SDN 0003.27 

Grating Efficiencies

1. Introduction

This design note summarizes the grating efficiencies for the GNIRS master rulings.

Three master ruling were produced for GNIRS by Richardson Grating Lab (we will use replicas made from these.) The groove frequencies are 10.44, 31.7, and 110.5 g/mm respectively. All three are supposedly blazed for 6.79 mm in first order Littrow. This corresponds to a first order blaze wavelength of 6.60 mm for the GNIRS layout (deviation angle of 27 degrees).

The 32 and 110 line gratings were ruling conventionally (“burnishing”), while the coarsest grating was cut. Richardson uses burnishing for rulings down to about 20 g/mm, according to John Hoose.

2. Efficiency Measurements

2.1 110 g/mm Grating

The curve for this grating is shown below.

The efficiency curve is measured relative to an aluminum reference, so the total efficiency of any replica must be corrected for the reflectivity of the coating. A gold coating will reduce the peak efficiency by ~1%.

The curve is measured in fourth order, so it is directly representative of the performance in the H band. Performance in lower orders will be slightly better, while performance in higher orders should be somewhat worse.

Note that the efficiency curves for the two polarizations are somewhat different; this effect is expected. If one takes an average, the peak efficiency is just under 90%, probably around 87% is one allows for the gold coating on the replica. The efficiency is measured close to Littrow, so the peak should occur around 1.70 mm, with the 50% efficiency points at 1.52 and 1.96 mm. The curve is consistent with these values.

2.1 32 g/mm Grating

The data for the 32 g/mm ruling are shown below

The peak efficiency for this ruling is under 60% - about 55% including coating reflectivity. The locations of the peak and 50% points are expected to be the same as for the 100 g/mm grating. The peak is slightly displaced to the blue (by about 0.02 mm) and the efficiency curve is broader than the predictions (1.47-1.97 mm vs. 1.52-1.96 mm). The broader curve and the low efficiency are probably related; the cause would be some loss of flatness of the facets which act like a range in the blaze angle. If this is so, the lower orders will show better performance but the higher orders will be worse. It’s not clear to what extent the lost power in the main order will be in the adjacent orders (in which case cross-dispersed mode will pick up some of the flux), and to what extent it will be sent even further off.

2.3 10 g/mm Grating

The data for the third grating are shown below.

The peaks at the shortest wavelengths are probably artifacts of the measurement process; the test set-up will pick up adjacent orders if the dispersion is low enough (as it is here).

The peak efficiency is very good – probably over 95% even allowing for the coating. But one should note that it is significantly displaced to the red, by ~0.08 mm. The 50% points are similarly displaced. In GNIRS, the use off-Littrow shifts the curve to the blue by about 0.04 mm, but the result will still be poorer efficiency at the blue ends of the various filter passbands. In cross-dispersed use, the grating tilt should be adjusted slightly so the center wavelength corresponds to the peak wavelength, since loss in one order will be compensated in the adjacent order.

The technology for cutting gratings is supposed to produce more ghosts, according to John Hoose. We have not seen bad effects with similar rulings in the CTIO IRS, but GNIRS will be more sensitive, so we should check for them.

3. Discussion

The 110 g/mm ruling is excellent, and it is unlikely that one could do better. The other two have some problems, neither of which is fatal.

The 32 g/mm grating has low efficiency. The grating will be used primarily in cross-dispersed mode with the short cameras, and for R~5400 with the long cameras. In the latter case, the better performance of the 110 g/mm grating will likely lead people to prefer that grating with the short cameras for similar resolution. In cross-dispersed mode, there may be some gains from light picked up in adjacent orders for the higher orders.

Given the much higher efficiency of the 10 g/mm grating, one is tempted to consider attempting to cut a ruling for 32 g/mm. On the other hand, Richardson stops using this technology at ~20 g/mm based on experience. In part this is due to more ghosting. It may be worthwhile for Gemini to consider eventually replacing the 32 g/mm grating, based on performance of the 32 g/mm and 10 g/mm gratings seen in the completed instrument.

The 10 g/mm grating has excellent efficiency but the blaze peak is displaced somewhat from nominal. This will mainly affect long-slit work where critical features occur near the blue edge of the filter passband. If only a particular feature matters, it may be efficient to work in the next higher order. The error in the blaze angle is about 0.1 degree, which is consistent with the other rulings – the 32 g/mm grating has a blaze error of almost exactly the same size in the other direction (which is about 1/3 as large in wavelength). It does not appear that there is a lot to be gained here by having another ruling made.

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