[NRAO] 7th NRAO Synthesis Imaging Summer School - June 2000 Prev
Error Recognition - S.T. Myers Page 12
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  8 Real and Imaginary Parts  
 
 
  • Transform properties determined by Fourier kernel:

    exp( i Phi ) = cos Phi + i sin Phi

  • Fourier Transform of a real function (eg. sky brightness) is Hermitian (conjugated on reflection):

    Real <==> Real Even + Imag Odd
    Imaginary <==> Real Odd + Imag Even

    Real & Even <==> Real & Even
    Real & Odd <==> Imag & Odd

    Even <==> Even
    Odd <==> Odd

  • The sky brightness distribution is assumed to be real, and thus its transform should be Hermitian

  • At any given time the complex visibility on a given baseline is measured, and its complex conjugate is used as the reflected baseline visibility, guaranteeing a real Image Plane

 
 
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