also overplotted the results by blank-field ERO searches performed by Daddi et al.(2000), Roche et al.(2002), and Moustakas et al.(1997). G.P. Smith et al. (2002) surveyed lensed EROs behind 10 massive clusters of galaxies around $z\sim$0.2 to a depth of $K$ $\sim$ 20.6, and measured the surface density of 1.2 arcmin$^{-2}$ for $R_{\rm{c}}-K \geq$ 5.3. They corrected the amplification effect from gravitational lensing using their own lens model, and estimated the corrected surface densities at $K$ $\leq$ 21.6 as 2.5 arcmin$^{-2}$. The values are very similar to our result. As shown in figure 9, there is little difference between both samples at the overlapping magnitude ranges, and can be considered to be within error bars for $R_{\rm{c}}-K' \geq 5.3$ samples.

For a surface-density enhancement evaluation, we also calculated corrected surface densities in the areas which are shown in figure 3 by rectangles with dotted lines. In MS $0451.6-0305$ field, 6 EROs in $\sim$0.6 arcmin$^2$ area, and the corrected surface density is 46.2 arcmin$^{-2}$ down to $K'_{\rm{source}}=21.0$ at $z_{\rm{source}}$=3.0, or 30.8 at $z_{\rm{source}}$=1.5. In MS $0440.5+0204$ field, 3 EROs brighter than $K'=20.6$ are within 0.1 arcmin$^{2}$ area, and corrected surface density is 62.5 arcmin$^{-2}$ down to $K'_{\rm{source}}=21.0$ at $z_{\rm{source}}$=1.5. They are 