal ray angle inside the solid immersion lens. A small amount of defocus is found to be a good compensator of the phase apodization for low nSIL and h. After proper defocus is applied, asymmetry of focus in the spot may remain, primarily due to the uncompensated amplitude apodization. Simplification of the phase and amplitude characteristics is accom- plished by applying a Jones-matrix expansion to the transmission coef- ficient through the gap. Simulation and experiment quantify the effect with a simple solid immersion lens geometry. © 2002 Society of Photo-Optical

Marginal rays in tapered gradient-index lenses

Marginal rays are used to study the limitations of the spatial and angular extents of light beams by stops and apertures in tapered gradient-index lenses. The results are applied to two kinds of taper functions and compared to selfoc lenses.

Self-focusing and frequency broadening of an intense short-pulse laser in plasmas.

An intense ultrafast laser pulse propagating through a plasma undergoes self-focusing and self-phase-modulation as a result of relativistic mass nonlinearity. The inclusion of a quartic (r4) term in the expansion of the eikonal in the radial coordinate r allows the modification of the shape of the radial intensity profile. The front of the pulse, under the combined effects of time-dependent self-focusing and frequency downshifting, acquires a severely distorted temporal shape. The radial profile for I(lambda)2(mu) < 2.8 x 1018 W/cm2, where I is the axial laser intensity and lambda(mu), is the laser wavelength in micrometers, is transformed from a Gaussian to a super-Gaussian because of the faster convergence of the marginal rays than the paraxial rays. In the opposite case of I(lambda)(2)(mu) > 2.8 x 10(18) W/cm2 when nonlinear plasma permittivity approaches saturation, the radial profile in the axial region becomes broader than the Gaussian.

Confocal Raman Microspectroscopy through a Planar Interface

We have developed a model to describe the effect of refraction through a planar interface on the collection efficiency and depth of focus when performing confocal Raman microspectroscopy. The planar interface introduces spherical aberration, which can substantially degrade the performance of the microscope, especially for large-numerical-aperture microscope objectives. This spherical aberration will increase the range of focal depths spanned by the paraxial and marginal rays of the illuminating laser beam within the sample. In the collection path, it will also distort the scattering volume defined by the confocal aperture; this results in a dramatic fall in the collected light intensity with increasing depth. We demonstrate that there is an optimum numerical aperture for collected light intensity at a given depth. The prediction of this theoretical model is compared to empirical results obtained by mapping the stress distribution within the diamond anvil of a high-pressure cell. Both the collected Raman intensity and the effective depth of focus are compared to the predictions from the theory.

Corneal wave aberration from videokeratography: accuracy and limitations of the procedure.

A procedure to calculate the wave aberration of the human cornea from its surface shape measured by videokeratography is presented. The wave aberration was calculated as the difference in optical path between the marginal rays and the chief ray refracted at the surface, for both on- and off-axis objects. The corneal shape elevation map was obtained from videokeratography and fitted to a Zernike polynomial expansion through a Gram-Schmidt orthogonalization. The wave aberration was obtained also as a Zernike polynomial representation. The accuracy of the procedure was analyzed. For calibrated reference surface elevations, a root-mean-square error (RMSE) of 1 to 2 microm for an aperture 4-6 mm in diameter was obtained, and the RMSE associated with the experimental errors and with the fitting method was 0.2 microm. The procedure permits estimation of the corneal wave aberration from videokeratoscopic data with an accuracy of 0.05-0.2 microm for a pupil 4-6 mm in diameter, rendering the method adequate for many applications.

Longitudinal spherical aberration and mass of bi-aspheric aphakic rigid contact lenses

The purpose of this study is to calculate the longitudinal spherical aberration and thickness, and consequently the mass of aphakic corneal contact lenses in air to determine optimum lens designs. The longitudinal spherical aberration has been calculated by the ray tracing method through the aspheric surfaces. The volume of the lens was computed by solving integrations of rotationally symmetric bodies. The results show that longitudinal spherical aberration can be made zero in ellipsoid–ellipsoid designs for back vertex powers ranging from +8 to +20 dioptres (for a 4mm marginal axial ray height). A reduction in mass of about 23% was obtained when the anterior surface became ellipsoid and posterior surface spherical for back vertex power +20 dioptres.

Lake Sturgeon Abundance and Harvest in Black Lake, Michigan, 1975–1999

Abstract The population of lake sturgeon Acipenser fulvescens in Black Lake, Michigan, has supported a popular winter spear fishery since 1948, but status of the population had not been assessed since the mid-1970s. We sampled the population during May–Jul 1997 with 20.3- and 25.4-cm-stretch-measure gill nets with the objective of estimating population size using the Schnabel method. We also examined harvest data from voluntary registration of speared fish spanning the years 1975–1999 to evaluate the impact that harvest may have had on the population. During 24 sample periods, we tagged and measured 192 lake sturgeon between 75 and 193 cm total length and removed the marginal pectoral fin ray from a subsample of those fish to estimate age. We also recaptured 14 lake sturgeon during the 24 sample periods. Captured fish ranged in age from 9 to 64 years. The estimated size of the 90 cm and larger lake sturgeon population was 1,241 fish. Based on the length frequency of the catch, there were 549 harvestable-s...

