Efficiency Calibrations

Although we can predict the efficiency of the PN.S component-by-component, what we ultimately want to know is the real-world efficiency, measured empirically on the telescope.

Standard stars

We begin by using some standard stars for flux calibrations. The procedure is to take a short dispersed exposure of the star, centred in the image to eliminate vignetting effects. We take the total flux from the star in a central column of its dispersed image (where the dispersion is along the x-direction). This will result in an approximation for the measured flux at a given wavelength -- a more accurate calculation would integrate over the filter response curve and the seeing profile. But as long as the instrument response curve (including filter) is very flat over the spectral range subtended by the seeing circle, the approximation is very good; (for Filter #1, good for seeing with FWHM << 3").

This procedure is illustrated by the following image, where the yellow box shows the pixels used for the stellar flux:

Here following are descriptions of efficiency measurements using standard stars, with a summary table at the end.

BD +33 26 42
The first star is BD +33 26 42. The first left-arm exposure is #3175. After subtracting off the background level, a single central column is found to have 10205 counts from the star. With a gain of 2.3, this gives 23500 e-. The expected photon count calculation begins by using a flux table (see the ING and ESO webpages); note the tabulated Oke standards should have 0.04 mag subtracted off, though it isn't entirely clear if this has already been done or not. The flux of this star at 5028.2Å (the estimated peak throughput wavelength of our filter) is 2.2594x10-13 erg/cm2/sec/Å. With a photon energy of 3.9506x10-12 ergs and a telescope collecting area of 124700 cm2, this gives a flux at the instrument of 7132 photons/sec/Å. With our instrumental dispersion of 0.776 Å/pixel, and an exposure time of 30.0 sec, this gives 166000 photon counts in a column.

So the efficiency of the left arm is 23500 / 166000 = 14.1%. To subtract the effects of air/dust extinction, we take an estimated exctinction relation of 0.128 mags/airmass (see CMT webpage), and an airmass of 1.0065. This leaves a "vacuum" efficiency into the left arm of 15.9%. A similar calculation for the same exposure into the right arm gives 17.4%, for a total instrument efficiency (telescope + instrument + detectors) of 33.3%.

Six exposures of this star were taken in succession during a focussing operation. The efficiency came out nearly the same for all of them: 32.1% with a scatter of < 0.2%. This implies that the throughput is reliable/stable over short time scales.

Three nights later the same star was observed again, with the CCDs in the slow rather than fast readout mode. The calculation this time is rather iffy because the seeing was very poor, causing some spectral blending with an adjacent faint star. The estimated total efficiency in this case (accounting for the blending effects) is 34.3%.

Feige 110
We next compare the standard star Feige 110. With two exposures of 120.0 sec each, we calculate a total efficiency of 29.1% (13.8% left, 15.3% right). However, at this point in the night of 16 Jul, the dust content was rapidly increasing, so the extinction correction could be significantly off.

Feige 15
With two exposures on Feige 15 of 120.0 sec each, we find a total efficiency of 28.9% (13.8% left, 15.1% right). Again, the dust content was uncertain, and the source flux calibration (Stone) was low-resolution, introducing an additional uncertainty. Another exposure three nights later gives 34.1% efficiency (16.4% left, 17.7% right). In this case, the sky background has a strong gradient, which may not be sufficiently subtracted.

BD +25 39 41
This star has one exposure at either end of the last night, each with a very different airmass. In principle, this could allow us to solve for the actual extinction, but doing so gives a total efficiency of 43.1%, which seems unrealistic. Note that the exctinction could vary over the night anyway.

The average efficiency for the two exposures is 36.0% (17.2% left, 18.8% right). However, the source is again low-resolution, and one of the exposures has a strong sky gradient.

BD +28 42 11
This star has one exposure, giving a total efficiency of 32.8% (15.6% left, 17.2% right). Again the sky gradient is large, and there is a bad row (bleed?) that may cause problems.

BD +17 47 08
This star was observed on 18 Jul, when there was a large amount of dust evident in the atmosphere. The CMT monitor was apparently down, so we don't have an estimate for the extinction. Taking a value of 0.2 mag/airmass for the extinction, which is probably a lower limit, we find for the one centred image a total efficiency of 31.9% (15.1% left, 16.8% right).

