Table 2
Estimation of the limiting magnitude mT in each of the K, H, J, and R bands.
K | H | J | R | Unit | ||
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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 |
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Fried parameter | r 0 | 41 | 28 | 22 | 7 | cm |
Coherence time | τ 0 | 8.9 | 6.1 | 4.7 | 1.5 | ms |
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Telescope diameter (2r0) | D | 81 | 56 | 43 | 14 | cm |
Fringe sensor frequency (1 /τ0) | f | 112.7 | 165.1 | 211.8 | 666.7 | Hz |
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Photons per exposure | N hν | 10.7 × 106 | 5.5 × 106 | 2.7 × 106 | 0.24 × 106 | hν |
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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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