Note: these example use pre-launch calibration values and should not be relied
upon for planning observations.
First time users of these tools should read the associated help discussion. Note that when using MULTIACCUM, NREAD should be left at its default value of 1, except when using the MIFxxx sequences when it should be set to 8.
Example 1: Signal to Noise with Low Background
Here, the program has been used to model two sources being observed using Camera 1 through the F160W filter, see Figure 6.1. In the left panel we see the case of a 0.1Jansky (H=10.0) source. For a source this bright, we see that whenever it is observed in any mode other than Bright Object Mode (i.e., integration times longer than about 0.2 seconds), the signal to noise obtained is always the same however many readouts are made at the beginning and end of the integration.
Figure 6.1: Signal to Noise with Low Background
In these modes (ACCUM, or MULTIACCUM), the observation of the source in question is always photon-noise limited, and so the read noise of the detector is irrelevant, and the signal to noise increases roughly as the square root of the integration time. In the right panel is shown the case of a 10µ Jansky source (observed through the same filter). In this case, the number of readouts does have an effect on the signal to noise obtained for integration times less than about 1000 seconds. Where the signal to noise obtained is about 5 (integration times of a little less than a minute), increasing the number of readouts by a factor of ten can improve the signal to noise obtained by up to a factor of three or thereabouts. This example illustrates an important point: so long as the background is relatively faint, then if the signal to noise obtained is low, it is probably possible to improve it without increasing the integration time, by increasing the number of readouts. A balance should be sought between the integration time saved by doing this and any extra overhead incurred by making multiple readouts. Example 2: Signal to noise with high background
Figure 6.2 shows what happens at longer wavelengths. Here we see two sources, with fluxes of 0.1 Jansky (K=9.5) and 100µ Janskys observed through the F237M filter with Camera 2. Here the background radiation is so bright that even at very short exposure times the number of readouts makes little difference to the signal to noise obtained. For the 100µ Jy source, even when the signal to noise has dropped so low that the source is no longer detected, the number of readouts makes no difference. When the background is bright compared to the source, the observations will invariably be photon-noise limited, and so the only means of improving the signal to noise is to increase the integration time. Multiple initial and final reads are pointless in such cases.
Figure 6.2: Signal to noise with High Background
Example 3: Exposure Time Determination
Figure 6.3 illustrates the various parameters that are important in constructing a NICMOS observation, using output from the tools. We plot the flux required to obtain a signal to noise of 10, 25, 50 and 100 on a point source against integration time. Four cases are considered, and plotted in the Figure; these cases are identified as A, B, C, and D.
Figure 6.3: Effect of Parameters on NICMOS Observation
In case A, we see that we can obtain a signal to noise of 100 in an integration time of about 2000 seconds. However, the exclusion curves reveal that with such a long integration time the detector is saturated. This does not mean, however, that a signal to noise of 100 cannot be achieved for this source: it simply means that such a signal to noise cannot be achieved in a single exposure. Instead, to achieve such a high signal to noise it will be necessary to make a number of separate exposures (ACCUM or MULTIACCUM mode) and co-add the results. If the source of interest is actually fainter than this, and we merely needed to get a signal to noise of 100 on this bright target in order to get sufficient signal to noise on some nearby or surrounding fainter target, we could use MULTIACCUM mode, and repair the saturated core of this bright source. Example 4: Exposure Time Calculation for the Calibration Star P041-C
In this example we derive exposure times for the calibration star P041-C (see Table 15.4) for the purpose of characterizing the medium band filters F222M and F237M (CO band and continuum), and the narrow band filters F215N and F216N (Br 
and continuum) in Camera 2.
The K magnitude of P041-C is 10.56, corresponding to 0.037 Jansky at 2.2 microns. The star is a solar analog and we assume its color temperature to be 5800 K. The saturation diagrams produced for each filter by the WWW NICMOS exposure time calculator show that the source will saturate the two medium band filters after only 40 seconds of exposure, due to the high background which affects the 2 micron wavelength window. In the two narrow band filters, the saturation limit will be reached after an exposure of about 300 seconds. Since we want to remain well within the linear response regime of the detector, we choose exposure times which are a half of the saturation limit, namely, 20 seconds for the medium band filters and 150 seconds for the narrow band filters. With these times, the signal to noise ratio versus time diagram produced by the calculator indicates that SNR=280 in the F222M and F237M filters and SNR=315 in the F215N and F216N filters will be obtained. Such high signal to noise ratios are unlikely to be achievable, due to calibration limitations (such as flat field response and dark current); we expect, however, to be able to reach SNRs around 50-100.
Examples of Calculations by Hand
Example 1: Exposure Time for an Emission Line Source
We consider here the example of a diffuse Planetary Nebula with a diameter of 3.0 arcsecs, a Br emission line determined from the ground to have a strength of 10-13 W/m2 and negligible continuum. The surface brightness of the nebula in the line is assumed to be uniform, and the observation will be made with Camera 2 in the F216N filter. We wish to obtain a signal to noise of 20 on each pixel. Two reads at the beginning and end of the exposure will be made.
l is 9.5 x 1018 e-/sec/(W/m2), as determined by the ETC. We therefore determine the signal generated in the detector is Cl = 2.0x10-5x0.62x0.85x4.16x105 = 4.4 e-/sec.
