Estimation of Cross Directional Properties: Scanning versus Stationary Sensors

Periodic time varying Kalman filter calculations for problems involving scanning sensors are solved using "lifting" techniques common for multirate systems. The solution of this problem is used to compare the performance of scanning sensors versus stationary sensors in the estimation of cross directional properties. Furthermore, we examine controller performance when the outputs from the Kalman filter are used as inputs to a state feedback control law. Although adding sensors may significantly enhance the estimates of cross directional properties, feedback of these improved estimates may translate to lower levels of improvement in cross directional variations

The Anisoplanatic Point Spread Function in Adaptive Optics

The effects of anisoplanatism on the adaptive optics point spread function are investigated. A model is derived that combines observations of the guide star with an analytic formulation of anisoplanatism to generate predictions for the adaptive optics point spread function at arbitrary locations within the field of view. The analytic formulation captures the dependencies of anisoplanatism on aperture diameter, observing wavelength, angular offset, zenith angle and turbulence profile. The predictions of this model are compared to narrowband 2.12 um and 1.65 um images of a 21 arcsec binary (mV=7.3, 7.6) acquired with the Palomar Adaptive Optics System on the Hale 5 meter telescope. Contemporaneous measurements of the turbulence profile made with a DIMM/MASS unit are used together with images of the primary to predict the point spread function of the binary companion. Predicted companion Strehl ratios are shown to match measurements to within a few percent, whereas predictions based on the isoplanatic angle approximation are highly discrepant. The predicted companion point spread functions are shown to agree with observations to 10%. These predictions are used to measure the differential photometry between binary members to an accuracy of 1 part in 10^{3}, and the differential astrometry to an accuracy of 1 mas. Errors in the differential astrometry are shown to be dominated by differential atmospheric tilt jitter. These results are compared to other techniques that have been employed for photometry, astrometry, and high contrast imaging.Comment: 26 pages, 7 figure

The one-loop effective potential of the Wess-Zumino model revisited

The full one-loop supersymmetric effective potential for the Wess-Zumino model is calculated using superfield techniques. This includes the K\"ahler potential and the auxiliary field potential, of which the former was originally computed in 1993 while the latter is derived for the first time. In the purely bosonic sector our results match those of older component field calculations. In light of prior contradictory results found in the literature, the calculation of the leading term in the auxiliary field potential is approached in a variety of ways. Issues related to conditional convergence that occur during these calculations and their possible consequences are discussed.Comment: 32 page