The LETG/HRC-S spectral extraction region has a 'bow tie' shape,
narrow in the middle and widening on the outer plates to accommodate the
inherent astigmatism of the LETG's Rowland-circle geometry.
The figure at right (vertical axis highly stretched)
is based on MARX simulations;
the true spatial distribution of the dispersed spectrum
differs in several small but sometimes significant ways from the ideal:
Together, these effects can add up to deviations of more than ± 6 pixels in the tg_d direction (near the plate ends), although errors are more typically 1 or 2 pixels. For comparison, the current extraction region half width is 12.45 pixels (80 μm, 5.31e-4 deg) in the central region. At 170 Å the half width is 42.1 pixels (270.7 μm, 19.96e-4 deg).
The intention of our analysis is to straighten and align dispersed spectra, and then calibrate the intrinsic cross-dispersion profile. We can then define a narrower spectral extraction region which will contain nearly the same enclosed energy fraction (EEFRAC) as the current region but a proportionally smaller background signal. The result is a better calibrated EEFRAC only 1-2% smaller than the original with ~25% (TBD) less background.
We use bright, frequently observed continuum sources to provide complete wavelength coverage with high signal. Mkn421 and PKS2155 are used for short wavelengths (<~60 Å) and HZ43 for longer wavelengths. Emission lines from Capella, a bright coronal source, are used to tie together the short- and long-wavelength calibration. All the observations we use were made on-axis (Yoffset=0) and were processed to Level 2 using the latest CALDB. The LETGS Background Filter was then applied, and time periods with DTF<0.98 (indicating significant background flaring) were removed to improve S/N. HRC background is also spatially nonuniform during flares. (Show figure? BG crowned as f(crsu), LESF shadow, nonuni as f(crsv?). Why would it be crowned across short axis?)
tg_d profiles are extracted for each dispersion-axis tap (crsv) with the implicit assumption that profiles are (over short spatial scales) predominantly a function of location along the detector rather than a function of wavelength. Analysis of a few off-axis observations confirms this. Binning by tap typically provides a few thousand events (and thus centroiding errors of a couple/few percent of the profile FWHM) and good sampling of the dispersed spectrum's wiggles. Within a tap, tg_d is binned by 0.00005 degrees (~1.2 pixels) on the central plate and 0.00007 to 0.00010 degrees on the outer plates (where the profiles are wider--see Fig. 1). Wider bins may obscure detail while narrower bins may have too few counts, causing interpolation errors.
The findcenter.f program reads the tg_d profile data and computes medians (50% of events below and above) as well as tg_d values for cumulative fractions of 1, 2, 3, 4, 5, 10, and 25% (and 75 ... 99%) of net (background-subtracted) events, with interpolation between bins for greater accuracy. The background level is determined from counts in the range tg_d=-0.023:-0.013,0.012:0.0205 for the negative order and tg_d=-0.026:-0.015,0.012:0.0205 for the positive order. Background is not perfectly flat, but these ranges provide a good estimate of the level under the primary dispersed spectrum. Cross-dispersion orders 1--4, important at short wavelengths (see the faint "whiskers" of orders 1 and 2 in Fig. 1), are excluded when determining the background level, but not when determining the cumulative count fractions (which are relative to the total counts falling interior to the background regions, i.e., tg_d=-0.013:0.012 for the negative order and tg_d=-0.015:0.012 for the positive order).
Note that the cumulative count fractions calculated by findcenter.f are not the same as CALDB EEFRACs. The latter fractions are relative to the total diffracted flux of the primary 1st order integrated over 2π steradians. If there are no cross-dispersion orders in the X-ray region then the EEFRACs will be ~0.905 times the findcenter.f EE fractions, where 90.5% is the total power of the primary 1st order, which includes diffraction from the coarse support structure but not cross-dispersion orders from the fine-support structure. For reference, the cross-dispersion orders contain ~9.5% of the total flux, with 1.7% in 1st order, 1.6% in 2nd, 1.3% in 3rd, 1.0% in 4th, etc. As another example, if the 1st cross-dispersion orders are in the tg_d analysis range and the findcenter.f cumulative count fraction is 0.95 then the EEFRACS is (0.905+0.017)*0.95 = 0.876. This is only approximate. A non-negligible fraction of events (especially at high energies) are scattered beyond the tg_d inspection region used by findcenter.f. I'll have to rely on MARX/SAOSAC sims to estimate that.
