We can compare the success of these various imaging pathways on a wide range of simulated data through standard measures of imaging success such as the dynamic range and fidelity index, or more subjectively through looking at the final reconstructions side by side. The fidelity image, first introduced by Cornwell, Holdaway, and Uson (1993) to measure the success of image simulation, is an image of the quantity one over the fractional pixel error. The fidelity index, renamed here as the median fidelity, is the median pixel value of the fidelity image after clipping the low fidelity points which occur in very faint pixels and pixels whose fidelity is very high by chance. Since most pixels in our model images are fairly low brightness, the median fidelity emphasizes the great sea of low brightness pixels. A reconstruction with a median fidelity of 20 is considered highly successful. For the current investigation, we further define the first moment of the fidelity, which is the mean fidelity weighted by the pixel value raised to the first power. The first moment fidelity is less sensitive to errors in the low brightness pixels and better gauges the success of the reconstruction of the bright, compact features in the image. Both fidelities measure the quality of image reconstruction on source, while the dynamic range measures the level of error off source relative to the brightest reconstructed feature.
Figure 1 shows the images of a series of simulations
with 
, 
, 
, and 
rms phase errors,
reconstructed with no correction, with the statistical phase
deconvolution, and with the the visibility amplitudes corrected. As
can be seen in the first column, as the phase errors increase, the
detailed structure of the source gets smeared and the flux scale goes
down. In the two correction techniques, the right flux scale is
maintained even in the presence of the largest phase errors. However,
inconsistencies in the amplitude corrected data scatter flux all over
the image, limiting the dynamic range as well as the fidelity of the
image. The statistical phase deconvolution method appears to be
superior and results in a very good reconstruction even with 70 degree
rms phase errors. Note that the point spread function used in the
statistical phase deconvolution method embodies both the loss in
resolution and the loss in sensitivity since the phase errors are
spreading the beam about and even cancelling part of the beam flux.
The resolution and sensitivity loss are represented as a function of
phase error in Figure 2. Finally, the dynamic range and
fidelities are plotted for each reconstruction scheme as a function of
rms phase error in Figure 3.