On the Sharpeming of Observational Data with Special Application to the Darkening of the Solar Limb

Fellgett, P. B.; Schmeidler, F.

doi:10.1093/mnras/112.4.445

Cited by 13 publications

(3 citation statements)

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“…Trumpler and Weaver (1953) for references). Typical instances are the instrumental blurring of (i) optical spectra (van Cittert 1931; Burger and van Cittert 1932;van de Hulst 1941van de Hulst , 1946, (ti) X-ray spectra (Stokes 1948;Paterson 1950;Waser and Schomaker 1953), and (iii) solar limb darkening curves (Fellgett and Schmeidler 1952). A good survey of various methods of dealing with twodimensional examples arising in astronomy is given by Burr (1955).…”

Section: Formal Solution By Fourier Transformsmentioning

confidence: 99%

Aerial Smoothing in Radio Astronomy

Bracewell¹,

Roberts²

1954

Aust. J. Phys.

226

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SummaryWhen an aerial is used to survey the distribution of radio brightness over the sky, the observed distribution is smoother than the true distribution; the broader the beam of the aerial, the greater the smoothing. It is shown that the aerial does not register those spatial Fourier components of the true distribution having frequencies beyond a cut-off determined by the aerial aperture. Components of lower frequency are registered but their relative strengths are altered.Two important consequences follow. (i) There are invisible distributions which produce no response when scanned by the aerial. Consequently there is not a unique solution to the problem of correcting for aerial smoothing. The established method of correcting by successive smoothing, leads to the principal 8olution, in which Fourier components accepted by the aerial have been restored to their full values, but the components rejected by the aerial are still not represented. (ii) In conducting a survey it is sufficient to observe at discrete intervals. The measuring points must be closer together than half the period of the Fouri,er component at cut-off. For an aperture of width w, this peculiar interval is equal to fA/w (radians).

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Section: Formal Solution By Fourier Transformsmentioning

confidence: 99%

Aerial Smoothing in Radio Astronomy

Bracewell¹,

Roberts²

1954

Aust. J. Phys.

226

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show abstract

“…This means that complete sharpening can never be achieved except in theoretical problems. Following a suggestion by Fellgett and Schmeidler (1952), if we are given the autocorrelation function of the errors in g(x, y), we can use the Wiener-Kolmogaroff smoothing theory (Bode and Shannon 1950) to determine a solution giving the best possible compromise between errors due to magnification of the errors in g(x, y) and errors due to incomplete sharpening. But the difficulty of measuring the autocorrelation function would seem to make this method of little practical value.…”

Section: The Formal Solutionmentioning

confidence: 99%

“…This process is tedious, but has been used successfully to sharpen the observed light curves of external galaxies with circular symmetry. Numerical integration of Fourier transforms has been used similarly in one dimension by Stokes (1948) and by Fellgett and Schmeidler (1952).…”

Section: The Use Of Fourier Transformsmentioning

confidence: 99%