The CIAO tool celldetect is used in Standard Data Processing to determine the position of 0th order, which is then used as the origin for the grating coordinates tg_d and tg_r. Errors of a few tenths of a pixel in 0th order are common in Archive data (although data processed after Oct 2013--TBD***--use different celldetect parameter values that yield better results). The easiest way to improve those positions is to use dmstat on the 0th order position listed in the evt2 region block, e.g.,
dmlist "archive_evt2.fits[region]" data |grep circle Use the circle coordinates in the next step. dmstat "/archive_evt2.fits[(x,y)=circle(xxx,yyy,12)][cols sky]"|grep meanThe improved 0th order position is then used to reprocess the data by following this or some other *** thread.
After reprocessing the data using new 0th order positions we extracted tg_d profiles for each crsv and then ran findcenter.f to compute tg_d medians. To remove the wiggle from our results and enable a better determination of the (relative) tilt of each spectrum we computed the average tg_d median as f(crsv) for each source and subtracted that curve from the results for each ObsID. Results, grouped by source, are shown below.
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| Fig 2. tg_d medians vs crsv, after subtracting the average tg_d median for each source. Tilts are therefore relative to the average tilt for each source. For continuum sources, only points with errors of less than 1e-5 degrees (about 1/4 pixel) are plotted. Errors for Capella's lines' medians are explicitly shown. | |||
As can be clearly seen in the left-panel plots, LETG/HRC-S spectra have a time dependent tilt. (LETG/ACIS spectra probably do too, but the extraction region is wider and the spectra shorter so the effects are negligible.) Right-panel plots show results after tilts (derived from linear error-weighted fits) are removed. Note that even after correcting the 0th order positions and tilts, some spectra (e.g., 3rd right panel for HZ43) have a general tg_d offset. This seems to be correlated with the time of year and may therefore be a thermal effect. There also appears to be a slight time-dependent curvature, particularly on the inner plate (e.g., upward curvature for early Mkn421 observations and downward for later). The earliest observations also show relatively large deviations in tg_d offsets and/or curvature near 0th order, but this wavelength range is usually unimportant for LETG observations. [See /data/letg4/bradw/EEFRACS2013/Mkn421/averesids.sm--exclude 0th, average resids, and plot vs time.]
Within each source-group, tilts are well determined relative to the group average and we removed the tilt in each observation by running a script called *** to adjust the tg_d value for every event in a given observation's event file. All the files for a given source were then combined using dmmerge in order to improve statistics. (The two weakest PKS2155 spectra were not included in that source's combined file.)
Defining an absolute tilt is somewhat arbitrary because of the spectral wiggles. Because of minimal wavelength overlap of the continuum sources, there is also some ambiguity in how tilts are measured on the inner versus outer plates. Capella spectra, which have prominent lines on all three plates, were analyzed to address the latter issue but limited statistics (see error bars in Fig 2) prevented a definitive calibration. We therefore adjusted the tilts of the four composite spectra by eye in order to obtain the best agreement among them (in both Figs. 3 and 4) while also aiming to make the wiggles symmetric about tg_d=0 (Fig. 3). In the overlap region at wavelengths beyond |λ|~70|Å, higher order diffraction contributes most of the events seen in the hard continuum source spectra, which broadens the tg_d profile and skews the median. We therefore ignore those results and use only data from HZ43. Similar effects might be expected just short of the C-K absorption edge (because 1st order is much reduced) but we do not observe anything obvious. Likewise, results from HZ43 become increasingly suspect toward shorter wavelengths because of decreasing flux.