Longitudinal spherical aberration and mass of bi-aspheric aphakic rigid contact lenses.

The purpose of this study is to calculate the longitudinal spherical aberration and thickness, and consequently the mass of aphakic corneal contact lenses in air to determine optimum lens designs. The longitudinal spherical aberration has been calculated by the ray tracing method through the aspheric surfaces. The volume of the lens was computed by solving integrations of rotationally symmetric bodies. The results show that longitudinal spherical aberration can be made zero in ellipsoid-ellipsoid designs for back vertex powers ranging from +8 to +20 dioptres (for a 4 mm marginal axial ray height). A reduction in mass of about 23% was obtained when the anterior surface became ellipsoid and posterior surface spherical for back vertex power +20 dioptres.

Exact calculation of the circle of least confusion of a rotationally symmetric mirror

The position and dimensions of the circle of least confusion (CLC) on axis for a lensless Schmidt camera telescope operating at F(0.82) are calculated. The camera is to be used in the fluorescence detector of the Pierre Auger Observatory. Our analysis was developed for an aspherical mirror for any on-axis position of the point light source. Our technique uses the intersection of the marginal ray from one side of the aperture with the caustic produced by the intermediate rays from the opposite side of the aperture to locate the CLC.

Simultaneous measurement of thicknesses and refractive indices of multiple layers by a low-coherence confocal interference microscope

We propose a novel technique for simultaneous measurement of layer thicknesses and refractive indices of multiple layers. It is based on a combination of a confocal microscope and low-coherence interferometry. We derived an expression for the geometrical thickness and the refractive index of each layer from both tracing of a marginal ray accepted by a microscope objective and optical path matching conditions. Experimental verification of this method is illustrated by several samples that have a maximum of 13 layers. The geometrical thicknesses and refractive indices thus derived agreed well with those measured by a micrometer or cited from the literature.

Sturgeon Fin Ray Removal is Nondeleterious

Abstract Marginal pectoral fin rays were removed from cultured shortnose sturgeon Acipenser brevirostrum and wild Atlantic sturgeon A. oxyrinchus oxyrinchus to evaluate the impact on growth and survival. Shortnose sturgeon were examined after 98 d and Atlantic sturgeon were examined after 183 d. There were no significant differences between control (no fin ray removed) and treatment fish in growth (weight or length) or survival of either species, and all wounds had healed. Removal of pectoral fin rays for age analyses had no apparent deleterious effects on these sturgeon species.

Examination of the effect of the fibrous structure of a lens on the optical characteristics of the human eye: a computer-simulated model

We introduce a model of the human eye for which we take into consideration the laminated nature of lens fibers. The thickness of each lamina is 5.6 µm; thus the lens comprises 300 eccentric lenses of minute dimensions. The index gradient of the lens is such that the index of refraction increases exponentially from the lens core to its peripheral zone. A vector ray-tracing technique is employed to study the optical haracteristics of the system. Both paraxial and marginal rays are simulated, and the angles of incidence vary from 0° to ±20°. Special attention is given to the meridional caustic surfaces as well as the wave-front distortion of the refracted rays. A quasi-Newton optimization technique is employed to obtain the best parameters for the system. A computer modeling program, written in FORTRAN 77, is used to simulate a ray's refraction through the multisurfaces of the eye. The results show full agreement with previous data and that the cornea is responsible for eliminating possible spherical aberration of the system.

Polarization aberrations 1 Rotationally symmetric optical systems

The polarization in isotropic radially symmetric lens and mirror systems in the paraxial approximation is examined. Polarized aberrations are variations in the phase, amplitude, and polarization state of the electromagnetic field across the exit pupil. Some are dependent on the incident polarization state and some are not. Expressions through fourth order for phase, amplitude, linear diattenuation, and linear retardance aberrations are derived in terms of the chief and marginal ray angles of incidence and the Taylor series expansion coefficients of the Fresnel equations for reflection and transmission at uncoated and thin-film-coated interfaces. Applications to polarization ray tracing are discussed.

Spectral shift due to source correlation for paraxial rays

A study of the spectral shift due to source correlation is carried out when a different area of the lens, used to produce a secondary source, is exposed to light. It is observed that with the experimental set up used no spectral shift is produced for marginal rays but for paraxial rays spectral shift is inevitable.

Relationship between toughness, cell wall deformations and density in Eucalyptus pilularis

Wood toughness, the abundance of cell wall deformations in fibre cell walls adjacent to the marginal ray cell and wood density have been found to be interrelated in Eucalyptus pilularis. The relationships were closer in individual trees rather than when data for all trees studied were combined. Cell wall deformations were found to be more abundant in the fibre wall adjacent to the marginal ray cell.

The distribution of cell wall deformations in fibres adjacent to rays in Eucalyptus pilularis

The distribution of cell wall deformations in the fibre walls adjacent to rays has been examined in five 40 year old Eucalyptus pilularis trees. This distribution was found to be related to both height and distance from the pith within these trees. Growth stresses are thought to influence the formation of fibre cell wall deformations at the ray-fibre contact area except at the marginal ray cell. Deformations in the fibre cell wall, which were at a maximum frequency at the marginal ray cell ray-fibre contact area, are considered to be due to the inflection of the fibre wall around the ray cell.