An Etymological Dictionary of Astronomy and Astrophysics
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1) A mathematical combination of two functions which involves multiplying the value of one function at a given point with the value of another function, the weighting function, for a displacement from that point and then integrating over all such displacements. The process is repeated for every point of the function. Convolution expresses how the shape of a function is altered by the other. In mathematical terms, the convolution of two functions f(x) and g(x) is defined by: f*g = ∫f(u)g(x - u) du, integral from -∞ to +∞.
2) Astro.: Convolution describes how an instrument, through its transfer function, affects an input signal. → deconvolution.

Verbal noun of → convolve.

A theorem stating that the → Fourier transform of the convolution of f(x) and g(x) is equal to the product of the Fourier transform of f(x) and g(x): F{f*g} = F{f}.F{g}.

→ convolution; → theorem.

A mathematical operation that allows to restore the original input signal, such as an astronomical image or spectrum, to its state before being affected by the → atmospheric turbulence and the → transfer function of the instrument. → convolution.

From → de- + → convolution.

An algorithm used to improve the resolution of an image particularly when the convolving function is well defined. Also called deconvolution code.

→ deconvolution; → algorithm.

A → cross correlation technique for computing average profiles from thousands of → spectral lines simultaneously. The technique, first introduced by Donati et al. (1997, MNRAS 291,658), is based on several assumptions: additive → line profiles, wavelength independent → limb darkening, self-similar local profile shape, and weak → magnetic fields. Thus, unpolarized/polarized stellar spectra can indeed be seen as a line pattern → convolved with an average line profile. In this context, extracting this average line profile amounts to a linear → deconvolution problem. The method treats it as a matrix problem and look for the → least squares solution. In practice, LSD is very similar to most other cross-correlation techniques, though slightly more sophisticated in the sense that it cleans the cross-correlation profile from the autocorrelation profile of the line pattern. The technique is used to investigate the physical processes that take place in stellar atmospheres and that affect all spectral line profiles in a similar way. This includes the study of line profile variations (LPV) caused by orbital motion of the star and/or stellar surface inhomogeneities, for example. However, its widest application nowadays is the detection of weak magnetic fields in stars over the entire → H-R diagram based on → Stokes parameter V (→ circular polarization) observations (see also Tkachenko et al., 2013, A&A 560, A37 and references therein).

→ least; → square; → deconvolution.