Also taken were images with the star in each of the four corners of the field of view. This gives a rough idea of the vignetting function. The total efficiency at a distance of 5.7 arcmin from the field centre is still about 28.2%.

Below is a summary table of efficiency calculations. Note that these values have not yet been corrected for the 0.04 mag offset of the Oke calibrators.

Name Exposure effleft effright efftot caveats
BD +33 26 42 3175/76 15.3 16.8 32.1
BD +33 26 42 3177/78 15.3 16.6 31.9
BD +33 26 42 3179/80 15.3 16.8 32.1
BD +33 26 42 3181/82 15.4 16.6 32.0
BD +33 26 42 3183/84 15.6 16.7 32.4
BD +33 26 42 3185/86 15.6 16.7 32.3
BD +33 26 42 avg of 16 Jul 15.4 16.7 32.1
BD +33 26 42 3688/89 16.2 18.1 34.3 blending with adjacent star
BD +33 26 42 3378/79,etc 3.9 3.6 7.5 intermittent clouds
BD +33 26 42 3390/91 4.5 4.8 9.3 intermittent clouds
Feige 110 3279/80 13.9 15.4 29.2 uncertain extinction
Feige 110 3281/82 13.8 15.2 29.0 uncertain extinction
Feige 110 average 13.8 15.3 29.1 uncertain extinction
Feige 15 3283/84 13.8 15.2 29.0 low-res source calibration; uncertain exctinction
Feige 15 3285/86 13.8 15.0 28.7 low-res source calibration; uncertain exctinction
Feige 15 avg of 16 Jul 13.8 15.1 28.9 low-res source calibration; uncertain exctinction
Feige 15 3750/51 16.4 17.7 34.1 low-res source calibration; strong sky gradient
BD +25 39 41 3690/91 18.0 19.3 37.2 low-res source calibration
BD +25 39 41 3752/53 16.4 18.3 34.7 low-res source calibration; strong sky gradient
BD +25 39 41 average 17.2 18.8 36.0 low-res source calibration; strong sky gradient
BD +28 42 11 3754/55 15.6 17.2 32.8 strong sky gradient; bad row
BD +17 47 08 3597/98 15.1 16.8 31.9 low-res source calibration; unknown (high) extinction -> prob. lower limit on eff
BD +17 47 08 3599/600 13.9 14.2 28.1 vignetted; low-res source calibration; unknown (high) extinction -> prob lower limit on eff
BD +17 47 08 3601/02 13.0 15.6 28.7 vignetted; low-res source calibration; unknown (high) extinction -> prob lower limit on eff
BD +17 47 08 3603/04 13.5 15.2 28.8 vignetted; low-res source calibration; unknown (high) extinction -> prob lower limit on eff
BD +17 47 08 3605/06 14.1 13.4 27.4 vignetted; low-res source calibration; unknown (high) extinction -> prob lower limit on eff

In principle, looking at the sources at different airmasses (different sources at same time, same source at different times) could resolve the uncertainties about the exctinction level. But trying this with these data produces very inconsistent results.

The net result of all this is that we had only one reliable standard star measurement, that of BD +33 26 42, which gives a total efficiency of 32.1%. The sources of uncertainty include: the "central column" approximation (?%), the measurement uncertainty (0.2%), the extinction uncertainty (2%), the calibrator uncertainty (1%), and the gain uncertainty (2%?). So our estimate for the efficiency can be stated as 33.3%±1.0%. This compares very well with the predicted throughput of 33.0%. Note also that changes were made in the readout mode of the CCDs after observing this star. It will be important to get a better series of standard star observations in our next run.

Galactic PNe

We obtained images of several PNe in our own galaxy with known 5007Å line fluxes, for comparison...

Extragalactic PNe

There were a number of fields taken in nearby galaxies with PNe with previously measured magnitudes m5007. These included: M31, M32, M110, NGC 185, And IV, M51, M101. These will be somewhat tricky to compare because the low velocities put them on the edge of our filter bandpass. For some of them, we will also have to first do a full velocity calibration of the instrument...

last modified by AJR, 8 August 2001