IOC First Light / Focus Star S/N v.s. Telescope Temperature

Kate Su, John Stansberry, Chad Engelbracht, Erick Young, Jeonghee Rho

Photocurrent due to Star and Telescope Background

We computed the expected photocurrent from the star (HD 53501) that will be used for 24um First Light and as one of two stars in the Focus Confirmation task, the photocurrent expected from the sky, and that expected from the telescope mirrors as a function of temperature (at 33, 34, 35, and 38 K). The results are shown below in the form of radial profiles through the stellar PSF for each of the 5 backgrounds (low sky, and the 4 telescope temperatures).

The calculation assumed:

The star photocurrent was calculated based on the 24 µm point-source saturation value given in the SIRTF handbook:

Saturation in 1 sec: 5.6 Jy = 6x104 DN/1sec ( = 3x105 e-/1sec )
Saturation in 3 sec: 5.6 Jy / (3sec + 1sec dead time) = 1.4 Jy
1.2 Jy source (HD 53501) = 1.2/1.4 * 6x104 DN = 5x104 DN in 3 sec
HD 53501 = 2.5x105 e-/3sec = 8.3x104 e-/sec
In a 3 second DCE HD 53501 will produce 2.5x105 e- in the PSF peak.

An independent estimate was done using the band-integrated response values in Table 8.2 of the SOM. That calculation is described in detail here. In summary the count rate in the core of the PSF at 24 µm resulting from that is:

24 &miocro;m peak for 1Jy source = 4.2x104 e-/s = 8.4x103 DN/s
HD 53501 peak (1.2 Jy) = 5.0x104 e-/s = 1.0x105 DN/s
In other words, the responsivity calculated in this manner is only 60% of the responsivity calculated from out quoted saturation limits above. If this is the true responsivity, then the number of electrons collected at the peak of the PSF of HD 53501 in a 3 second DCE will be 1.5x105, rather than the 2.5x105 e- calculated above.

Photocurrent due to Natural Background

The conversion from surface brightness to DN/sec and e-/sec can similarly be derived from the saturation limits in the SIRTF manual:

440 MJy/sr saturates in 10sec = 6x104 DN / 10 sec ( = 3x105 e-/10 sec )
1 MJy/sr = 6x104 DN / 10 sec / 440 = 13.6 DN/s ( = 68 e-/sec )
From that we find the count rates due to natural background for various pointings of interest to be:

This estimate was also made independently using the band-integrated response values in Table 8.2 of the SOM. That calculation is described in detail here. In summary the count rates computed in this manner are:

These count rates are not as discrepant from the saturation-estimated ones for point sources, being about 94% of those. The reason for this difference is the "dead time" in the exposure which is taken into account in scaling the point-source saturation limit from 1 sec to 3 sec. That correction is negligible for the 10sec surface-brightness saturation case, but important for the 1 sec point-source case.

Results for HD 53501

We originally did these calculations using the saturation-derived count rates, and the figures and values below reflect that. As discussed above the count rate for a given source brightness is significantly uncertain (see the mips-100 cookbook for even more estimates...), so these results are likewise uncertain.

The figures below show profiles of signal (electrons collected in a 3 sec DCE) or signal to noise ratio vs. distance from the center of the PSF of HD 53501. The total count rate (star + background) assumes a very low sky background of 800 e-/second (labeled "natural bak" in the figures). To first order the effects of higher backgrounds can be seen by looking at the curves for higher mirror temperatures (although there is an unquantified effect of telescope temperature on the quality of the flat-field, as George has pointed out). Note that this calculation ignores any degradation of S/N by imperfections or low S/N in the flat-field itself.

The Focus Confirmation task is particularly sensitive to SNR within the second dark Airy ring of the PSF (at a radial distance of about 6-8 pixels). Because the analysis tool does an azimuthal average we show both the SNR per pixel (3rd plot) and SNR per pixel times distance from the center (sqrt(r^2)) (4th plot). The key features of the plots seem to be the lack of a strong relationship between SNR and telescope mirror temperature at the temperatures of interest for Campaigns D1 and D2.


Figure 1. Electrons collected at 24 µm in a 3 sec. DCE vs. distance from the center of the PSF. The various curves are for different telescope temperatures. The natural background (equivalent to the very darkest 24 µm sky) is present in all curves.


Figure 2. Same as figure 1, but the background has been subtracted. The background was calculated from the images themselves, and slight innacuracies in that value produce the slight offsets in flux within the 2nd Airy minimum around 6 - 8 pixels.


Figure 3. Signal to noise ratio per pixel, computed from
SNR = (e- from star) / sqrt( (e- from star) + (e- from background) ).


Figure 4. SNR from Figure 3 scaled to account for the fact that the Focus Characterization analysis relies on azimuthal averaging. Because of that the SNR increases as the square-root of the number of pixels in an annulus, i.e. proportionally to sqrt(r^2). For the lowest background case the SNR in the 2nd dark Airy ring is around 40 - 50. Is believed