= \left\{r(z) \vec{\theta},~ r(z)\right\}$, where $r(z)$ is the comoving distance to $z$. Note that the above expression does not include the effect of the peculiar velocities of the gas in the IGM.

-   We use the one-dimensional ${\delta T_{\rm b}}$ profile to generate the spherically symmetric ${\delta T_{\rm b}}$ map in the simulation box. The comoving length and grid resolution of the simulation box in the angular directions are determined by $\theta_{\rm max}$ and $\Delta \theta$ respectively. The same two quantities along the line of sight are determined by the frequency band width ($B_\nu$) and frequency resolution ($\Delta \nu_c$) of the observation.

-   We generate the two-dimensional baseline distribution (or $uv$ coverage) $n^{i,j}_{\rm B}$ in a $N_{\rm pixel}\times N_{\rm pixel}$ grid for $t_{\rm obs}^{uv}=4$ h of observation at a region with declination $\delta_{\rm dec}=-30^{\circ}$, while the integration time is taken as $\Delta t_{c}=$10 sec. To incorporate the effect of the empty pixels in the two-dimensional baseline distribution, we first obtain the visibilities of the signal at each $uv$ grid point and then multiply the signal with the baseline ($uv$) sampling function, i.e., zero at $uv$ grids which are empty and unity otherwise. We then obtain the final image (which is 