Teague introduced a phase retrieval method that uses the image shape moments. More recently, an independent
study arrived at a similar technique, which was then applied to in-situ full-field image-quality evaluation of
spectroscopic systems. This moment-based wavefront sensing (MWFS) method relies on the geometric relation
between the image shape moments and the geometric wavefront modal coefficients. The MWFS method allows
a non-iterative determination of the modal coefficients from focus-modulated images at arbitrary spatial resolutions.
The determination of image moments is a direct extension of routine centroid and image size calculation,
making its implementation easy. Previous studies showed that the MWFS works well in capturing large low-order
modes, and is quite suitable for in-situ alignment diagnostics. At the Astronomical Instrumentation conference
in 2012, we presented initial results of the application of the moment-based wavefront sensing to a fiber-fed astronomical
spectrograph, called VIRUS (a set of replicated 150 identical integral-field unit spectrographs contained
in 75 unit pairs). This initial result shows that the MWFS can provide accurate full-field image-quality assessment
for efficiently aligning these 150 spectrographs. Since then, we have assembled more than 24 unit pairs
using this technique. In this paper, we detail the technical update/progress made so far for the moment-based
wavefront sensing method and the statistical estimates of the before/after alignment aberrations, image-quality,
and various efficiency indicators of the unit spectrograph alignment process.