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| Fig. 3. Median tg_d values for combined spectra, with tilt and offset adjustments to make the wiggle symmetric about tg_d=0. tg_d values are multipled by 1000 for convenience and units are degrees. Tilts are in units of degrees per tap, also multipled by 1000. Legend example: blue points are for 18 combined HZ43 spectra, with a tilt correction of 0.00090 and global offset of 0.043. The composite wiggle curve is shown in black; some points near 0th order and the ends of the inner plate were adjusted by hand because the true errors are larger than indicated by the purely statistical error bars. (The lower panel in the linked figure plots the same data without the global offsets, and therefore shows the true wiggle correction curve.) | Fig. 4. Time dependent tilts. Uncertainties on each point (other than for Capella) are small, so the observed scatter is real and probably caused by observation-specific thermal conditions. There is no apparent correlation with aimpoint jumps. The solid black line can be used to estimate the tilt in any observation, and the gray band denotes the degree of uncertainty that would cause a 1-pixel error at 170 Å. |
With a consistent measure of tilt across all three plates, the tilt-versus-time curves from all 4 sources can be plotted together, as shown in Fig 4. The gray band represents a tilt uncertainty that would cause 1 pixel of error at 170 Å (proportionally less at shorter wavelengths), which is much larger than any errors in the wiggle calibration. Error bars on the points in Fig. 4 are quite small, so the jump between the blue HZ43 points around 2010 is real. The cause of this jump and other scatter is unknown, but probably thermal; there is no correlation with aimpoint jumps or any other parameters that we investigated. The 2007--2013 trend does not seem to continue in 2014.
With the wiggle and time-dependent tilt thus calibrated an observer can apply adjustments to any LETG/HRC-S observation and obtain a corrected event file... *** blah blah.
Errors on tg_d in the corrected L2 event file should be no more than about 0.5 pixels on the central plate and 1.5 near the ends of the outer plates. If the source is bright enough one can probably reduce these errors to only a few tenths of a pixel by measuring the residual tilt and overall tg_d offset and applying another round of corrections. A slightly narrower spectral extraction region could then be used but the net benefit would be only a few percent reduction in the included background.
For clarity, what's above here should only talk about tg_d medians and fixing the event data (get better 0th order position, remove wiggles and tilt). What comes next is recalibrating the EEFRACs table and choosing an optimal extraction region. Add data from KT Eri (20-40+ Å) and RS Oph (15-30 Å), which have super-high rates (low BG, high stats) and no higher-order contamination (unlike Mkn421). Make high-stat tg_d profiles, carefully treat BG and Xdisp orders, extract new EEFRACs with proper 2π normalization (and adjust HRC-S to get same EA), specify optimized extraction region. DTF filtering NOT applied to RS Oph or KT Eri data because of telem saturation; in this case, BG is negligible even with flaring and DTF filtering reduces the S/N. LSF distortion is not a concern for anything but 0th order.
After applying tilt and wiggle corrections to the combined data we can calibrate the tg_d profile, or cross-dispersion Line Spread Function, and create new EEFRAC tables for the LSFPARMs files in the CALDB (give link), along with a narrower spectral extraction region.
The hard-source spectra we used to calibrate spectral tilt and wiggles have relatively strong higher orders, which will tend to broaden the measured LSF. We therefore include observations of the very bright continuum sources RS Oph (ObsIDs 7296, 7297) and KT Eri (ObsIDs 12097, 12100, 12101, 12203) in our analysis. RS Oph covers from 15-30 Å and KT Eri from 20 to ~50 Å (see Fig. 8) and have essentially no higher order contamination in those wavelength ranges. The observations we use were obtained when those sources were extremely bright, often exceeding the HRC-S telemetry limit. High rates can cause deformations in the core of the 0th order PSF but did not affect the LSF of dispersed spectra, except for ObsID 12203 (see Fig. 9) which we do not include in further analysis. DTF filtering, which applied to Mkn421, PKS2155, and HZ43 data in order to eliminate periods of background flaring, was not applied to RS Oph or KT Eri data because that would remove data during the many periods of telemetry saturation. Note that background is almost negligible during those very-high-rate observations.
