Grating and Grism efficiency plots

Old Red side data

Table of Contents

Summary

The efficiency of the LRIS in the spectroscopic mode is measured from observations of standard stars taken with a slit 4 arcsec wide. The efficiency at the peak of the blaze is found to be 34% for the 300 g/mm grating, 40% for the 600 g/mm grating, and at least 36% for the 1200 g/mm grating. This efficiency includes the optics internal to the LRIS and the LRIS detector. The losses in the two telescope mirrors and in the earth's atmosphere have been removed. These numbers are uncertain by a few percent because of lack of knowledge of the exact reflectivity as a function of wavelength of the Keck telescope mirrors.

The efficiency for the spectroscopic mode of the LRIS under the most favorable circumstances (coincidence of the wavelength of the grating blaze and of maximum quantum efficiency of the LRIS detector) predicted in writing by Bev Oke prior to completion of the instrument was 38%.

An example is given of how to use the data in this document to predict count rates in LRIS exposures.

I. Introduction

The efficiency of the LRIS in the spectroscopic mode is determined using spectra of standard stars taken through a slit 4 arcsec wide (to ensure that all the stellar light goes through the slit into the spectrograph). This analysis was carried out in a preliminary way by Bev Oke in 1993; here we expand on his earlier work. Data from two photometric nights (February 24 and 25, 1995) with good seeing, under 1 arcsec in both cases, were used, and standard stars were chosen from the list of Oke (1990).

The spectra available, all taken by myself during my personal observing time, are listed in Table 1. They provide full coverage of the wavelength regime for the 300 g/mm grating, reasonable coverage for the 600 g/mm grating, and partial wavelength coverage for the 1200 g/mm grating.

Note that G191B2B is an extremely blue star. Classified as a DA0, it has AB(4000) - AB(7000) = -1.07 mag. Thus an order blocking GG495 filter was used on the longest wavelength exposure of it with the 600 g/mm grating. Without this filter, contamination of the red spectrum of this very blue star by second order blue light is apparent at wavelengths longer than 7000Å. An order blocking filter perhaps should have been used for the 8200Å spectrum with the 300 g/mm grating of G138-31, but this star is much redder with AB(4000) - AB(7000) = +0.54 mag, so contamination from the overlapping second order blue spectrum can perhaps be ignored.

To aid in planning observations, I have calculated the efficiency of LRIS. Here I have removed the earth's atmosphere using a mean extinction curve for Mauna Kea from the CFHT (Boulade 1987, Beland, Boulade, and Davidge 1988). The area of the Keck telescope primary mirror is taken as 72.295 m^2, the value given for the net usable primary area in the f/15 configuration with the baffles retracted in Nelson (1994). I have also removed the reflection losses at the primary and secondary telescope mirrors using the standard curve for the reflectivity of aluminum given in the Handbook of Physics (3rd edition, 1972, table 6g_2) scaled to a reflectivity of 86% at 6700Å (Bida 1995). One can change the results by a few percent by adopting different assumptions regarding the mirror reflectivity as a function of wavelength and its normalization.

Thus the efficiency determined here for LRIS includes those optical elements interior to LRIS, the collimator, the lens camera, and the grating, as well as the detector. The last two of these dominate the losses.

I have also computed from the observed spectra the detected electrons/sec/pixel above the atmosphere for a star with AB = 20 mag for each of the 3 gratings over the available wavelength range. The AB system is defined in Oke and Gunn (1983), and for AB = 20 mag, the flux f_nu = 3.6×10^-28 ergs/cm^2/sec/hz independent of wavelength. The approximate relationship between the AB and Johnson magnitude systems is given in Table 2 using the absolute calibration for the the latter from Section 97 of Allen (1973).

Tables 3, 4, and 5 list the efficiency and the expected detection rate (detected electrons/sec/pixel in the dispersion direction, i.e. summed along the length of the slit) for an object with AB = 20 mag for the three gratings currently in use with LRIS. Note that the detection rate is extrapolated to airmass 0.0, i.e. above the atmosphere.

The peak efficiency is 34% at the blaze of the 300g/mm grating, 40% at the peak of the blaze of the 600g/mm grating, and 36% (or perhaps slightly higher) at the peak of the blaze of the 1200 g/mm grating. As expected, the efficiency falls as one moves away from the blaze of the grating. The detected electrons/sec/pixel behaves in a manner that can be explained by recalling that the dispersion (Å/pixel on the CCD) decreases by a factor of 2 between each grating. That parameter too shows a rolloff away from the grating blaze. Throughout, the quantum efficiency of the CCD is also included, but it varies somewhat more slowly with wavelength than does the grating efficiency.

