13.1.1 Direct Fourier Transform

The simplest approach would be to directly compute $\sin$ and $\cos$ functions in Eq.13.4 for all combinations of visibilities and pixels in the image. This is straightforward, but slow. For typical data set from the VLA, which contain up to 10⁵ visibilities per hour and usually require large images ( $1024 \times 1024$ pixels), the computation time can be prohibitive. On the other hand, the IRAM Plateau de Bure interferometer produces about 10⁴ visibilities per synthesis, and only require small images ( $128 \times 128$). The Direct Fourier Transform approach could actually be efficient on vector computers for spectral line data from Plateau de Bure interferometer, because the $\sin$ and $\cos$ functions needs to be evaluated only once for all channels. Moreover, the method is well suited to real-time display, since the dirty image can be easily updated for each new visibility.