Comparison to measured IRCAL results

The background and limiting magnitudes for the existing camera and AO system were measured and reported in [12] and are reproduced in Table 2. The model had to be adjusted to include off-axis emission because the IRCAL cold stop is 18% oversized. Strehl ratio for the $K$ band was derived from [13] and scaled for other bands using the relation:

$$S = \tr {exp}\left[-\left(\frac{\lambda_0}{\lambda}\right)^2 \log\left(\frac{1}{S_0}\right)\right]$$ (5)

where $S_0$ is the reference Strehl (0.42 in LGS mode and 0.65 in NGS mode in the $K$-band) and $\lambda_0$ the central wavelength of the reference filter. Filter curves were derived from those displayed in the IRCAL manual on the Lick Observatory website.³

Table 2: Mt. Hamilton measured sky background by the Gemini instrument and IRCAL. IRCAL J-band sky background was not reported in [12] but estimated later. The values above are from the IRCAL manual on the Lick Observatory website.

Filter	Gemini sky b/g	IRCAL sky b/g	Total
	mag arcsec$^{-2}$	mag arcsec$^{-2}$	Throughput
J	16.1	16.0	0.08
H	14.3	14.4	0.16
K	13.0	9.3	0.13
Ks		10.3	0.14

Gemini in Table 2 is an older infrared camera and the measurements for it are taken from [14]. The sky backgrounds predicted by the ShaneAO model with no dust coating the optics and a 3% dust coating for the existing system (IRCAL) are in Table 3. The predicted values are in good agreement with the measured values.

Table 3: Mt. Hamilton predicted sky background and throughput numbers by the model of the current Shane AO system with IRCAL.

Filter	dust=0.0	dust=0.03	Avg trans
	mag arcsecs$^{-2}$	mag arcsecs$^{-2}$	dust=0.03
J	15.80	15.80	0.112
H	13.80	13.77	0.131
K	9.75	9.31	0.136
Ks	10.53	10.10	0.139

Compared to Keck, the dust fraction had to be increased to 3% to better match the IRCAL system's magnitudes and throughput. Since Mauna Kea (the site for the Keck telescopes) is at $\sim 3.5$ times the altitude of Mt. Hamilton, increasing the dust fraction for IRCAL by a similar factor seems reasonable. Coating degradation (2.5% for Aluminum and 1% for other surfaces) is the same for both comparisons.

Given the variation in NIR sky emission, the numbers in Tables 2 and 3 are in very good agreement. Further validation is provided by comparing limiting magnitudes for point sources using a natural guide star (NGS) as measured and reported in [12] and available online⁴ versus those predicted by our model in Table 4. The unusually low measured throughput in the $J$ band is not reproduced by the model but the decrease in throughput between $J$ and $H$ bands is.

Table 4: Point source limiting magnitudes (Vega system): IRCAL measured and predicted by the model (300s Fowler sample - 16 reads, SNR=5)

Filter	IRCAL	IRCAL model
	measured	predicted
J	21.8	21.46
H	20.5	20.45
K	17.8	18.15
Ks	18.3	18.34