FP-Splits White Paper

We present a summary of our analysis of a sample of observations taken with focal-plane (FP) splits. This technique is used to alleviate the fixed pattern noise in FUSE spectra. We have made signal-to-noise ratio measurements in order to determine how efficient FP-splits really are.

For Cycle 5 proposers, as simple rules-of-thumb, we recommend that:

For LWRS observations and for LiF1 observations in the MDRS slit (at least for brighter targets with relatively short required exposure times) proposals should request a total exposure time which is a factor 2 above that needed to achieve the photon-noise S/N. This is as, depending on where in each detector your wavelengths of interest are located, photon noise statistics are not allways achieved after regular length FP-SPLIT observations.

For MDRS SiC observations and for HIRS LiF1 data, where drifts in and out of the aperture causes loss of flux, we recommend that exposure times be multiplied by an additional factor 2 .

Table of Contents

1.0 Introduction

2.0 Observations

3.0 Analysis

4.0 Discussion

4.1 WD2331-475 and WD0004+300

4.2 WD2309+105

4.3 G191-B2B

4.4 HD93521

5.0 Conclusions

FUSE spectra are affected by detector fixed-pattern noise (FPN) that cannot easily be removed using traditional flat-fielding techniques. Flat-field data obtained before launch cannot be used to correct in-orbit data due to slight variations in detector pixels registration which are presumably due to thermal effects. Although the effect of fixed-pattern noise is mitigated by a combination of mirror and grating motions, the signal-to-noise in FUSE spectra is generally less than expected from pure photon statistics. Note that for LWRS observations of sufficient length, thermal motions (in X and Y) will tend to smear out the FPN at some level. The remedy that is currently recommended to alleviate the FPN problem is to use so-called focal plane (FP) splits, which consist of taking spectra at different positions on the detector. The spectra are co-aligned and combined with the expectation that the FPN will be smeared out. The technique has been used in several observations and has shown to significantly improve the signal-to-noise ratios of bright target spectra over standard non-FP-split observations. As an example, we show in Fig. 1 a comparison of the LiF1B spectrum of the hot white dwarf WD2309+105 obtained with and without FP-splits, which illustrates that the FPN has been much reduced in the Fp-split spectrum. The spectrum in the lower panel has a much noisier appearance despite similar photon statistics and exhibits the jig-saw pattern characteristic of the FPN.

Figure -1. A comparison between the LiF 2B spectrum of WD2309+105 taken with and without FP-SPLITS.

How best to conduct Fp-splits remains uncertain. For instance, is it necessary to do FP-splits at 4 focal plane assembly (FPA) positions as it is commonly done? What should be the minimum signal-to-noise ratio required per exposure? Do we really need a S/N of at least 30 per exposure to get a significant improvement over no FP-splitting or could we get comparable results with somewhat lower S/N of 20-25?

In an attempt to answer some of these questions, we have analyzed a selection of FUSE observations made using FP-splits. In section 2, we summarize the selected observations and explain our selection criteria. In section 3, we describe the technique used to measure the SNR and summarize the results for each star. In section 4, we discuss our findings and came-up with recommendations on how best to conduct FP-splits observations. We finish with a few concluding remarks.

Although there is an FPSPLIT keyword in FUSE data files headers, we found that its value is not always populated even if an observation was performed using FP-splits. We found that it is more appropriate to search the FUSE database (using A. Fullerton's fuselog) for observations for which the value of the X position of the LiF1 FPA differs from the nominal value of 117 microns. This search lead to numerous observations (over one thousand individual exposures) and further trimming of the list was thus required. In order to make meaningful S/N measurements, it is better to choose stars with spectra that are sufficiently bright (more than a few times 10^-12 erg cm^-2 s^-1 Å^-1) and with not too many photospheric or interstellar absorption lines. A natural choice would be to use DA white dwarfs stars that have been observed either as part of the calibration effort or within the D/H guaranteed time programs.

