The Gaussian formula and spherical aberration of the static and moving curved mirrors from Fermat's principle

The Gaussian formula and spherical aberrations of the static and relativistic curved mirrors are analyzed using the optical path length (OPL) and Fermat's principle. The geometrical figures generated by the rotation of conic sections about their symmetry axes are considered for the shapes of the mirrors. By comparing the results in static and relativistic cases, it is shown that the focal lengths and the spherical aberration relations of the relativistic mirrors obey the Lorentz contraction. Further analysis of the spherical aberrations for both static and relativistic cases have resulted in the information about the limits for the paraxial approximation, as well as for the minimum speed of the systems to reduce the spherical aberrations.Comment: 15 pages, 7 figures, uses iopart. Major revisions on the physical interpretations of the results. Accepted for publication in J. Op

Crowded-Field Astrometry with the Space Interferometry Mission - I. Estimating the Single-Measurement Astrometric Bias Arising from Confusion

The accuracy of position measurements on stellar targets with the future Space Interferometry Mission (SIM) will be limited not only by photon noise and by the properties of the instrument (design, stability, etc.) and the overall measurement program (observing strategy, reduction methods, etc.), but also by the presence of other "confusing" stars in the field of view (FOV). We use a simple "phasor" model as an aid to understanding the main effects of this "confusion bias" in single observations with SIM. This analytic model has been implemented numerically in a computer code and applied to a selection of typical SIM target fields drawn from some of the Key Projects already accepted for the Mission. We expect that less than 1% of all SIM targets will be vulnerable to confusion bias; we show that for the present SIM design, confusion may be a concern if the surface density of field stars exceeds 0.4 star/arcsec^2. We have developed a software tool as an aid to ascertaining the possible presence of confusion bias in single observations of any arbitrary field. Some a priori knowledge of the locations and spectral energy distributions of the few brightest stars in the FOV is helpful in establishing the possible presence of confusion bias, but the information is in general not likely to be available with sufficient accuracy to permit its removal. We discuss several ways of reducing the likelihood of confusion bias in crowded fields. Finally, several limitations of the present semi-analytic approach are reviewed, and their effects on the present results are estimated. The simple model presented here provides a good physical understanding of how confusion arises in a single SIM observation, and has sufficient precision to establish the likelihood of a bias in most cases.Comment: 28 pages, 20 figures, 1 table; to appear in December 2007 issue of PAS

Development of sputtered techniques for thrust chambers

Procedures for closing out coolant passages in regeneratively cooled thrust chambers by triode sputtering, using post and hollow Cu-0.15 percent Zr cathodes are described. The effects of aluminum composite filler materials, substrate preparation, sputter cleaning, substrate bias current density and system geometry on closeout layer bond strength and structure are evaluated. High strength closeout layers were sputtered over aluminum fillers. The tensile strength and microstructure of continuously sputtered Cu-0.15 percent Zr deposits were determined. These continuous sputtered deposits were as thick as 0.75 cm. Tensile strengths were consistently twice as great as the strength of the material in wrought form

Coherent flash of light emitted by a cold atomic cloud

When a resonant laser sent on an optically thick cold atomic cloud is abruptly switched off, a coherent flash of light is emitted in the forward direction. This transient phenomenon is observed due to the highly resonant character of the atomic scatterers. We analyze quantitatively its spatio-temporal properties and show very good agreement with theoretical predictions. Based on complementary experiments, the phase of the coherent field is reconstructed without interferometric tools.Comment: Submitted to Phys. Rev. Let

Solid Freeform Fabrication of Functional Silicon Nitride Ceramics by Laminated Object Manufacturing 1

The processing of silicon nitride (Si3N4) structural ceramics by Laminated Object Manufacturing (LOM) using ceramic tape preforms was investigated. The key processing stages involved green shape formation (which used the LOM process), followed by the burnout of all organics, and final densification by pressureless sintering. Two material systems were considered. These were a) monolithic Si3N4 and b) a preceramic polymer infiltrated Si3N4. The raw materials for the process were tape preforms of Si3N4, which were fabricated by standard tape casting techniques. Mechanical property data obtained for the LOM processed Si3N4 showed high strength and fracture toughness values. The room temperature and high temperature (1260 o C) flexural strengths were in the range of 700-900 MPa and 360-400 MPa, respectively. The fracture toughness averaged from 5.5-7.5 MPa.m1/2. These strength and fracture toughness values are comparable to those reported for conventionally prepared Si3N4 ceramics. Thus, this research demonstrated that the LOM technique is a viable method for preparing functional Si3N4 ceramics with good physical and mechanical properties.Mechanical Engineerin

Si3N4 emissivity and the unidentified infrared bands

Infrared spectroscopy of warm (about 150 to 750 K), dusty astronomical sources has revealed a structured emission spectrum which can be diagnostic of the composition, temperature, and in some cases, even size and shape of the grains giving rise to the observed emission. The identifications of silicate emission in oxygen rich objects and SiC in carbon rich object are two examples of this type of analysis. Cometary spectra at moderate resolution have similarly revealed silicate emission, tying together interstellar and interplanetary dust. However, Goebel has pointed out that some astronomical sources appear to contain a different type of dust which results in a qualitatively different spectral shape in the 8 to 13 micron region. The spectra shown make it appear unlikely that silicon nitride can be identified as the source of the 8 to 13 micron emission in either NGC 6572 or Nova Aql 1982. The similarity between the general wavelength and shape of the 10 micron emission from some silicates and that from the two forms of silicon nitride reported could allow a mix of cosmic grains which include some silicon nitride if only the 8 to 13 micron data are considered

Development of sputtered techniques for thrust chambers, task 1

Filler materials proposed for use in the sputter fabrication regeneratively cooled thrust chambers were evaluated. Low melting castable alloys, CERROBEND. CERROCAST, and CERROTRU, slurry applied SERMETEL 481 and flame-sprayed aluminum were investigated as filler materials. Sputter deposition from a cylindrical cathode inverted magnestron was used to apply an OFHC copper closeout layer to filled OFHC copper ribbed-wall cylindrical substrates. The sputtered closeout layer structure was evaluated with respect to filler material contamination, predeposition machining and finishing operations, and deposition parameters. The application of aluminum by flame-spraying resulted in excessiver filler porosity. Though the outgassing from this porosity was found to be detrimental to the closeout layer structure, bond strengths in excess of 10,500 psi were achieved. Removal of the aluminum from the grooves was readily accomplished by leaching in a 7.0 molar solution of sodium hydroxide at 353 K. Of the other filler materials evaluated, CERROTRU was found to be the most suitable material with respect to completely filling the ribbed-wall cylinders and vacuum system compatibility. However, bond contamination resulted in low closeout layer bond strength with the CERROTRU filler. CERROBEND, CERROCAST, and SERMETEL 481 were found to be unacceptable as filler materials

Phase operators, phase states and vector phase states for SU(3) and SU(2,1)

This paper focuses on phase operators, phase states and vector phase states for the sl(3) Lie algebra. We introduce a one-parameter generalized oscillator algebra A(k,2) which provides a unified scheme for dealing with su(3) (for k < 0), su(2,1) (for k > 0) and h(4) x h(4) (for k = 0) symmetries. Finite- and infinite-dimensional representations of A(k,2) are constructed for k < 0 and k > 0 or = 0, respectively. Phase operators associated with A(k,2) are defined and temporally stable phase states (as well as vector phase states) are constructed as eigenstates of these operators. Finally, we discuss a relation between quantized phase states and a quadratic discrete Fourier transform and show how to use these states for constructing mutually unbiased bases