Off-axis Source Research Articles

Imaging performance of mirror pairs for grazing-incidence applications: a comparison

The eight distinct reflection configurations for pairs of toroidal mirrors are investigated by numerically calculating their aberration patterns for on- and off-axis source points. The best performance is obtained for a Z-shaped configuration where the two mirrors deflect in opposite directions across a common interior sagittal and tangential focus. Imaging properties can be improved significantly in some cases by replacing the toroidal elements with their elliptical or parabolic equivalents. The best overall performance is obtained with parabolic mirrors in a U-shaped configuration.

Noise characteristics of heated high velocity rectangular jets

A comprehensive experimental investigation of the noise emission from a rectangular jet has been carried out. In order to provide information pertinent to the operating conditions of jet engines, this study was conducted with a wide range of jet velocities and temperatures. A substantial effort has been made to present the information in this paper in such a fashion as to delineate the effects of turbulent mixing and acoustic shielding. To aid in this process, a round jet with an equal area nozzle was also tested over the same ranges of velocity and temperature. As a result of this study, it is concluded that an observed reduction in overall acoustic power of the rectangular jet, when compared to a round jet, is mainly the result of the shielding effects of the mean velocity and temperature fields rather than due to any turbulent mixing phenomenon. Acoustic shielding predictions were found to be qualitatively valid in the vicinity of the peak intensity but were inadequate at shallow angles to the jet axis. In order for shielding theory to properly predict the noise of non-circular jets, at shallow angles, it appears that it will be necessary to include the effects of jet spreading and subsequent degeneration to a circular jet as well as the effects of off-axis source locations.

Asymmetrical sound channel axis propagation

An acoustic experiment was conducted utilizing the asymmetrical sound channel axis propagation paths of the Mediterranean within the Algero-Provencal Basin. Acoustic transmission loss in 94-Hz bands from 94 to 2250 Hz was obtained as a function of range using shipboard deployed explosive caps, half and one pound charges, and a fixed receiver in the channel. The experimental results are compared with the output of an acoustic model at 94 and 562 Hz. A measure of the attenuation coefficients is obtained over the frequency range which is independent of the acoustic model and is in agreement with data from other investigators. This axis data was transformed to develop the acoustic field for the case of off-axis source locations by a procedure devised to decrement the signal intensity as a function of arrival time. Estimates of the arrival time are based upon an inverse sound speed gradient representation of the medium. The resulting range-depth contours for 281 Hz are compared with outputs from NRL acoustic model TRIMAIN.[Work supported by NAVSEA, Code 06H1.]

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.

Efficiency of a stepped reflector when fed from an off-axis source

A correlation technique has been used to find the efficiency of a stepped reflector, given the focal-region field and the aperture field of the feed. The scanning properties of the antenna predicted by this theory agree well with existing experimental data.

Image Formation of a Reflecting Cone for an Off-Axis Source*

For a point source placed in front of a reflecting cone, expressions have been found for the shape of the virtual image and for the amplitude of the real-image field. Both the virtual and the real images have the same axis of symmetry, which passes through the vertex of the cone and lies in the plane containing the point source and the cone axis. The angle between the axis of symmetry and the axis of the cone is equal in magnitude but opposite in sign to the angle between the latter and the line joining the point source and the cone vertex. The projection of the virtual image onto a plane perpendicular to the axis of symmetry is an ellipse. Both the real and virtual images have two planes of symmetry that are the planes containing, respectively, the major and minor axes of the virtual image. The irradiance distribution along the axis of symmetry in the real-image field varies as the square of a Bessel function of zero order and of the first kind. The analytical expression found for the real-image field gives the expected behavior of the field when the cone becomes a plane. It also obeys the energy-conservation law.

A power-series buildup factor formulation. Application to rectangular and off-axis disk source problems

A power-series buildup factor formulation. Application to rectangular and off-axis disk source problems

Distribution of neutrons in media with a cylindrical interface boundary and off-axis source distribution

Distribution of neutrons in media with a cylindrical interface boundary and off-axis source distribution

Ring focus in a thin magnetic-lens beta-ray spectrometer.

The paths of electrons in a thin magnetic-lens type of spectrometer are described by a non-linear differential equation. The equation was numerically integrated to obtain a set of electron trajectories originating from a point source on the axis of the instrument. Trajectories for off-axis sources were approximated. On the basis of these trajectories, the location and some properties of ring focus were studied. Theoretically calculated line shapes are compared for axial and ring focus. For reasonable values of resolution, the transmission of the spectrometer would be roughly doubled by performing the momentum discrimination by a ring focus baffle instead of by a small counter on the axis.