Off-axis Point Source Research Articles

Neutron penetration in labyrinths under different beam losses

Multiple analytical methods and Monte Carlo simulations were performed to evaluate neutron penetration in straight and curved labyrinths. Factors studied included variations in beam losses of off-axis point source, on-axis point source, and line source. For the straight labyrinth, it was found that the analytical expressions neglect the dose rate platform appearing at the bend of the labyrinth, and the agreement between analytical methods and Monte Carlo estimation was related to the type of neutron source term. For the curved labyrinth, the neutron attenuation length obtained under different conditions was nearly identical and appeared to be in quite good accord with the empirical formula calculation. Moreover, the neutron energy spectra along the centerline distance of the labyrinth were also analyzed. In the first leg, differences in beam loss led to variance in the distribution of spectra, while in the second and subsequent legs, the spectra were similar, where the main contributors were thermal neutrons. This work is valuable for practical design of the labyrinths in the accelerator facilities.

Ring-shaped dysphotopsia associated with posterior chamber phakic implantable collamer lenses with a central hole.

To evaluate the incidence of central hole-induced ring-shaped dysphotopsia after posterior chamber phakic implantable collamer lens (ICL) with central hole (hole ICL) implantation and to investigate the causes of central hole-induced dysphotopsia. The clinical study enrolled 29 eyes of 15 consecutive myopic patients implanted with hole ICL. The incidence of ring-shaped dysphotopsia after hole ICL implantation was evaluated. In the experimental simulation study, non-sequential ray tracing was used to construct myopic human eye models with hole ICL and ICL without a central hole (conventional ICL). Simulated retinal images measured in log-scale irradiance were compared between the two ICLs for an extended Lambertian light-emitting disc object 20cm in diameter placed 2m from the corneal vertex. To investigate the causes of hole-induced dysphotopsia, a series of retinal images were simulated using point sources at infinity with well-defined field angles (0 to -20°) and multiple ICL models. Of 29 eyes, 15 experienced ring-shaped dysphotopsia after hole ICL implantation. The simulation study using an extended Lambertian source showed that hole ICL-evoked ring-shaped dysphotopsia was formed at a retinal field angle of ±40°. Component-level analysis using a well-defined off-axis point source from infinity revealed that ring-shaped dysphotopsia was generated by stray light refraction from the inner wall of the hole and the posterior ICL surface. Hole ICL-evoked ring-shaped dysphotopsia was related to light refraction at the central hole structure. Surgeons are advised to explain to patients the possibility of ring-shaped dysphotopsia after hole ICL implantation.

Optical systems with circular apertures protected by plane-parallel entrance windows in wide-angle radiation fields

Optical systems protected by plane-parallel entrance windows from external environmental conditions were studied to determine the radiant fluxes passing through their circular apertures from wide-angle on-axis and off-axis point sources. The study was performed for the case when the windows, the internal environments, and the external environments of these optical systems were considered as three different homogeneous isotropic and attenuating media. All considerations were made for ideal plane-parallel windows illuminated by an arbitrary radiation field applying the multiple-reflection theory. As a result of this study a multi-domain integral equation method based on a mathematical formula expressed by a series of multiple-reflected fluxes of radiation within the plane-parallel window was proposed. The applicability of the method was tested using computer simulations for an isotropic point source and a small area Lambertian source represented by a point-source model. The computed results were validated by the optical software for layout and optimization program from Lambda Research Corporation (USA). The selected results were illustrated graphically and analyzed. The numerical simulations have shown high accuracy and efficiency in the calculations for arbitrary emitting point sources. The potential applications of the presented method include optical sensing and metrology of noncollimated radiation from the various on-axis and off-axis point sources.

Radiant fluxes from on- and off-axis point sources irradiating a circular disc through two different homogeneous isotropic media

The multidomain integral equation method is used to calculate fluxes of radiation from various on- and off-axis point sources passing through two different homogeneous isotropic media and striking a surface of a circular disc perpendicular to the optical axes of these sources. This method is dedicated to radiation passing through attenuating or nonattenuating media with a Fresnel interface and is applicable for arbitrary radiation patterns of point sources. The paper presents, firstly, the generalized multidomain integral equation method, expressed by double iterated integrals, for calculating radiant fluxes from arbitrary emitting point sources. This generalized method is simplified then to the form of multidomain single integral equation method applicable for rotationally symmetrical radiation patterns with optical axes perpendicular to the disc. Next, the simplified method is used for computer simulation of radiant fluxes incident on the disc from small Lambertian and Gaussian sources represented by point source models. All numerical results obtained from this simulation have shown high accuracy and efficiency of the presented method. Selected results are illustrated graphically and validated by Optical Software for Layout and Optimization (OSLO) from Lambda Research Corporation. Potential applications of the presented method include optical sensing and metrology, optical coupling, immersion microscopes, light-extraction problems and creative lighting design.

