deletions | additions       diff --git a/subsection_Sub_mosaic_Imaging_To__.tex b/subsection_Sub_mosaic_Imaging_To__.tex  index 0b18520..c6328a3 100644  --- a/subsection_Sub_mosaic_Imaging_To__.tex  +++ b/subsection_Sub_mosaic_Imaging_To__.tex 
...
g = 2^{-\left({2R_g \over \theta_P}\right)^2} \qquad \Leftrightarrow \qquad R_g = \theta_P\,\sqrt{-{\ln\,g \over 4\,\ln\,2}}  \end{equation}  where $\theta_P$ is the FWHM of the beam at the frequency of interest. For example, for $g=0.2$, $R_g=0.76\,\theta_P$. We will adopt $R_g = 0.8\,\theta_P$ at which the Gaussian response is $g=0.17$.  In Figure~\ref{fig:submosaic} we illustrate the size of a sub-mosaic of side length $L_{sub}$ relative to a primary beam of representative radius $R_g$. The data to be imaged must include fields with centers within a distance $R$  \begin{equation}  R < R_{fld} \qquad\qquad R_{fld} = 0.5\,L_{sub} + R_g  \end{equation}  of the sub-mosaic center in each dimension ($R_{fld}$ defines the bounding box of field centers). Strictly speaking, for OTFM these should be individual visibility pointing centers, but for simplicity in selection we will restrict this to field phase centers and select $R \leq R_{fld}$. This diagram also illustrates that the maximum image size that can/should be made for this data is of length $L_{img} = L_{sub} + 4\,R_g$. In practice, we will truncate this a bit to $L_{img} = L_{sub} + 2\,R_g$, which in most cases will be large enough to clean out sources outside of the edge of the sub-mosaic.  For the VLASS, the largest beam size is $\theta_P=21.1^\prime$ near 2~GHz (Figure~\ref{fig:sbandbeam}), and thus we use $R_g = 0.8\,\theta_P = 1000^{\prime\prime}$ rounding to a convenient value. Thus, for a sub-mosaic of $L_{sub}=2\,R_g=2000^{\prime\prime}$ we find all the fields within $R_{fld}=2\,R_g=2000^{\prime\prime}$ and make an image of larger size $L_{img}=4\,R_g=4000^{\prime\prime}$.