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Table 2

Estimation of the limiting magnitude mT in each of the K, H, J, and R bands.

K H J R Unit

Wavelength λ 2.22 1.60 1.26 0.64 μm
Bandwidth Δλ/λ 0.23 0.23 0.16 0.23
Zero magnitude flux m 0 670 1080 1600 3080 Jy

Fried parameter r 0 41 28 22 7 cm
Coherence time τ 0 8.9 6.1 4.7 1.5 ms

Telescope diameter (2r0) D 81 56 43 14 cm
Fringe sensor frequency (1 /τ0) f 112.7 165.1 211.8 666.7 Hz

Photons per exposure N 10.7 × 106 5.5 × 106 2.7 × 106 0.24 × 106 hν

Limiting magnitude m 100% 13.3 12.6 11.8 9.2 mag
(phase SNR of 10) m 5% 10.1 9.4 8.6 5.9 mag

Notes. The assumptions are a seeing strength of 1.5′′, a seeing speed of τ0 =1.5 ms. From these, the telescope diameter D and the fringe tracker rate fFT can be deduced at each wavelength. The limiting magnitude mT is given in each band considering a reasonable T = 5% total transmission to the fringe tracker (T = 100% gives an indication of the transmission loss effect).

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