MIRLIN Sensitivity Estimates

March 27, 2002 Update

The sensitivity at Palomar is actually similar to that at the IRTF over the 10 µm window (the 20 µm window is usually opaque!). Recent observations also show a 90 mJy, 5 sigma in 1 minute, point source sensitivity at N.

March 15, 2001 Update

Sept., 2000 Update

The Data

IRTF (Jan 20, 1998 - one of the best night MIRLIN's ever had)

Palomar (Apr, 1996)

Keck (Mar 13, 1998 - a medium quality Mauna Kea night)

To make a detection prediction, grab the appropriate number from above, multiply by the desired signal-to-noise ratio, divide by the sqrt of the on-source integration length (per beam), multiply by 2 if the object will appear on-chip in only one of the four positions of a chop/nod sequence (sqrt(2) for 2 of 4, 1 for 4 of 4), and multiply by the sqrt of the area you expect the star to fill (don't be too optimistic with this one).

e.g. How faint a thing can I see at the 10 sigma level with the N5 filter using a total of 1 real hour of IRTF time? Assuming you are chopping/nodding, one hour of telescope time will give you about 12 minutes per beam. So,
40 mJy * 10 sigma / sqrt (720 sec) * 2 * sqrt (1.0 sq arcsec) = 30 mJy

Commentary

The first table (above) shows the (rather out of date) numbers for the Palomar 5-m telescope for the filters with wavelengths < 15 µm. The weather was mostly clear, but it was warm and there was a persistent thin cirrus cloud cover on all three nights; the weather was never really good enough to try any of our 20 µm filters. All values are believed to be correct as of mid-1996 and they should give you some feel for how well we are doing. (Note: we have improved various things in the system, in particular, the match of the Lyot stop to the pupil image, and the elimation of the ground noise mentioned below. Thus we should now be doing somewhat better than this.) Here is the general procedure I used to derive these numbers:

1. Obtain image of star with chop/nod mode (4 frames).
2. Place square aperture over star. Record sum of all pixels in that box.
3. Place an annulus around this aperture so that it measures only blank sky. Record standard deviation per pixel.
4. The S/N per beam is the signal (step 2) divided by the noise (step 3) divided by the square root of the number of pixels in the box times the square root of the number of frames.
5. The limiting flux is flux of the star times the square root of the single beam integration length divided by the S/N (step 4).

The above measurements were derived by looking at the standard star beta Leo on three successive nights. For all filters except M and the CVF at 10.3 µm, the chop frequency was approximately 4 - 5 Hz. The predictions are based on a spreadsheet which makes (hopefully) reasonable estimates of system throughput, atmospheric transmission as a function of wavelength, detector quantum yield, etc. While the large discrepancy at M causes me some concern (though it is likely due to the antireflection coatings on our pupil lens), the agreement to within a factor of two for the other wavelengths (given the cirrus, etc.) is very encouraging.

In the next test, the N filter was selected, the integration length was set to 6.0 msec, and the number of coadds and chops was varied to set the chopping secondary frequency. The following results were obtained:

The difference between the first table's N sensitivity and the 4-5 Hz equivalent in this table is due to the fact that there is a ground loop present in the system through the filter wheel and temperature controllers. These cables were removed for the chop frequency test and thus lowered the noise.

The IRTF numbers presented in the second table above, were obtained in Jan., 1998 when the weather was simply outstanding. The last night of the run was the best night I've had at any telescope, anywhere, with any instrument, and I don't expect to get another like it for quite some time. Thus it was a great night to show off the sensitivity ;-) The general observing procedure was the same as that for the Palomar data. A number of standards of varying brightness were observed to make certain things scaled properly. The M filter is likely discrepant due to the AR coatings; I don't know why the Q1 filter is so much worse than the model. For N, the array saturated in the shortest integration time, and the detector bias had to be reduced more than I would have liked to try this measurement; I therefore doubt this number has much bearing on reality. The Keck predictions have been scaled from the IRTF model, except for M and Q1, which were scaled directly from the measurements.

What is the difference between point source sensitivity and extended source sensitivity?

Point source sensitivity attempts to take into account how many pixels a star is blurred over and how large a false aperture one must use in order to measure the flux of that star. Extended source sensitivity merely assumes that the object is uniform over a 1 arcsecond squared box (as in the tables above). To derive the point source sensitivity, multiply the above numbers by the square root of the number of pixels in your false aperture; e.g. if you find that a 17 x 17 pixel box is appropriate, this implies a 2.55 x 2.55 arcsecond box, thus the point source sensitivity at N on Apr 22 could be expressed as 97 mJy, 1 sigma/1 sec.

All this is well and good, but how faint a source can I actually see?

This is a non-trivial question, but this is what I found. The following image panel attempts to demonstrate the technique: I took a blank sky chop/nod quartet in which there was a total of 2 minutes integration per beam (6 msec integration time, 4 coadds, 5000 chops; this is real data taken with the broadband N filter). I then added artificial point sources in a square chop/nod pattern with a randomly placed origin so I couldn't cheat too much. The PSF was gaussian with a FWHM corresponding to the diffraction limit of a 5 m telescope at 10.8 µm and I assumed it was contained completely within a 1 arcsec^2 box. I found that I could reliably see a 20 mJy source most of the time, and I could rarely see a 15 mJy source. Using our table above, if the 1 sigma/1 sec limit is 25 mJy, I was detecting the artificial source at S/N = (20 mJy / 25 mJy) / sqrt(4 frames) * sqrt(120 sec) = 4.4. Thus if you believe your source should give you a S/N of 5 or better in your integration length and aperture size, you should be able to see it. For the record, the faintest object thus far detected with MIRLIN is the blazar 1611+343 at 7 mJy in a 20 minute exposure (per beam) at Palomar.

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