High Signal-to-Noise Ratio Observations

The maximum achievable signal-to-noise (S/N) ratio of STIS observations for well exposed targets is, in general, limited by the S/N ratio and stability of the flatfields. CCD reference flats are obtained monthly. Ultimately, CCD flats in the pipeline should have an effective illumination of up to 10⁶ electrons/pixel. Thus, it should be possible to achieve a S/N ratio of a several 100 over larger spatial scales given sufficient source counts. The limitation is the temporal stability of the CCD reference flats, which sow variations of a few tenths of a percent. Dithering techniques can and should be considered for high S/N CCD observations (see "Patterns and Dithering" on page 229). The realizable S/N ratio for spectroscopy will be less in the far red due to fringing, unless appropriate fringe flats are applied (see the caveats on long-wavelength spectroscopy in the red in CCD Spectral Response).

Observations of bright sources using the MAMA detectors may not match the S/N ratios achievable with the CCD, both because the S/N ratio of the MAMA flatfields is limited by the long integration times needed to acquire them (see Summary of Accuracies), and because the MAMA flats may be somewhat time variant (see MAMA Signal-to-Noise Ratio Limitations). S/N ratios of ~50:1 should routinely be achievable for spectroscopic observations of bright sources with the MAMAs if supported by counting statistics. It is possible to achieve even higher S/N ratios (>100:1 per wavelength bin), given sufficient counts from the source. If your program requires high S/N ratios, we recommend using some form of dithering (described below) and co-adding the spectrograms to ameliorate the structure in the flatfields.

Kaiser et al. (1998, PASP, 110, 978) and Gilliland (STIS ISR 98-16) reported quite high S/N ratios for spectrograms of bright standard stars obtained during a STIS commissioning program. The realizable S/N ratio depends on the technique used to correct for the flat-field variations, as shown in Table 12.2. The S/N ratios quoted are for wavelength bins from an extraction box of 2 x 11 lowres pixels (2 in AXIS1 or dispersion, 11 in AXIS2 or across the dispersion). In the table, the Poisson limit is just the S/N ratio that would be expected on the basis of counting statistics alone; "No Flat" means the realized S/N ratio without applying any flatfield at all to the data; "Reference Flat" means the realized S/N ratio after applying the best available reference flat, and the "Full FP-SPLIT Solution" is discussed under FP-SPLIT Slits for Echelle Observations below. Clearly, S/N ratios in excess of 100:1 per resolution element are well within the capabilities of the MAMAs for spectroscopy.

Table 12.2: Results of S/N Ratio Tests with STIS MAMAs in Orbit

Grating	Poisson Limit	No Flat	Reference Flat	Full FP-Split Solution1
E140M	470	200	3602	390
G140L	295	90	180	N/A
E230M	400	250	320 2	380
G230M	200	100	150	N/A

1 Results obtainable in echelle modes using the FP-SPLIT slits and an iterative solution for the spectrogram and flatfield. 2 Results obtained using the FP-SPLIT slits and simply shifting, and co-adding the spectrograms after flat-fielding.

Dithering

In first-order spectroscopic modes, improved S/N ratios can be achieved by stepping the target along the slit, taking separate exposures at each location, which are subsequently shifted and added in post-observation data processing (pattern=stis-along-slit, see "Patterns and Dithering" on page 229). This stepping, or dithering, in the spatial direction effectively smooths the detector response over the number of steps, achieving a reduction of pixel-to-pixel nonuniformity by the square root of the number of steps, assuming the pixel-to-pixel deviations are uncorrelated on the scale of the steps. In imaging modes, the same dithering can be done in two dimensions, i.e., the steps need not be along a straight line (see "Dither Strategies" on page 234). For echelle modes, stepping along the slit is possible only with the long echelle slit (6"x0."2), but see long-slit echelle spectroscopy, above, and note the ameliorating effects of Doppler smearing as noted below.

In a slitless or wide-slit mode, stepping along the dispersion direction provides another method to achieve high S/N ratio data. Data so obtained permit, at least in principle, an independent solution for spectrogram and flat field, but at a cost of lower spectral resolution and line-profile confusion due to the wings of the LSFs transmitted through a wide slit (see "Spectral Purity, Order Confusion, and Peculiarities" on page 355). Such an approach for STIS data has not been attempted as of this writing.

FP-SPLIT Slits for Echelle Observations

A special kind of dithering in the spectral direction is possible for echelle-mode observations with one of two sets of fixed-pattern (or FP-SPLIT) slits. These slit sets are each comprised of a mask with five apertures that are all either 0."2 x 0."2 or 0."2 x 0."06 in size. A schematic of the configuration is shown in Figure 12.4. During a visit, the target is moved from one aperture to another, and the slit wheel is repositioned, so that the spectrogram is shifted (relative to the detector pixels) along the dispersion direction only. The slits are spaced to place the spectrogram at different detector locations, so that flat-field variations can be ameliorated by co-adding many such spectrograms. The FP-SPLIT slits can be a good choice for obtaining high S/N ratio echelle data, since it is usually not possible to dither in the spatial direction.

Figure 12.4: Schematic of the STIS Fixed-Pattern Slit Configuration. AXIS1 corresponds to the dispersion direction, and AXIS2 to the spatial direction. Dimensions are not to scale. 