Effects of capillary reflection in the performance of the collimator of the Large Area Detector on board LOFT

The Large Observatory For X-ray Timing (LOFT) is one of the candidate missions selected by the European Space Agency for an initial assessment phase in the Cosmic Vision programme. It is proposed for the M3 launch slot and has broad scientific goals related to fast timing of astrophysical X-ray sources. LOFT will carry the Large Area Detector (LAD), as one of the two core science instruments, necessary to achieve the challenging objectives of the project. LAD is a collimated detector working in the energy range 2-50 keV with an effective area of approximately 10 m^2 at 8 keV. The instrument comprises an array of modules located on deployable panels. Lead-glass microchannel plate (MCP) collimators are located in front of the large-area Silicon Drift Detectors (SDD) to reduce the background contamination from off-axis resolved point sources and from the diffuse X-ray background. The inner walls of the microchannel plate pores reflect grazing incidence X-ray photons with a probability that depends on energy. In this paper, we present a study performed with an ad-hoc simulator of the effects of this capillary reflectivity on the overall instrument performance. The reflectivity is derived from a limited set of laboratory measurements, used to constrain the model. The measurements were taken using a prototype collimator whose thickness is similar to that adopted in the current baseline design proposed for the LAD. We find that the experimentally measured level of reflectivity of the pore inner walls enhances the off-axis transmission at low energies, producing an almost flat-top response. The resulting background increase due to the diffuse cosmic X-ray emission and sources within the field of view does not degrade the instrument sensitivity.

Radiant fluxes from various off-axis point sources incident on a circular disk

A general multidomain integral formula is presented for calculating fluxes of radiation striking a circular disk from various off-axis point source types embedded in an attenuating or nonattenuating medium. This formula is expressed by double line integrals of radiant intensity and sine functions with respect to the polar and horizontal angles determining the angular distribution of the emitted radiation. The formula reduces to single line integral expressions when radiation does not depend on the horizontal angle and is directly applicable for calculating fluxes of revolutional symmetry around the optical axis of the source perpendicular to the disk. The applicability of this reduced formula is tested by computing radiant fluxes from Lambertian and Gaussian point sources using a simple numerical procedure for single integrals. The computed data are illustrated graphically, tabulated, and validated using OSLO. Finally, the accuracy, similarity, and applicability of the results provided by the integral formula and the OSLO program are analyzed. Numerical results have shown the effectiveness of the presented formulas for calculating radiant fluxes from various on- and off-axis point sources passing through a nonattenuating or attenuating homogeneous isotropic media and incident on a circular disk perpendicular to optical axes of these sources. Practical applications of these formulas include optical sensing and metrology, optical coupling, fiber optic for biomedical measurements, and creative lighting design.

Turbid Scene Enhancement Using Multi-Directional Illumination Fusion

Ambient light is strongly attenuated in turbid media. Moreover, natural light is often more highly attenuated in some spectral bands, relative to others. Hence, imaging in turbid media often relies heavily on artificial sources for illumination. Scenes irradiated by an off-axis single point source have enhanced local object shadow edges, which may increase object visibility. However, the images may suffer from severe nonuniformity, regions of low signal (being distant from the source), and regions of strong backscatter. On the other hand, simultaneously illuminating the scene from multiple directions increases the backscatter and fills-in shadows, both of which degrade local contrast. Some previous methods tackle backscatter by scanning the scene, either temporally or spatially, requiring a large number of frames. We suggest using a few frames, in each of which wide field scene irradiance originates from a different direction. This way, shadow contrast can be maintained and backscatter can be minimized in each frame, while the sequence at large has a wider, more spatially uniform illumination. The frames are then fused by post processing to a single, clearer image. We demonstrate significant visibility enhancement underwater using as little as two frames.

Three-dimensional locating of paraxial point source with axicon

This Letter presents a theoretical and experimental study of an axicon illuminated by an off-axis paraxial point source. The Fresnel diffraction integral is applied to show that a paraxial point source produces a Bessel beam. A simple analytical relationship is demonstrated between the location of the point source and the spatial frequency and the center of the resulting Bessel beam in the image plane of a camera. Finally, experimental verification is given by translating a point source of light along the optical axis of an axicon and comparing the resulting predicted and recorded beam intensity profiles. The resulting images are then analyzed to predict the location of the point source with excellent accuracy.

