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: http://www.adass.org/adass/proceedings/adass02/P3-6/
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Definition 1.1. A space of complex functions dual
to the brightness distribution
and risen by an
operator
, is called a space of visibility functions or
spatial coherency.
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(1) |
Definition 1.2. Let us define an object as a domain of the Universe that is a subject of the investigation whose brightness distribution could be represented as a 2-D function with infinite spatial frequency spectra.
Definition 1.3. Let us define an image of the object as a result of creation
by unknown spatial brightness distribution
In other words, we have an original object located somewhere in the space (Universe) and we can observe only some projection of this object on this space. For example, one of the projections of the object can be its electromagnetic emission of the object in a given spectral band and in a given moment of time.
Let us consider a metrics
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(2) |
There exist a few possible approximating functions:
Let us consider an expression
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(3) |
Let us consider a discrepancy
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(4) |
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(5) |
Let us represent a complex function
as a time series in the neighborhood of a point
. Then
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(6) |
Both values are complex ones and can be represented as
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(7) |
Example. If
(no amplitude calibration) then
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(8) |
A value
describes derivatives of the second order that is necessary to take
into account for Space VLBI imaging.
Definition 5.1. If for any three radio telescopes
In case of a High Orbiting SVLB mission a good (u,v)-coverage does not
guarantee high quality images because
The software project, Astro Space Locator (ASL) for Windows 9x/NT/2000 (code name ASL_Spider 1.0) is developed by the Laboratory for Mathematical Methods of the ASC to provide a free software package for VLBI data processing. We used the Microsoft Windows NT/2000 and MS Visual C++ 6.0 on IBM compatible PCs as the platform from which to make data processing and reconstruction of VLBI images.
A generalized self-calibration (GSC) algorithm was developed. The solution was obtained as a
non-linear optimization in the Hilbert space .
GCS describes not only the first derivatives but also of the second derivatives that is
necessary to take into account for Space VLBI imaging.
A global fringe fitting procedure is just an initialization (zero iteration) of GSC.
GSC allows to obtain more stable and reliable results than traditional self-calibration algorithms.
Schwab, F. R. 1981, VLA Scientific Memorandum, No. 136, NRAO