With echelle modes, Doppler-induced spectral shifts move the spectrogram on the detector. In reality, the STIS flight software automatically applies an onboard compensation for Doppler motion for echelle and medium-resolution, first-order data taken in ACCUM mode (see Chapter 11). The MAMA control electronics corrects (to the nearest highres pixel) the location of each event for the Doppler shift induced by the spacecraft motion prior to updating the counter in the image being collected. Thus, the flat-field correction for any image pixel would be an appropriately weighted average over a small range of nearby pixels and the effect of spacecraft-induced Doppler shifts is therefore to naturally provide some smoothing over the flat fields in the echelle modes.

The source of the Doppler-induced spectral shifts during an exposure is the variation of the projected HST spacecraft velocity along the line of sight to the target. Column 2 of Table 12.3 gives the maximum shift in highres pixels that would apply, based upon an HST orbital velocity of ~7.5 km/s during an orbit. The actual shift will of course depend upon the cosine of the target latitude, i, above or below the HST orbital plane, and upon the sine of the orbital phase at which the exposure is obtained. (Note that in general the observer can predict neither the latitude nor the orbit phase of the exposures in advance with any precision.) Column 3 gives, for a target lying in the HST orbit plane, the maximum duration of an exposure for which the Doppler shift will be one highres pixel or less; the actual duration will scale as sec(i), so that targets near the CVZ are scarcely affected by Doppler motion. This information on T_max is relevant only if you are trying to derive the flatfield response simultaneously with the source spectrogram (see below) and not for the straightforward flat-field and shift-and-add methodology described above.

Table 12.3: Effect of Doppler Shift on Exposure Times

Grating	Maximum Doppler Shift (hi-res pixels)	Tmax1 (minutes)
E140H	11.41	2.7
E140M	4.59	7.0
E230H	11.41	2.7
E230M	3.00	11.3

1 For inclination i = 0; actual duration will scale as sec (i). See text for details.

Obtaining the Highest S/N Ratio with the FP-SPLIT Slits

As described above, the FP-SPLIT slits have been used with the echelles to provide signal-to-noise as high as ~350 with the direct shift-and-add method. Additionally, data obtained with the FP-SPLIT slits make it possible to solve independently for the fixed-pattern (i.e., the flat-field variation) and the source spectrogram. An iterative technique for combining FP-SPLIT data was applied successfully to data obtained with GHRS (see Lambert et al., ApJ, 420, 756, 1994), based on a method described by Bagnuolo and Gies (ApJ, 376, 266, 1991). This same technique was applied by Gilliland (STIS ISR 98-16) to STIS observations of a standard star. The S/N ratio that was achieved with these slits is summarized in the last column of Table 12.2, which shows that the FP-SPLIT slits can offer some advantage when one is attempting to achieve the highest possible S/N ratio. In general, though, it may be difficult to improve upon the S/N ratio that can be achieved by simply calibrating with the standard flatfield and co-adding the spectrograms.

There are a number of caveats to use of the FP-SPLIT slits to solve independently for the spectrogram and flatfield. The most notable is that the targets must be relatively bright point sources. The restriction to bright targets results both from the need to limit the duration of individual exposures to keep the Doppler-induced spectral shifts to less than one highres pixel, and from the need to have appreciable counts in the individual exposures-at least in the orders of interest. Very high counts in the sum of all exposures are essential for a good (and stable) solution to both the spectrogram and the underlying flatfield.

If you are using the FP-SPLIT slits to distinguish the signature of the flatfield from the target spectrogram, then Doppler smearing (and the discrete compensation) will defeat that solution. In this case, the exposures must be kept as short as if there were no Doppler compensation at all, if the goal is to solve for the pixel-to-pixel variation at a precision higher than that of the available flat-field reference files.

The utility of FP-SPLIT observations is also limited by the modest range of slit offsets in wavelength space, and by the distribution and character of the features in the target spectrum itself. That is, if the spectrum in the order(s) of interest is dominated by absorption over a width comparable to or larger than the largest offset range, the solution may not be stable or unique. A corollary is that some of the spectral orders must contain moderately prominent spectral features with good signal in order to distinguish the spectrum from flat-field variations. Table 12.4 gives the FP-SPLIT offsets for each grating, including offsets in Ångstroms for typical central-wavelength settings.

Table 12.4: Magnitude of Spectrogram Offset for the FP-SPLIT Slits

Grating	Minimum Offset (hires pix)	Maximum Offset (hires pix)	CENWAVE (Å)	Max. Offset @CENWAVE (Å)
E140H	2.128	26.383	1416	0.164
E140M	2.778	34.444	1425	0.535
E230H	2.128	26.383	2390	0.277
E230M	2.857	35.429	2340	1.382

A final complication concerns the ability of the MSM to move the slit wheel from one FP-SPLIT slit to the next such that the spectrogram is offset in the spectral direction only. Experience in orbit suggests that such a one-dimensional shift is typical, but that both the uncertainty in the MSM repeatability and thermal changes in the STIS optical bench can result in shifts of more than one lowres pixel in the spatial direction. In this case the solution for the underlying flatfield would have to be generalized to two dimensions to achieve the highest accuracy.