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Image reconstruction in radio astronomy with non-coplanar synthesis arrays

Goodrick, Lee (2015-03)

Thesis (MEng)--Stellenbosch University, 2015.


ENGLISH ABSTRACT: Traditional radio astronomy imaging techniques assume that the interferometric array is coplanar, with a small field of view, and that the two-dimensional Fourier relationship between brightness and visibility remains valid, allowing the Fast Fourier Transform to be used. In practice, to acquire more accurate data, the non-coplanar baseline effects need to be incorporated, as small height variations in the array plane introduces the w spatial frequency component. This component adds an additional phase shift to the incoming signals. There are two approaches to account for the non-coplanar baseline effects: either the full three-dimensional brightness and visibility model can be used to reconstruct an image, or the non-coplanar effects can be removed, reducing the three dimensional relationship to that of the two-dimensional one. This thesis describes and implements the w-projection and w-stacking algorithms. The aim of these algorithms is to account for the phase error introduced by non-coplanar synthesis arrays configurations, making the recovered visibilities more true to the actual brightness distribution model. This is done by reducing the 3D visibilities to a 2D visibility model. The algorithms also have the added benefit of wide-field imaging, although w-stacking supports a wider field of view at the cost of more FFT bin support. For w-projection, the w-term is accounted for in the visibility domain by convolving it out of the problem with a convolution kernel, allowing the use of the two-dimensional Fast Fourier Transform. Similarly, the w-Stacking algorithm applies a phase correction in the image domain to image layers to produce an intensity model that accounts for the non-coplanar baseline effects. This project considers the KAT7 array for simulation and analysis of the limitations and advantages of both the algorithms. Additionally, a variant of the Högbom CLEAN algorithm was used which employs contour trimming for extended source emission flagging. The CLEAN algorithm is an iterative two-dimensional deconvolution method that can further improve image fidelity by removing the effects of the point spread function which can obscure source data.

AFRIKAANSE OPSOMMING: Tradisionele beeldvormingstegnieke in radio-astronomie aanvaar dat die interferometriese skikking samevlakkig is. Dit beteken dat die twee-dimensionele Fourier verhouding tussen helderheid en sigbaarheid geldig bly en dat die Vinnige Fourier Transform aangewend kan word. Klein hoogtevariasies in die skikkingsvlak bring die w-ruimtelike frekwensiekomponent mee, wat ’n faseverskuiwing in die inkomende seine tot gevolg het. Dus, in praktyk, moet die bydrae van die nie-samevlakkige basislyneffekte in ag geneem word om sodoende die akkuraatheid van die data te verhoog. Twee benaderings kan gevolg word om die nie-samevlakkige basislyneffekte in ag te neem: Metodes wat die volle drie dimensionele helderheid en sigbaarheidsmodel gebruik kan toegepas word om ’n beeld te herbou, andersins kan die nie-samevlakkige effekte verwyder word om sodoende die drie-dimensionele verhouding te verminder tot ’n twee-dimensionele verhouding. Hierdie tesis beskryf en implementeer die ‘w-projeksie’ en ‘w-stapel’ algoritmes. Die doel van hierdie algoritmes is om die fasefout wat deur nie-samevlakkige sinteseskikkingskonfigurasies veroorsaak word, reg te stel. Hierdie regstelling maak die herwinde sigbaarheid van die beeld meer getrou aan die werklike helderheidsverspreidingsmodel. ’n Bykomende voordeel van die algoritmes is beeldvorming van wye-veld ruimtewaarnemings. In ‘w-projection’ word die w-term in die sigbaarheidsdomein in ag geneem deur die ruimtelike frekwensiekomponent met behulp van ’n konvolusiekern vanuit die probleem te verwyder. Die twee-dimensionele Vinnige Fourier Transform kan gevolglik toegepas word. Soortgelyk hieraan, wend die ‘w-Stacking’ algoritme ’n fasekorreksie aan tot ’n reeks beeldlae, om sodoende ’n beeld te verkry wat die nie-samevlakkige basislyneffekte in ag neem. Die KAT7 teleskoop is gebruik in die simulasie en analiese van die tekortkominge en voordele van beide algoritmes. ’n Hibriede weergawe van die Högbom CLEAN algoritme is bykomend oorweeg. Hierdie algoritme is ’n iteratiewe twee-dimensionele dekonvolusiemetode wat die betroubaarheid van beelde verbeter deur die verskansingseffek van puntverspreidingsfunksies te verwyder. Verder gebruik die Högbom CLEAN algoritme kontoersnoeiing om uitgebreide bron-emisies te identifiseer.

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