The dark current we take to be 0.1e-/sec, from Table 7.1. The read noise from Table 7.1 is 28e- for this detector. The required signal to noise is 25.2. We can now use equation (5), and we find that the time required is 507 seconds. It must be borne in mind that this is only the on source time, and that another 507 seconds observation of the background will be required.
Example 2: Exposure Time for a Line Plus Continuum Source
In this example we consider the case of a galaxy which is to be observed with Camera 1 using the F095N and F097N filters. It is expected to have a uniform surface brightness of 0.2 Jansky/arcsec2 in the continuum and 4.2x10-15 W/m2/arcsec2 in the line. The redshift of the galaxy is 0.005. A signal to noise of 20 is required in the [SIII] line image after the continuum has been subtracted. The continuum spectral energy distribution is flat enough in this wavelength region that differences in continuum level between 0.95 and 0.97 microns can be ignored.
c from Table 6.3 is 3.83 x 104 for the [SIII] continuum filter. The pixel surface area is 1.85 x 10-3 arcsec2. Therefore the continuum signal in the F097N filter is Cc=0.2 x 3.83 x 104 x 1.85x10-3 = 14 e-/sec (from equation 1 on page 92).
In the line filter we have to consider the contributions both from the line and from the continuum. The continuum surface brightness is as used above, and the efficiency constant c is 3.45 x 104 from Table 6.3. This gives us a continuum signal of 0.2 x 3.45 x 104 x 1.85 x 10-3 = 13e -/sec. The line efficiency factor l is 4 x 1017 (e-/sec/(W/m2). Therefore, the signal generated by the line is Cl = 4.2 x 10-15 x 4 x 1017 x 1.85 x 10-3 = 3.1 e-/sec. Thus the combined signal in the F095N filter should be 16e-/sec.
The signal rates are roughly the same for the two images, so each will contribute roughly equal amounts of noise to the final image. (Note that if the continuum was much fainter than the line emission, the continuum image would contribute much less noise to the final result than the F095N image. If the item of interest is the resulting line image, it does not make sense to integrate for a long time to obtain good signal to noise on the continuum image, since it will not significantly affect the signal to noise in the final image. In our example here, both images contribute similar amounts of noise to the result, and so it is equally important to obtain high signal to noise for both images.) Therefore the signal to noise required in each image is roughly (16/31) x 20 x 20.5, or 146.
Finally, we should comment on two aspects of this proposal. First, the signal to noise being requested is very high. It is far from clear that the various calibration data needed will be of sufficiently high signal to noise to allow a signal to noise of 146 in the final product. In practice, a signal to noise of 100 is probably an impressive goal to aim for. Second, although the redshift of this galaxy is rather low, the line is on the edge of the filter curve. For sources with large redshifts, care is needed to check whether emission lines of interest fall into any of the available filters.
NICMOS Grism Sensitivity on the Web
As already mentioned, software tools are available on the NICMOS WWW pages to assist in the preparation of grism observations and proposals. These tools are exactly analogous to the tools previously described for imaging observations, and the same caveats apply. Since grism data will be difficult to interpret in the case of extended sources, these tools only deal with point sources.
Grism Sensitivity Curves
This tool is exactly analogous to the imaging tool described earlier. The same calculations are carried out in the same manner. The differences are that in this case the PSF is considered to be one dimensional only, and calculations must be carried out separately for various wavelengths inside the grism bandpass. In practice, we choose 3 wavelengths inside the grism bandpass, and carry out calculations at each of the three wavelengths for signal to noise ratios of 10 and 100. The results of this calculation were plotted in the previous section. Signal to noise for a Particular Source
To obtain a signal to noise ratio for a particular source, with known flux density and color temperature, another tool is available. Currently the source flux must be for the central wavelength of the grism bandpass; eventually it will be possible to enter the flux at one of the standard IR photometric bands. The source currently is represented by a blackbody spectrum; eventually it may be possible to adopt a model atmosphere spectrum, or enter a user-supplied spectrum or a power-law continuum. The output from this code is time against wavelength for a set of signal to noise ratios (currently 10, 25, 50 and 100). Saturation and Detector Limitations
Again, this tool is analogous to the corresponding image mode tool. It generates the fluxes required to saturate the detector and for the photon noise to exceed the detector noise as a function of time. In principle this information should be calculated as a function of wavelength; however, since the sensitivity inside the grism passbands is only very weakly a function of wavelength, we carry out the calculations only for the central wavelength. Departures from this value will only be significant for wavelengths near the ends of the spectrum where the grism throughput is changing rapidly. WWW Access to Grism Tools
If you select the grism spectra option, you will be offered choices almost identical to those for the imaging tools, except that now only one camera (Camera 3) is available.