\begin{table}%t5
\caption{Raw, differential number counts and galaxy densities.}
\label{counts_K}
\small%\centerline
 {
  \begin{tabular}{ccccc}
\hline
\hline
$K_{\rm{vega}}$& total    & $N_{\rm raw}$               & $N_{\rm corr}$              & $\sigma$ \\
               & counts$^a$   & $0.5$~mag$^{-1}~\rm{deg}^{-2}$ & $0.5~$mag$^{-1}~\rm{deg}^{-2}$ & \\
\hline
15    &  62    &    363  &   199    &   34	\\ 	    
15.5  &  100   &    585  &   322    &   43	\\	  
16    &  133   &    778  &   520    &   55	\\	  
16.5  &  178   &   1041  &   801    &   68	\\	  
17    &  302   &   1766  &  1374    &   90	\\	  
17.5  &  402   &   2351  &  2006    &  108	\\	  
18    &  660   &   3859  &  3462    &  142	\\	  
18.5  &  1007  &   5889  &  5514    &  180	\\	  
19    &  1309  &   7655  &  7275    &  206	\\	  
19.5  &  1881  &  10~999  & 10~614    &  249	\\	  
20    &  2671  &  15~619  & 15~157    &  298      \\
\hline
\end{tabular}}
\medskip
$^a$ Column 2 lists the raw, differential number counts per half magnitude bin. Raw number densities and differential galaxy densities after correction for star contamination are given in Cols.~3 and~4, and their $1\sigma$~error bar in Col.~5.
\end{table}