3 One-telescope equipment detection limit

Assuming standard flux calibration (Fukugita et al. 1995), we can set the detection limit in the R band. The number of collected electrons per s per pixel is

$$N = 5.7 \ 10^{4} \left (\frac{D}{1~{\rm m}} \right)^{2} \fr... ...hbox{$^{\prime\prime}$}} \right)^{2} 10^{{-0.4} (b_R - 20.5)}.$$ (1)

In the context of our example? is normalized to 1 for a sky brightness magnitude $b_R = 20.5~{\rm arcsec}^{-2}$.

Assuming Poisson statistics for the photonic signal the limit magnitude m_R for the detection of the OT is

$$m_R = 5.78 + 0.5 b_R + 2.5 \cdot {\rm Log} \left [{210~D \ov... ...} \left (\frac{\eta~\tau}{0.6} \right )^{\frac{1}{2}} \right ],$$ (2)

where $\alpha$ is the detection level and $\tau$ the exposition time; units are: D in m, d in arcsec, $\tau$ in s. For the parameters of the example this corresponds to $m_R \sim 16$.Concerning the data flux, taking into account displacement times, 10 hours of continuous accumulation would produce 24000 frames, i.e. about 1.92 Gbytes/night.