12.5 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 flat fields. CCD flat-field observations are obtained monthly. Ultimately, CCD reference flats in the pipeline should have an effective illumination of up to 10⁶ e^–/pix. Thus, it should be possible to achieve a S/N ratio of several hundred over larger spatial scales given sufficient source counts. The limitation is the temporal stability of the CCD reference flats, which show variations of a few tenths of a percent. Dithering techniques can and should be considered for high S/N CCD observations (see Section 11.3). 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 Section 7.2.4).

Two observing techniques have been employed to obtain higher S/N ratios in STIS CCD spectra of relatively bright stars. In the first method, high total counts are built up by deliberate saturation of the detector at a fixed pointing. The excess charge "bleeds" along the columns, but, for GAIN=4, the total accumulated charge is preserved in each column. In this way, S/N ratios of order 1000 have been achieved (Gilliland et al. 1999, PASP, 111, 1009; Bohlin & Gilliland 2004, AJ, 127, 3508). The second method uses spatial scanning – trailing the target along one of the long STIS slits, roughly perpendicular to the dispersion. The aim is again to build up high total counts in each spectral element, but without saturating the individual pixels in the detector. As discussed in more detail in Section 12.12, spatial scanning can enable better flat fielding, more robust removal of cosmic rays, and more complete removal of the strong fringing seen in STIS CCD spectra at wavelengths longer than about 7000 A. In a first application of this method, Cordiner et al. (2017, ApJ, 843, L2) achieved S/N ~ 600-800 in G750M spectra near 9300 A, consistent with expectations based on photon statistics. Two subsequent special calibration programs have demonstrated total flux reproducibility at a level ~30 ppm in repeated G750L spatial scans of the relatively bright exoplanet host star 55 Cnc obtained over several HST orbits (STIS September 2020 STAN).

The S/N ratio of MAMA flat fields is limited by the long integration times needed to acquire them and the limited lamp lifetimes. (See Section 16.1). S/N ratios of ~100:1 should routinely be achievable for spectroscopic observations of bright sources with the MAMAs if supported by counting statistics. If a 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 flat fields.

Kaiser et al. (1998, PASP, 110, 978) and Gilliland (STIS ISR 1998-16) 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 2x11 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 flat field 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 Section 12.5.2 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.

¹ Results obtainable in echelle modes using the FP-SPLIT slits and an iterative solution for the spectrogram and flat field.
² Results obtained using the FP-SPLIT slits and simply shifting and co-adding the spectrograms after flat fielding.
³ Results obtained using the FP-SPLIT slits and simply shifting and co-adding the spectrograms after flat fielding.

12.5.1 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 Section 11.3). 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 Section 11.3.5). For echelle modes, stepping along the slit is possible only with a long echelle slit (e.g., the 6X0.2 or 52X0.1 apertures, or one of the available but unsupported long-slit apertures), but see Section 12.2 above, and note the ameliorating effects of Doppler smearing as noted below. In practice, using the FP-SPLIT slits (see Section 12.5.2) provides a better means of dithering echelle observations.

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 Section 13.7). Such an approach for STIS data has not been attempted as of this writing.

The three scanned STIS echelle modes (E140H, E230H, and E230M), have a number of secondary wavelength settings defined with broad overlap in their wavelength coverage. Using two or more of these overlapping wavelength settings is another simple way to move a given feature to different parts of the detector.

12.5.2 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 0.2X0.2 or 0.2X0.06 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. However, since S/N=100 is routinely achieved using the normal echelle apertures, the FP-SPLIT slits are rarely used.

For the echelle modes, Doppler-induced spectral shifts, due to the variation of the projected HST spacecraft velocity along the line of sight to the target, move the spectrogram on the detector.  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 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 orbital 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 continuous viewing zone (CVZ) are scarcely affected by Doppler motion. This information on T_max is relevant only if one is trying to derive the flat-field response simultaneously with the source spectrogram (see below) and not for the straightforward flat field and shift-and-add methodology described above.

The STIS flight software automatically applies an onboard compensation for Doppler motion for echelle and MAMA medium resolution, first-order data taken in ACCUM mode (see Chapter 11). The MAMA control electronics correct (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.

Table 12.3: Effect of Doppler Shift on Exposure Times.

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 spectrum. 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 1998-16) 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 flat field and co-adding the spectrograms.

There are a number of caveats to the use of the FP-SPLIT slits to solve independently for the target spectrum and flat field. 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 target spectrum and the underlying flat field.

If one is using the FP-SPLIT slits to distinguish the signature of the flat field from the target spectrum, then Doppler smearing (and the discrete compensation for that smearing) 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.