We briefly summarize the observations selected for this analysis in Table 1:

The first step in the process was to combine exposures taken at each of the FPA positions. We have also coadded the exposures from all FPA positions. Note that we excluded exposures when the target was obviously outside the aperture, which happens more frequently in the SiC channels. We have also binned the spectra by 4 pixels using the cf_arith program in CALFUSE. The spectra were converted to ASCII lists using Jerry Kriss' IRAF script listfuse and then converted into an IRAF compatible format using the IRAF task rspectext found in the onedspec package. This program linearizes the wavelength scale. The continuum normalization and signal-to-noise measurements are made using the multi-purpose IRAF task named splot with the commands 't' and 'm'. The measurements are made over carefully selected narrow spectral bands which are devoid of stellar or interstellar features. We note that for some sub-exposures, the measured S/N exceed the photon noise suggesting that the data are perhaps a bit smoothed by the data reduction procedures. We have checked that the linearization of the wavelength scale does indeed smooth the data but at a moderate level. The SNR increases by about 10 to 15%.

The signal-to-noise measurements are summarized in tables 2 to 8. The structure of all the tables is similar. Each entry in the tables corresponds to the measured signal-to-noise ratio over a given band-pass (specified at the top of the columns in units of Å below the channel name). In most cases, we list the measurements made on the combined spectra observed at a given FPA position (listed in the first column). We also provide the S/N measured on the summed spectra at the 4 FPA positions (labeled 'Summed') and the expected S/N (labeled 'Poisson'). The photon statistics S/N is listed in parentheses next to the measured value. It is computed by taking the square root of the number of counts per bin in the selected band-pass. We also find that the photon statistics S/N predicted using the FUSE exposure time calculator tool found on FUSE web-site agree well with those calculated from counts spectra.

We have made signal-to-noise measurements on FUSE observations of white dwarfs in order to quantify the improvements produced by use of the FP-split technique. This analysis will provide some guidance to guest investigators as to the exposure time required to achieve the required signal-to-noise ratio (SNR). It is generally assumed that a signal-to-noise ratio of the order of 30 per resolution element is the best that can be done with FUSE if no attempt is made to mitigate the fixed pattern noise. This number is likely a conservative estimate because it mostly applies to observations for which there was little or no grating mirror motion or channel drift.

4.1 WD2331-475 and WD0004+300

One of the main uncertainties with the FP-split technique is whether or not it is necessary to get a SNR of 30 at each sub-exposure or if a somewhat lower SNR of 20-25 would achieve comparable results. The observations analyzed here can provide some of the answers. The first two observations listed in Table 1 (P1044203/WD2331-475 and P2041102/WD0004+330) are examples of the latter case for which the SNR at each of the FPA positions is mostly in the 20-25 range (Tables 2 and 3). In both cases, the SNR of the combined spectra taken at the four positions nearly matches the expected SNR from photon statistics. This suggests that for moderately bright targets or for modest SNR requirements (in the 40-50 range), a SNR of 20-25 per FPA position is sufficient to produce an improved result.

The star WD0004+300 has been observed two additional times (P2041103 and P2041104) in FP-split mode and we expect a SNR in the range of 60-80 in the combined spectra (Table 4). The S/N level in the final combined spectra is mostly what is predicted with a few exceptions where it is about 65 percent of the expected S/N. This shows that FP-Splits are not always successful. We think that portions of the spectra were afflicted by FPN on a scale larger that could have been removed by the FP-splits. We also measured the S/N in the SiC channels and find that we mostly reached the noise level expected from photon statistics, although this star is admittedly a bit faint in the SiC channels.

The next star we analyzed, the white dwarf GD 246 (or WD2309+105), is significantly brighter and has been observed both with and without FP-Splits (Tables 5 and 6). The FP-split observation (P2042401), for which the SNR mostly exceeds 30 in each of the sub-exposures at the different FPAs positions, also leads to fairly good results. Again the SNR of the combined spectra nearly achieve what we would expect from photon statistics. As for the previous stars, the technique seems not to work uniformly well (for example over the 1052-1054 bandpass in LiF1A). Some regions of the spectra appear to be more affected by large-scale fixed pattern noise, and in those cases the FP-split technique will not be as effective.