Quantitative measurement of large-aperture aspheric surfaces by off-axis Ronchi test

An off-axis Ronchi test based on the phase-shifting technique is presented to measure the aspheric mirror quantitatively. In this paper, slopes of deviations from the mirror's ideal aspheric shape are derived when an off-axis point source is used. By integrating these slopes, the deviations of the shape are obtained and then the tested shape can be reconstructed. Compared with the coaxial Ronchi test, the measurement error caused by combination fringes can be avoided, and this system is more flexible. In the experiment, a marked point is used to guide the phase unwrapping procedure, which improves the accuracy of extracting corresponding phase points. In addition, the method has strong anti-noise ability. The validity of the method has been verified by both computer simulations and a preliminary experiment.

ARC: an Achromatic Rotation-shearing Coronagraph

Context. Because of the larger size of future telescopes, the star leakage effect due to the finite diameter of the stars will become a major problem for coronagraphs with very small inner working angles (IWA). Aims. To reduce this star leakage, we propose a new instrumental concept, the Achromatic Rotation-shearing Coronagraph (ARC), that provides a variable IWA that is easily tunable to ensure the observation of Solar-like systems with an extremely large telescope. Methods. The ARC belongs to the nuller class of coronagraphs. It takes advantage of the achromatic dark output of a Mach-Zehnder interferometer (MZI). Field rotators set in the arms of the MZI rotate the π-phase shifted images of the MZI by an angle ψ. An on-axis point source (the star) is nulled as twin-images of an off-axis point source (the planet) are formed. For ψ = π, the ARC is equivalent to the achromatic interfero-coronagraph. For small ψ, the twin images of the off-axis source are formed close to each another, and eventually nulled if too close. In this way, the ARC can get rid of star leakage while optimizing the transmission of the planet. We describe the compensation of polarization effects induced by field rotators. An application to diluted apertures is shortly presented. Results. We perform the mathematical analysis of the technique using Cartesian and polar coordinates, and assuming that the system is optically perfect. Analytic expressions are given for the leakage in both the focal and aperture planes. Simplified expressions for the contrast and signal-to-noise ratio (SNR) in the focal plane are given for a circular aperture, explicitly showing that the level of star leakage decreases as sin 2 (ψ/2), while the SNR increases as the inverse of sin(ψ/2). Conclusions. The ARC is appropriate for the detection of exoplanets and is not intended to provide images of the environment of stars.

A fast, primary-interaction Monte Carlo methodology for determination of total efficiency of cylindrical scintillation gamma-ray detectors

A primary-interaction based Monte Carlo algorithm has been developed for determination of the total efficiency of cylindrical scintillation g-ray detectors. This methodology has been implemented in a Matlab based computer program BPIMC. For point isotropic sources at axial locations with respect to the detector axis, excellent agreement has been found between the predictions of the BPIMC code with the corresponding results obtained by using hybrid Monte Carlo as well as by experimental measurements over a wide range of g-ray energy values. For off-axis located point sources, the comparison of the BPIMC predictions with the corresponding results obtained by direct calculations as well as by conventional Monte Carlo schemes shows good agreement validating the proposed algorithm. Using the BPIMC program, the energy dependent detector efficiency has been found to approach an asymptotic profile by increasing either thickness or diameter of scintillator while keeping the other fixed. The variation of energy dependent total efficiency of a 3'x3' NaI(Tl) scintillator with axial distance has been studied using the BPIMC code. About two orders of magnitude change in detector efficiency has been observed for zero to 50 cm variation in the axial distance. For small values of axial separation, a similar large variation has also been observed in total efficiency for 137Cs as well as for 60Co sources by increasing the axial-offset from zero to 50 cm.

First Images of R Aquarii and Its Asymmetric H2O Shell

We report imaging observations of the symbiotic long-period Mira variable R Aquarii (R Aqr) at near-infrared and radio wavelengths. The near-infrared observations were made with the IOTA imaging interferometer in three narrowband filters centered at 1.51, 1.64, and 1.78 μm, which sample mainly water, continuum, and water features, respectively. Our near-infrared fringe visibility and closure phase data are analyzed using three models. (1) A uniform disk model with wavelength-dependent sizes fails to fit the visibility data, and is inconsistent with the closure phase data. (2) A three-component model, consisting of a Mira star, water shell, and an off-axis point source, provide a good fit to all data. (3) A model generated by a constrained image reconstruction analysis provides more insight, suggesting that the water shell is highly nonuniform, i.e., clumpy. The VLBA observations of SiO masers in the outer molecular envelope show evidence of turbulence, with jetlike features containing velocity gradients.