The LRIS Manual of Operations (Oke 1993) gives detailed estimates made prior to completion of the instrument of the transmission or reflectivity of the various optical elements in LRIS (including the CCD quantum efficiency as a function of wavelength). The maximum predicted efficiency for the spectroscopic mode, which occurs when the wavelength of the peak of the CCD quantum efficiency curve coincides with that of the grating blaze, is 38%. It is gratifying that the instrument as constructed comes so close to the predicted efficiency.

The figure for the 300 g/mm grating (Figure 1) has four sections. In the first, the raw data for the frame with the central wavelength of 6200Å is presented. The only processing done here is that sky and bias levels have been subtracted. No flattening corrections were applied during the analysis; it was assumed that summing along the slit would average things out sufficiently for these bright stars. The discontinuity in the middle of the spectrum is due to the small difference in the gain of the electronics for the two readout chains used for each half of the CCD. Occasional cosmic ray hits are apparent in the raw data.

The second panel of Figure 1 contains the detected elecrons/sec/pixel in the dispersion direction summed along the slit extrapolated to airmass 0 (i.e. above the atmosphere) for this spectrum. The dashed line is the flux in micro-Janskys of this standard from Oke (1990). The third panel shows the efficiency from the two specra available with the 300 g/mm grating, while the fourth shows the predicted detection rate above the atmosphere for AB = 20 mag.

The figure for the 1200 g/mm grating has the same 4 panels as does that of the 300 g/mm grating. Note that the peak efficiency here is at least 34%.

The figure for the 600 g/mm grating is similar except that only the efficiency and predicted detection rate (electrons/sec/pixel in the dispersion direction) extrapolated to airmass 0 (i.e. above the atmosphere) for AB = 20 mag are presented.

1. E₅₃₀₀ = system efficiency at 5300 Å
2. S₅₃₀₀ = observed signal [photons/sec/pix] for an AB=20 mag star at 5300 Å
3. E₆₆₀₀ = system efficiency at 6600 Å
4. S₆₆₀₀ = observed signal [photons/sec/pix] for an AB=20 mag star at 6600 Å
5. E₉₅₀₀ = system efficiency at 9500 Å
6. S₉₅₀₀ = observed signal [photons/sec/pix] for an AB=20 mag star at 9500 Å with GG495 filter

1. E₆₂₀₀ = system efficiency at 6200 Å
2. S₆₂₀₀ = observed signal [photons/sec/pix] for an AB=20 mag star at 6200 Å
3. E₆₆₀₀ = system efficiency at 6600 Å
4. S₆₆₀₀ = observed signal [photons/sec/pix] for an AB=20 mag star at 6600 Å

III. Prediction of Count Rates for Planned Observations

Here is an illustration of how to use the data in Tables 3, 4 and 5 for planning observations. We wish to observe an object whose V magnitude is 22. We assume that this is representative of the continuum flux, i.e. there are no strong emission lines. We plan to use the 300 g/mm grating and are interested in the predicted count rate at 5500Å.

From Table 3, we find that we can expect 5.0 detected electrons/sec/pixel above the atmosphere. If we observe at the zenith, we need to correct this for the transmission of 1 atmosphere. Since many people may not have ready access to the CFHT Bulletins, Table 6 gives the atmospheric extinction for Mauna Kea for blue wavelengths from Beland, Boulade, and Davidge (1988). (The extinction, except in the vicinity of the strong atmospheric absorption bands, in the region from 6500 to 10000Å is below 10%/airmass.)

The observed electrons/sec/pixel in the dispersion direction will thus be 0.895×5.0 for an object with AB = V = 20 mag, and 0.895×5.0×0.159 for the object of interest with V = 22 mag, or 0.712 detected electrons/sec/pixel along the dispersion direction.

To predict signal-to-noise ratios and exposure times one need to fold in 3 more factors, the slit loss, the sky brightness, and the seeing (or the spatial extent, if the object is not a point source), as well as the CCD performance (i.e. readout noise). The slit loss for a point source is determined by the slit width and the seeing. Point sources are extended in the spatial direction (along the slit) in accordance with the seeing and the scale of the LRIS camera, 4.67 pixels/arcsec.

References

• Allen, C. R. 1973, Astrophysical Quantities, 3rd edition
• Bida, T. 1995 (private communication of measurements of mirror reflectivity carried out at Keck)
• Beland, S., Boulade, O., & Davidge, T. 1988, CFHT Info. Bull., 19, 16
• Boulade, O. 1987, CFHT Info. Bull., 17, 13.
• Nelson, J. 1994, ``Keck Observatory Properties,'' Keck Observatory Report 209, available from CARA
• Oke, J. B. 1990, AJ, 99, 1621
• Oke, J. B. 1993, Manual of Operations for LRIS, available from CARA
• Oke, J. B., & Gunn, J. E. 1983, Ap.J., 266, 713