IRD

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Your integration time needs to be calculated considering both the following table and fiber injection efficiency (FIE; see below). The following table corresponds to only the observation of a star that enables a good AO correction and a good fiber injection. However, the degrated FIE for fainter stars makes your sensitivity lower.

This table shows predicted exposure times to obtain SN = 100 (= 10,000 photons in a pixel corresponding to 999 and 1620 nm) for a dwarf with an effective temperature of 3000 K or 5500 K, based on the total IRD throughput measured in 2018 June. This table assumes a good fiber injection due to a good AO correction.

Note: This calculation is based on the IRD's total throughput derived by observing HR 8634 (B type) in 2018 June. The throughput calculations include the influences of the atmospheric transmission, telescope, AO188 and its ADC, spectrometer, all fibers, and detector quantum efficiency. The model spectra used to infer the number of photons are the BT-Settl models, taken from http://perso.ens-lyon.fr/france.allard/. The IRD's total throughput depends on the AO188's performance, which changes as a function of seeing and the R-band magnitude of your target star (see below). Here, only photon noise is assumed; it may be needed to include readout noise in the case of short integration and/or observation of a faint object.

Fiber injection efficiency (FIE) is a function of the R'-band magnitude of a target (see the FIE figure ). The total system throughput used for the sensitivity calculation in the above table was derived by observing a star (HR 8634) brighter than R' = 12 under a seeing condition of ~0."7 (from CFHT seeing monitor), so the tabulated sensitivity calculations are based on a relatively optimized FIE (= 0.6 at 1.0 um). If your target is fainter than R' = 12, you need to correct the sensitivity estimate to account for an FIE degradation as described below:

(1) Calculate the R'-band magnitude of your target using the formula:
R' = R - 2.5 log10(A);   A = 0.43 (R - I)^2 - 0.38 (R - I) + 1.0.
(2) Given an R'-band magnitude, assumed seeing, and a wavelength, you can infer an FIE for your target according to the FIE figure.
(3) Given a base FIE, infer the sensitivity degradation for your target as: [your_FIE] / [base_FIE]. Here, the base_FIE is assumed to be 0.6 at Y and 0.65 at H.
(4) Correct the integration time calculated from the above table, to account for the sensitivity degradation.

Assume that a hypothetical target, which has R = 14 mag, I = 12 mag, and J = 10 mag, will be observed under a seeing condition of 0."65. Thus, its R' magnitude is calculated to be 13.3. According to the figure of fiber injection efficiency (FIE), the target gives an FIE of ~0.4 at 1.0 um. The corresponding throughput degradation at 1.0 um is approximated to be 0.4 / [base FIE of 0.6] ~ 0.67. Then, the base FIE of 0.6 is assumed according to the observation of HR 8634 in 2018 June (see above). When observing this hypothetical star, you need 1/0.67 times longer integration time than the base case (see the above table). In order to get photons of 10,000 e- (i.e., SNR = 100), you need 1111 times 1/0.67 seconds ~ 1660 seconds.