Optical radiation flux illuminating a circular disk from an off-axis point source through two different homogeneous refractive media

A general formula is derived for calculating the optical radiation flux that illuminates a circular disk from an off-axis point source if the disk and the source are embedded in two different homogeneous media and if the media form a refractive planar interface parallel to the disk. This formula is represented by a set of four different expressions, each valid for a different range of distances determining the position between the source and the disk symmetry axis. These expressions are given as double-definite integrals with the boundary conditions described by some transcendental equations. All expressions represent functions depending on the disk radius, on the distances between the refractive plane from the disk and from the source, on the distance between the source and the disk symmetry axis, on the refractive indices and on the absorption coefficients of both media embedding the source and the disk. In many practical situations the formula simplifies to a set of five single integrals that can be easily calculated numerically. For illustrative purposes some examples of the formula used for calculating optical radiative fluxes are presented and illustrated graphically.

Optical radiation flux illuminating a circular disk from an off-axis point source separated by a homogeneous plane-parallel plate.

In a number of techniques that measure weak fluxes of optical radiation, it is frequently necessary to keep a detector in a medium different from that of the radiating source by separating it from the source with a planar transparent window. However, sources such as systems of light-emitting diodes, large-fiber illuminators, and microscopic living objects that emit biological luminescence may sometimes be regarded as multiple-point sources. To estimate the fluxes of optical radiation illuminating a surface from a nonuniformly distributed multiple-point source, a method for calculating fluxes from a single off-axis point source is needed. A formula is derived to estimate a flux of temporally incoherent optical radiation incident on a circular disk from a single off-axis point source separated by a plane-parallel plate (PPP). This formula is expressed by a series of single integrals of some superposed elementary functions. These functions depend on the variables that characterize the point-source-plane-parallel-plate-circular-disk geometry and on the optical properties of the media that separate the source from the PPP and the PPP from the disk. The solution was obtained for isotropic media. For illustrative purposes some examples of the use of the formula are presented. The selected results are illustrated by three-dimensional surface plots and compared with the values of the fluxes calculated for radiation incident on the disk from a point source not separated by a PPP.

Iron K line profiles driven by non-axisymmetric illumination

Previous calculations of Fe K-alpha line profiles are based on axisymmetric emissivity laws. In this paper, we show line profiles driven by non-axial symmetric illumination which results from an off-axis X-ray point source. We find that source location and motion have significant effects on the red wing and blue horn of the line profiles. The disk region under the source will receive more flux, which is the most important factor to affect the line profiles. We suggest that at least part of the variation in Fe K-alpha line profiles is caused by the motion of X-ray sources. Future observations of Fe K-alpha line profiles will provide more information about the distribution and motion of the X-ray sources around black holes, and hence the underlying physics.

Collimation and focusing properties of a planar waveguide with hyperbolic secant refractive index profile: light deflector and collimator design

Light transmission through an inhomogeneous waveguide whose refractive index profile can be represented by one-dimensional hyperbolic secant function is analysed from a geometrical optics point of view. Focusing and collimation conditions are obtained and the design of a light deflector is proposed. The possibility of obtaining almost perfect collimation for an off-axis point source by polishing the exit face of the waveguide is considered.

Analytical Illuminance Calculation in a Multi-interface Optical System

An analytical expression for the illuminance over a receiver surface and an equation for the caustic surface are derived for rays which have passed through a multi-interface optical system. The results are expressed in terms of the intrinsic geometry of the deflector surface, that is, the Gaussian, mean, and normal curvatures, and the derivative of the incident ray vector over the deflector surface. The original source may be a plane wave, a point source, or an extended source. As a numerical example of this technique, the caustic surface and the line-spread function on different image planes are plotted for an off-axis point source of light whose rays are refracted by a thick double convex lens.

Boundary-diffraction Waves Due to a General Point Source and Their Applications to Aperture Systems

The diffraction field of a circular aperture with an off-axis point source is given by an infinite series of Bessel functions of integral orders and of the first kind. Because each function has a coefficient whose magnitude decreases with increase of the order of the function, the infinite series converges rapidly. The solution is used to study the properties of an ellipsoidal aperture system with an off-axis point source. From the results thus obtained, it is asserted that, with an input wave which is divided into circular zones having appropriate phase differences, the system may give a high irradiance at its principal focus.