same field, we can optimize to obtain an optimal product.

In this work, we make use of an updated version of the PFOF-generated group samples in MD04 and MD07 [@lin14], which are based on a set of linking lengths and threshold trained by using the spectroscopically identified group sample from DEEP2 [@ger12] in the PS1 MD07 field. The PFOF group samples are divided into two subsets, one with a richness of between 10 and 25 as the “group” sample and the other with a richness $> 25$ as the “cluster” sample. The richness cut roughly corresponds to a mass of $10^{13.2} < M_{\textrm{halo}} < 10^{13.8} M_{\odot}$ at $z$ $\sim$ 0.4 and $10^{13.4} < M_{\textrm{halo}} < 10^{14.0} M_{\odot}$ at $z$ $\sim$ 0.8, respectively. The combined catalog consists of 610 groups and 76 clusters at low redshift, and 875 groups and 61 clusters at high redshift.

![Galaxy surface density $\Sigma$ is plotted as a function of projected radius $r_p$ for the sample using real group galaxies (purple) and recovered group galaxies (green). The recovered surface density shows good consistency with the real surface density.[]{data-label="f1"}](f1.eps)

![image](f2.eps)

![Simulated quiescent fraction in 3D radius shown as a purple dashed line, while the green and gold 