FEATHER 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.