Interferometric Image Synthesis The Dirty Data Cube

3 Interferometric Image Synthesis The Dirty Data Cube 

The next step is the extraction of the spatial features of Sp, this is the dirty datacube, Sky. To extract the spatial features one has to perform the 2-dimensional Fourier Transform of the m v-map. Combining each baseline position bj and each wavenumber Vk the dirty datacube is calculated as 

The spectral results of the simulation are shown in Fig. 5.7 (left) for the central pixel of the gaussian source (blue), the point source (green) and the central pixel of the elliptical source (red). It can be observed that the emission and absorption line positions are detected but present a sine-shape this is due to the boxcar function 

Also present in the detected spectra is a modulation clearly noticeable for the point source (green). For comparison. Fig. 5.7 (right) shows the detected spectra for three positions in the sky, where a similar modulation appears. Again, this is due to the dirty beam, which is wavelength dependent as the frequency (or wavenumber) increases, the dirty beam narrows and so do the side lobes. By selecting a spatial position and increasing the frequency, the variation of size of the dirty beam causes a spectral modulation. 

Although for a binary system it is easy to model and correct this fact, when the number of sources increases or when extended sources are present on the sky, the correction of the modulation is not straightforward because in each spatial position there is the contribution of the dirty beam generated by each source present on the sky. For this reason, more complex data synthesis algorithms are required. 

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