Gaussian sources

In practical applications one uses Gaussian sources (I) or the so called Markovian random telegraph process. For both the formulation of the mean and the correlation function is sufficient to define the stochastic process. Later on we will define the value support of t) (Gaussian or dichotomic) and will give the mean and the correlation function, i.e. 

Next we consider several noise sources. They are Gaussian sources if their support of values is due to a Gaussian distribution. Contrary the dichotomic telegraph process assumes two values, i.e. = A and 2 = A. We will always assume A = — A. 

Figure 18.6 depicts the influence of a pulsating, circular, Gaussian source on the time variation of the material s surface temperature for Pe = 7 and K - °° [26], The dimensionless... 

In SkyParams.xlsx the user defines the sky map to be created if no science input map is used. The first sheet in the file is the one that the simulator reads, so different configurations can be stored in the same file. The first option is the Full Width Half Maximum (FWHM) if empty, a point source is created, if full, a Gaussian source is simulated with this FWHM. The user may input the source position in the sky at jc j)os and y j)os. If empty the simulator will display a sky grid where the user selects the position or a source by clicking on that position. Temp is for the temperature in Kelvin of a Blackbody spectrum, cut-on and cut-off will filter the Blackbody spectrum at the wavenumbers given at these parameters. For verification purposes, if the user inputs 1 the spectrum for that given source will be the one measured with the Cardiff-UCL FIRI testbed. If the user inputs 0 the spectrum will consist of a single wavenumber tone, defined at tone wl. 

The Sky map module is capable of placing point sources or gaussian sources on a sky grid defined by the FOV and the pixel resolution. Each source has its own spectrum, which can be loaded from data (i.e. the spectmm measured with the Cardiff-UCL testbed) or can be a black body of a given temperature and modified by... 

Fig. 4.3 Simulated sky datacube where 2 point sources (a, b) and 2 gaussian sources (c, d) with different spectra have been placed on a sky grid...

Figure4.3 shows an example of a simulated datacube, where 4 sources have been positioned on the sky grid (left) two gaussian sources, and two point sources. The spectra of these sources are different, corresponding to blackbodies of different temperatures which have been multiplied by Alters with different cut-on and cut-off wavenumbers (right). For the loading of more complex sky map data cubes such as science datacubes the simulator will interpolate or decimate to meet the instrument parameters.

Three different types of sources are positioned in the sky grid a point source, a gaussian source and an elliptical source, as shown in Fig. 5.2 (left). 

Spectrally, the gaussian source is a blackbody with a brightness temperature of lOOK and an emission line at 60cm . The point source corresponds to a blackbody at 2000 K, and the elliptical source is a blackbody at 50 K and an absorption line at 80cm . The spectra of the three sources is shown in Fig. 5.2 (right). 

The elliptical source could correspond to a circumstellar disk with an envelope size of 200AU at 150 pc. The gaussian source can also be a circumstellar disk of 80AU at 300pc but with a different orientation with respect to the observer plane. The point source can be considered a protostar at 50pc and with a radius Rsun- As the point source size is smaller than the pixel size on the sky grid, an emissivity parameter e has to be introduced, this is... 

Fig. 5.7 Spectral results of the Master simulation for the central pixel of the gaussian source blue), the point source green) and the central pixel eUiptical source red) left). Detected spectra for three positions in the sky where no source intensity is expected right)...

For a 2-iteration blind deconvolution, the results do not improve. Although the PSF beam size is still consistent with the one expected from theory, the ripples have vanished from the PSF and are still present in the recovered datacube. The spatial size of the gaussian source approximates to a point source for the maximum wavenumber image (right) and does not correspond to the expected spatial size. 

Finally, in Fig. 5.18 (left) the detected spectra for the central pixel of the gaussian source (blue), the point source (green) and the central pixel of the elliptical source (red) is shown. One can observe that the ripples due to the interferometric dirty beam have vanished and the detected spectra is in concordance with the input Master sky map. Again, for comparison. Fig. 5.18 (right) presents the detected spectra for three positions in the sky where no signal is expected. The presence of power in the low wavenumbers is due to the interferometric beam size. From 60cm the sources are resolved, the power in those pixels reduces and the modulation present in the dirty datacube (see Fig. 5.7) disappears because there are no ripples from the interferometric beam. 

Three different sources are available point source, gaussian source and elliptical source. The common parameters are x pos and y pos (in arcseconds), the temperature (in Kelvins), the cut-on and cut-off wavenumbers, the emission wavenumber (to place an emission line across the spectrum) and the absorption wavenumber (to place an absorption line across the spectrum). The specific parameters are ... 

Gaussian source The user inputs the FWHM (in arcseconds). 

The triangles in Fig. 7.2 represent data for linearly or partially polarized radiation, while the circle is for cross-polarized radiation (this is the one exception mentioned previously). The experimental measurements are consistent with the following interpretation. The laser output consists of a number of more-or-less independent Fabry-Perot modes which are changing during the pulse width due to heating of the laser junction 1.2A, The radiation may therefore be considered to behave as a Gaussian source with a coherence time rj (dv) 10 s. Since the intermediate-state lifetime for the doublequantum sodium photodetector is much shorter than the radiation coherence time, the irradiance fluctuations result in a factor of 2 enhancement of the single-beam photocurrents. As far as the irradiance cross-term is concerned. 

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