Spatial frequency response of an optical heterodyne receiver

The principles of transfer function analysis are applied to a passive optical heterodyne receiver to obtain the modulation transfer function (MTF). MTF calculations are performed based on an optical platform which is imaging vertically varying profiles at worst case shuttle orbit altitudes. An analysis of the derogatory effects of sampling (aliasing) and central obscurations on both resolution and heterodyne efficiency is given. It is found that the cascading property of MTF analysis must be carefully applied since the coherent transfer function of the optical receiver and that due to the local oscillator-detector combination are not separable but are related by the convolution of their products. Application of these results to the specific case of a space-lab type optical heterodyne receiver shows that resolutions of the order of 1.5-2.0 Km are possible for worst-case type orbital scenarios. Further, comparison of obscured-type receivers (e.g., Cassegrains) with unobscured receivers shows that both resolution and efficiency are severely degraded in an obscured-type receiver and consequently should not be used for a passive heterodyne detection scheme

Variational data assimilation using targetted random walks

The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis (offline hindcasting). In either of these scenarios it can be important to assess uncertainties in the assimilated state. Ideally it would be desirable to have complete information concerning the Bayesian posterior distribution for unknown state, given data. The purpose of this paper is to show that complete computational probing of this posterior distribution is now within reach in the offline situation. In this paper we will introduce an MCMC method which enables us to directly sample from the Bayesian\ud posterior distribution on the unknown functions of interest, given observations. Since we are aware that these\ud methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however more sophisticated MCMC methods are available\ud which do exploit derivative information. For simplicity of exposition we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number (Stokes flow) scenario in a two dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces

The expected background spectrum in NaI dark matter detectors and the DAMA result

Detailed Monte Carlo simulations of the expected radioactive background rates and spectra in NaI crystals are presented. The obtained spectra are then compared to those measured in the DAMA/NaI and DAMA/LIBRA experiments. The simulations can be made consistent with the measured DAMA spectrum only by assuming higher than reported concentrations of some isotopes and even so leave very little room for the dark matter signal. We conclude that any interpretation of the annual modulation of the event rate observed by DAMA as a dark matter signal, should include full consideration of the background spectrum. This would significantly restrict the range of dark matter models capable of explaining the modulation effect.Comment: 17 pages, 6 figure

On the Assouad dimension of self-similar sets with overlaps

It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our main result is the following precise dichotomy for self-similar sets in the line: either the \emph{weak separation property} is satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the \emph{weak separation property} is not satisfied, in which case the Assouad dimension is maximal (equal to one). In the first case we prove that the self-similar set is Ahlfors regular, and in the second case we use the fact that if the \emph{weak separation property} is not satisfied, one can approximate the identity arbitrarily well in the group generated by the similarity mappings, and this allows us to build a \emph{weak tangent} that contains an interval. We also obtain results in higher dimensions and provide illustrative examples showing that the `equality/maximal' dichotomy does not extend to this setting.Comment: 24 pages, 2 figure

The Global Star Formation Rate from the 1.4 GHz Luminosity Function

The decimetric luminosity of many galaxies appears to be dominated by synchrotron emission excited by supernova explosions. Simple models suggest that the luminosity is directly proportional to the rate of supernova explosions of massive stars averaged over the past 30 Myr. The proportionality may be used together with models of the evolving 1.4 GHz luminosity function to estimate the global star formation rate density in the era z < 1. The local value is estimated to be 0.026 solar masses per year per cubic megaparsec, some 50% larger than the value inferred from the Halpha luminosity density. The value at z ~ 1 is found to be 0.30 solar masses per year per cubic megaparsec. The 10-fold increase in star formation rate density is consistent with the increase inferred from mm-wave, far-infrared, ultra-violet and Halpha observations.Comment: 10 pages, 2 figures, Astrophysical Journal Letters (in press); new PS version has improved figure placemen