Extended source

Abstract Fundamentals of amplitude interferometry are given, complementing animated text and figures available on the web. Concepts as the degree of coherence of a source are introduced, and the theorem of van Cittert - Zemike is explained. Responses of an interferometer to a spatially extended source and to a spectrally extended one are described. Then the main methods to combine the beams from the telescopes are discussed, as well as the observable parameters - vibilities and phase closures. 

If we wish to include spectral coverage and extended sources into our considerations, we need to review the theory of diffraction and to introduce some concepts of coherence. 

We now turn our attention to extended sources which we will assume monochromatic for the time being. 

However, the response of a two-way interferometer to an extended source for a single baseline is not unique. The decrease in contrast indicates that the source is resolved by the baseline but does not give any information about the source s structure. The full information can only be obtained by measuring the two-dimensional visibility function as completely as possible, which implies measurements with many baselines. 

Figure 13. Modified Velocity Map Imaging spectrometer showing the double einzel lens, L, Li, and 5-eV kinetic energy initially transverse trajectories from an extended source volume with Vjgp = 3000 V, Vext = 0.695 x Vjep, and Vl = Vli = 1000 V. Taken with permission from Ref. [102]. Copyright (c) 2005, American Institute of Physics.

Adapted with permission from Bockelee-Morvan et al. (2002). Technique of observation. b Abundance given for nuclear + extended source. c Measured at = 2.9 AU. d Abundance given for extended source. e Probably a daughter species. 

The large rocking curve width associated with the extended source makes it easy to set up the Berg-Barrett topograph. This can be done with a counter but is most easily achieved with a phosphor screen and TV camera. The strength of the beams is such that only modest gain is needed and the equipment can therefore... 

High intensity, microwave powered emission sources have recently been developed that are reported to provide substantially higher DUV output than classical electrode discharge mercury lamps 76). These sources suffer from self-absorption of the intense 254 nm emission but have a relatively high output in a band between 240 and 280 nm. They are extended sources of finite size rather than point sources, and they must also be an integral part of a tuned, resonant microwave cavity. Consequently, extensive condenser design work would be required in order to utilize the microwave powered sources in projection printers. 

Figure 3-6 Diffusion in an infinite medium with an extended source, (a) The extended source with width 5 = 1 mm (b) the solution.

Diffusion in an infinite medium with an extended source... 

For one-dimensional diffusion in an infinite medium with constant D, if the initial condition is an extended source, meaning C is finite in a region ( 8, 8), and 0 outside the region (Figure 3-6a) ... 

The extended source can be viewed as a summation (or integral) of point plane sources. The mass density at each plane e ( 8,8) is Cod. At position x, which is distance x - away from this plane, according to Equation 3-45a, the concentration due to this plane source is... 

Problems with extended sources (sources over extended space) or continuous sources (sources over continuous time) can be solved by integrating the above solutions. 

There is a constant move toward the improvement of instrumentation technology. This ranges from new detector and source technologies, to new ways to make IR measurements and new ways to fabricate instruments. In the area of components, there are new MEMS-based sources, which operate at low power and provide extended source lifetimes, new tunable laser devices, new tunable filter devices, both broad and narrow range, and new detector arrays. Many of these devices are currently relatively high cost. However, most are made from scalable technologies, such as semiconductor fabrication technologies, and as such if the demand increases the cost can come down. Many can follow Moore s law of... 

This technique is particularly applicable for the emission study from extended sources which are homogeneous enough on a large scale. The accuracy of these determinations depends strongly on the validity of the Kz estimations. In addition, this model does not take into account the convection which is considered as negligible compared to the turbulence. This approximation seems to be justified for the first few meters above the ocean surface. The lifetimes measured were essentially lower than 9h with values as low as few minutes. The large variability obtained remains to be explained. 

The present equipment, based on Fourier-transform spectroscopy, makes use primarily of the so-called "throughput advantage", i.e., the data corresponding to all wavelengths of light are collected simultaneously from an extended source. These characteristics increase the sensitivity for TL emission spectroscopy and have achieved the aim of making it possible to study TL emission phenomena at low radiation levels, comparable with those received by the mineral or phosphor samples during their actual application. 

In X-rays, detections of such distant structures are easier because they appear as extended sources and because the field is not providing such extended sources at these wavelengths in general. The contamination by field X-rays point sources is, however, sometimes very strong. Another problem is to measure the precise redshift of these extended sources at the same time. In any case, optical observations are needed to complete X-ray observations in order to confirm the nature of the source and to estimate its redshift. 

Radiance — Radiance L refers to the radiation that comes from an extended source. It corresponds to the power transmitted through a surface per unit area of that surface, per unit solid angle, given in W sr-1 m-2. 

But besides an underproduction of CO by the calculations, HjO was also overproduced. This cannot only be caused by a simple overabundance of H O, since the model gives even lower production rates for H2O than those observed. Huebner and Giguere propose as an explanation the presence of an extended source of water vapor caused by icy grains, ejected from the nucleus, which reach considerable distances from the latter in the coma before they evaporate (Delsemme and Miller ). This would lower the -content in the inner coma and increase the CO" production, since CO" is lost by reacting with H O (reaction (2)). Moreover, the HjO abundance has been derived from the production rates of H and OH, and it cannot be excluded that H O is not the only parent of H and OH. 

Figure 1.14. Diagram illustrating the van Cittert-Zernike theorem. An extended source a illuminates a diffracting object in the xj -plane, a distance R away.

Eberhardt P. (1999) Comet Halley s gas composition and extended sources results from the neutral mass spectrometer on Giotto. Space Sci. Rev. 90, 45-52. 

For extended sources at close distances experimental calibration should be made. 

The Milagro detector s large field of view and continuous duty cycle make it an ideal instrument for the discovery of previously unknown sources. Recent publications cover topics including detection of the Crab Nebula[l], limits on TeV emission from GRB [2] and a TeV all-sky survey of the northern celestial hemisphere[3]. Recently we have presented papers on the detection of diffuse TeV emission from the Galactic plane[4], limits on TeV emission from satellite detected GRB[5], a study of nearby AGN[6] and limits on relic neutralino annihilation derived from TeV flux limits from the sun[7]. The focus of this paper is the search for extended sources of TeV gamma rays with the Milagro detector. 

III) Search for off-axis signal, within the telescope field of view (LOV). The so-called Lalse Source Method (LSM) has been implemented. A grid of 0.1° step size was defined in the LOV, and at each knot the analysis for point-like source has been applied. The method works also for slightly extended sources underestimating somewhat the 7 flux. 

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