Interferometric array assessment: Investigating UV coverage and imaging
Image quality assessment technology is introduced to assess interferometric array. Including existing assessments of Interferometric array, four categories of array assessment methods are concluded: assessing UV coverage directly, assessing UV coverage related to observing objects, assessing imaging quality related to observing objects and assessing imaging quality directly. A specific method in each category is proposed. All methods are used to design or optimize interferometric arrays, especially the early-stage study of Solar Low Frequency Array.
Interferometric array design: Optimizing the locations of the antenna pads
The design of an interferometric array should allow optimal instrumental response regarding all possible source positions, times of integration and scientic goals. It should also take into account constraints such as forbidden regions on the ground due to impracticable topography. The complexity of the problem requires one to proceed by steps. A possible approach is to rst consider a single observation and a single scientic purpose. A new algorithm is introduced to solve eciently this particular problem called the conguration problem. It is based on the computation of pressure forces related to the discrepancies between the model (as determined by the scientic purpose) and the actual distribution of Fourier samples. The flexibility and rapidity of the method are well adapted to the full array design. A software named APO that can be used for the design of new generation interferometers such as ALMA and ATA has been developed.
The Shapes of Cross-Correlation Interferometers
Cross-correlation imaging interferometers designed in the shape of a curve of constant width offer better sensitivity and imaging characteristics than other designs because they sample the Fourier space of the image better than other shapes, for example, “'s” or “'s.” In a cross-correlation interferometer each pair of antennas measures one Fourier component with a spatial wavenumber proportional to the separation of the pair. Placing the individual antennas of the interferometer along a curve of constant width, a curve that has the same diameter in all directions, guarantees that the spatial resolution of the instrument will be independent of direction because the measured Fourier components will have the same maximum spatial wavenumber in all directions. The most uniform sampling within this circular region in Fourier space will be created by the particular symmetric curve of constant width that has the lowest degree of rotational symmetry or fewest number of sides, which is the Reuleaux triangle. The constant width curve with the highest symmetry, the circle is the least satisfactory although still considerably better than 's or 's. In all cases, the sampling can be further improved by perturbing the antenna locations slightly off a perfect curve to break down symmetries in the antenna pattern which cause symmetries and hence nonuniformities in the sampling pattern in Fourier space. Appropriate patterns of perturbations can be determined numerically. As a numerical problem, optimizing the sampling in Fourier space can be thought of as a generalization of the traveling salesman problem to a continuous two-dimensional space. Self-organizing neural networks which are effective in solving the traveling salesman problem are also effective in generating optimal interferometer shapes. The Smithsonian Astrophysical Observatory's Submillimeter Array, a cross-correlation imaging interferometer for astronomy, will be constructed with a design based on the Reuleaux triangle.