In this paper we use the Cramer-Rao lower uncertainty bound to estimate the maximum precision that could be achieved on the joint simultaneous (or 2D) estimation of photometry and astrometry of a point source measured by a linear CCD detector array.
We develop exact expressions for the Fisher matrix elements required to compute the Cramer-Rao bound in the case of a source with a Gaussian light profile. From these expressions we predict the behavior of the Cramer-Rao astrometric and photometric precision as a function of the signal and the noise of the observations, and compare them to actual observations - finding a good correspondence between them. We show that the astrometric Cramer-Rao bound goes as $(S/N)^{-1}$ (similar to the photometric bound) but, additionally, we find that this bound is quite sensitive to the value of the background - suppressing the background can greatly enhance the astrometric accuracy. We present a systematic analysis of the elements of the Fisher matrix in the case when the detector adequately samples the source (oversampling regime), leading to closed-form analytical expressions for the Cramer-Rao bound. We show that, in this regime, the joint parametric determination of photometry and astrometry for the source become decoupled from each other, and furthermore, it is possible to write down expressions (approximate to first order in the small quantities F/B or B/F) for the expected minimum uncertainty in flux and position. These expressions are shown to be quite resilient to the oversampling condition, and become thus very valuable benchmark tools to estimate the approximate behavior of the maximum photometric and astrometric precision attainable under pre-specified observing conditions and detector properties.
Recently, the singular value decomposition (SVD) was applied to standard Gaussian ensembles of Random Matrix Theory (RMT) to determine the scale invariance in the spectral fluctuations without performing any unfolding procedure. Here, SVD is applied
directly to the $ u$-Hermite ensemble and to a sparse matrix ensemble, decomposing the corresponding spectra in trend and fluctuation modes. In correspondence with known results, we obtain that fluctuation modes exhibit a cross-over between soft and rigid behavior. By using the trend modes we performed a data-adaptive unfolding, and we calculate traditional spectral fluctuation measures. Additionally, ensemble-averaged and individual-spectrum averaged statistics are calculated consistently within the same basis of normal modes.
We study coherent wave scattering through waveguides with a step-like surface disorder and find distinct enhancements in the reflection coefficients at well-defined resonance values. Based on detailed numerical and analytical calculations, we can una
mbiguously identify the origin of these reflection resonances to be higher-order correlations in the surface disorder profile which are typically neglected in similar studies of the same system. A remarkable feature of this new effect is that it relies on the longitudinal correlations in the step profile, although individual step heights are random and thus completely uncorrelated. The corresponding resonances are very pronounced and robust with respect to ensemble averaging, and lead to an enhancement of wave reflection by more than one order of magnitude.
We study the electromagnetic transmission $T$ through one-dimensional (1D) photonic heterostructures whose random layer thicknesses follow a long-tailed distribution --Levy-type distribution. Based on recent predictions made for 1D coherent transport
with Levy-type disorder, we show numerically that for a system of length $L$ (i) the average $<-ln T> propto L^alpha$ for $0<alpha<1$, while $<-ln T> propto L$ for $1lealpha<2$, $alpha$ being the exponent of the power-law decay of the layer-thickness probability distribution; and (ii) the transmission distribution $P(T)$ is independent of the angle of incidence and frequency of the electromagnetic wave, but it is fully determined by the values of $alpha$ and $<ln T>$.
We present the first entirely ground-based astrometric determination of the proper motion for the Fornax Local Group Dwarf Spheroidal satellite galaxy of the Milky Way, using CCD data acquired with the ESO 3.5 m NTT telescope at La Silla Observatory
in Chile. Our unweighted mean from five Quasar fields in the background of Fornax, used as fiducial reference points, leads to $mu_alpha cos delta=0.62 pm 0.16$ $masy$, and $mu_delta=-0.53 pm 0.15$ $masy$. A detailed comparison with all previous measurements of this quantity seems to imply that there is still no convincing convergence to a single value, perhaps indicating the existence of unnacounted systematic effects in (some of) these measurements. From all available proper motion and radial velocity measurements for Fornax, we compute Fornaxs orbital parameters and their uncertainty using a realistic Galactic potential and a Monte Carlo simulation. Properties of the derived orbits are then compared to main star formation episodes in the history of Fornax. All published proper motion values imply that Fornax has recently (200-300 Myr ago) approached perigalacticon at a distance of $sim$150 kpc. However, the derived period exhibits a large scatter, as does the apogalacticon. Our orbit, being the most energetic, implies a very large apogalactic distance of $sim 950$ kpc. If this were the case, then Fornax would be a representative of an hypervelocity MW satellite in late infall.