The other observation of GD 246 we inspected, P1044101, was a regular ``fixed'' observation. It gave surprisingly good results although not as satisfactory as for the FP-split observation. Some of the measurements indicate SNR well above 30 (per 4 pixel bin), which suggests that the FPN is smoothed to certain level even in non FP-splits observations. In most band-passes, the SNR is significantly below the photon statistics SNR (by as much as 60%).

The next observation, of the standard star G191-B2B, is of interest because a dithering technique was applied. This observation was taken in the LWRS aperture and the target was moved at different positions within the aperture by applying small pointing offsets to the satellite. Note that this is not a supported observing mode with FUSE. Although decent SNR are achieved (see Table 7) in the combined spectra (in the 60-80 range), they are well below what we would expect from photon statistics. At first sight, this technique does not seem to work as well as FP-splits, although more tests could be done.

The last observation we have investigated is that of HD093521 (P1012604), which is a UV-bright star. Because it exceeds the FUSE flux brightness limit, it was observed in the SiC channels only. This case is a good test of the effectiveness of the FP-Splits for the SiC channels data. The results are summarized in Table 8. For this star, we have higher expectations, with predicted SNRs of the order of 100 (for spectra binned by 4 pixels). For the selected bandpasses, we mostly meet the predictions, which again suggests that the FP-split technique works rather well.

In general, the FP-split observation technique seems to be effective at reducing the fixed-pattern noise. In this analysis, we considered the rather simplistic shift-and-add approach, which is the approach actually utilized by the majority of observers. This technique assumes that the detector fixed-pattern noise will be averaged out the spectra taken at different position along the dispersion axis are coadded. Our analysis shows that ,at least for some band-passes, this technique effectively allows one to recover at least 70% of the SNR expected from photon statistics and even better over narrow bandpasses. The FP-splits typically shift the spectra by 40 pixels and will therefore not remove the FPN over larger scales. Some spectral regions, and even some channels, are more affected by the FPN, and in these cases we get less satisfactory improvements.

The results presented in Section 4 show that the improvement achieved by FP-splits after combining spectra from 4 sub-exposures typically behaves as one would expect from photon statistics, i.e. the SNR of the combined spectrum is about twice as large as that in each sub-exposure. Also, it seems to be independent of whether or not the SNR in each sub-exposure is in the 20-25 range or 30-40 range. This is likely a consequence of the fact that we have only done a shift and add analysis instead of a more sophisticated analysis in which one would try to solve for the fixed-pattern noise.

In an ideal situation, where there would not be any misalignment of the FUSE channels (i.e. target remains in the aperture), it would be sufficient to take spectra at four FPA positions each with an exposure a quarter of what is required for the required SNR. However, for the MDRS and HIRS apertures, thermal drifts of channels relative to LiF1 (the guide channel) cause an uncertain fraction of the light to be lost. Multiple peak-ups techniques are used to minimize this effect, but losses up to 50% of the planned integration time is common. This needs to be factored in observation planning. In that case, it would be wise to request twice the amount of exposure time. Note that FP-splits can also be performed through the LWRS aperture but are less warranted since thermal motions will in any case smooth the FPN to a certain extent. Sonneborn et al. (ApJ Suppl., 2002, vol. 140, 51) describe an LWRS FP-splits observation of the subdwarf BD +28^°4211 and reported a SNR of 100 per 0.05Å resolution element in the LiF channels and of 60 in the SiC channels near what is expected from photon statistics.

In summary:

• FP-splits are reasonably effective at reducing the FPN and can, over narrow intervals of continuum (4-5 resolution elements), procure spectra with a quality almost consistent with that expected from photon statistics.
• FP-splits do not perfectly remove the fixed pattern noise. Their effectiveness varies across the FUSE range and even seems to vary from one observation to another.
• Observers should request at least twice the exposure time needed to attain the SNR goals to compensate for loss of flux due to aperture misalignment in MDRS (and HIRS) observations.
• For the simple shift-and-add technique, it is not necessary to get a SNR in the 30-40 range per sub-exposure.
• FP-splits can be done in either LWRS, MDRS, and HIRS apertures.