20.2.3 Algorithm

FEATHER use the following steps

 - Make oversampled Fourier Transform of both HIGHres and LOWres images
 - Compute the truncation function f(r)
 - Make the Truncated compact Fourier Transform, f(r) x T(LOW)
 - Make the complement long baseline Fourier Transform, (1-f(r)) x T(HIGH)
 - Sum them T(ALL) = R x f(r) x T(LOW) + (1-f(r)) x T(HIGH)
      where R is a scale factor taken from FEATHER_RATIO
 - Make the inverse Fourier Transform
 - Truncate the resulting image to original size and Mask of the HIGHres
   images

If LOWres is a single-dish image, f(r) should normally be the beam of that telescope to use optimal Signal-to-noise ratio from that data set. However, because of pointing errors and other calibration issues such as spectral baseline, using a sharper transition function gives better results. FEATHER uses the function

     f(r) = exp(-(r/Radius)^Expo)

where Radius is taken from FEATHER_RADIUS and Expo from FEATHER_EXPO.