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| Fig. 8. Spectra used for central plate. The combined Mkn421 spectrum has by far the most counts but had the lowest (average) counting rate, and therefore relatively more background. It also has the largest contribution of higher order diffraction, which makes the LSF slightly broader than it is for the ideal 1st order spectrum. The KT Eri observation 12203 had the highest rate and its LSF was noticeably broader than the others (see Fig. 9). | Fig. 9. Comparison of background-subtracted LSFs (tg_d profiles) around +25 Å. Residual errors of up to 1/4 pixel in tg_d centroid were corrected for these plots to enable easier comparisons (but not in the evt files because such errors are representative of what users can expect). The LSF of Obsid 12203 is broader than the others and is not used in our calibration. More detailed study at other wavelengths confirms that data from other ObsIDs do not suffer from high-rate distortions, although the Mkn421 LSFs are broadened at some wavelengths by higher order contributions. (Key plot is upper left; others are sanity checks that will just be confusing to other people so I should remove them.) | Fig. 10. Cross-dispersion orders; profiles from - and + orders (primary and Xdisp) are combined. Large X's mark peaks that were superseded by other data. + signs mark the center of "background" regions on either side of a peak; note that this background includes intrinsic HRC background and underlying counts from the wings of the primary order. Dotted line marks the detector background level. The Mkn421 background levels were adjusted (- signs) as described in the text. |
As seen in Fig. 8, the short-wavelength range is only covered by Mkn421, which has significant higher order contamination that affects the LSF. An example, comparing to the "clean" LSF of KT Eri, may be seen here (25-40 Å, KT Eri in orange, Mkn421 in black). We can create model LSFs and EEFRACs via interpolation in the problematic ranges, but this requires calibration of the cross-dispersion orders diffracted by the LETG fine-support structure. Cross-dispersion intensities are also needed for proper normalization of the EEFRAC to 2π diffracted flux. [Why not use LETG/ACIS? Subarrays limit coverage of Xdisp orders to ~1/2 of HRC-S and pileup often messes up normalization to 0th. Also, I looked out to mX=12 with summed Mkn421 LETG/HRC (see $EE/XdispCal2/plotgrass12.ps). Tough to set the BG but it looks like 11 and 12 are significantly weaker than 10th.]
We used data from KT Eri and RS Oph as described above, along with Mkn421 data between 5.5 and 8.4 Å. Rates shortward of 5.5 Å drop rapidly so that 2nd order contamination in our chosen range is very small, and 3rd order is even less. The large number of events in this data set (about 550,000 in 0th order) provides adequate statistics to see to mX=10, with hints of 11th order (Fig. 10).
Event-file data were divided into thin triangular wedges (source center at pointy end) so that events of any given Xdisp order would all be collected together regardless of wavelength. Wavelength ranges for each source were chosen to provide optimal combinations of order coverage and S/N. Data from + and - primary orders and + and - Xdisp orders were combined, with the tg_d limit of ±0.021 deg chosen to maintain a flat detector background (i.e., without dither losses near the edges). Data were also analyzed separately (+ vs -) to confirm that results were the same within errors.
Skipping over much detail that I'll write up on some other page some day...The Mkn421 short-wavelength orders are so close together that their wings overlap and the real background levels can not be seen. We therefore adjusted them so that results for orders 3 and 4 matched those from RS Oph and KT Eri, scaling the background adjustments for each peak by its intensity. The net change was to increase each peak by about 5%. 0th order intensity was determined by subtracting all higher Xdisp peaks from the full-width total counts, blah blah. The SRON final calibration report suggests (pg 81, Fig 7.1) that Xdisp orders reach a minimum around mX=11 with damped oscillation beyond that. Based on fits to our results using a sum of squared sinc functions and the SRON report's caveats about PSF wings and background we believe that their results (using Al-K) are too high for orders 1, 2, and >10. Our model predicts that orders beyond 10 have a combined intensity of 0.0049 relative to 0th. Results are listed below. (Plots and analysis in /data/letg4/bradw/EEFRACS2013/XdispCal2.)
Order Intensity relative to 0th, with statistical uncertainty 1 0.00837 0.00010 (but 0.00759 ± 0.00035 for HZ43 70-82 Å) 0.00831 0.00010 if HZ43 results included--I use this 2 0.00781 0.00010 3 0.00678 0.00010 4 0.00569 0.00016 5 0.00405 0.00013 6 0.00316 0.00013 7 0.00191 0.00012 8 0.00113 0.00012 9 0.00086 0.00012 10 0.00046 0.00011 >10 0.0049 ? Total 0.04506 ±0.00041 * 2 for both sides --> 0.0901 +/- 0.0008 not including uncertainty in orders beyond mX=10.
We find that Xdisp orders have a total of 9% as much flux as the primary order, vs. the expected 11%. The 1st order intensity may also differ depending on wavelength, even at low energies where grating-bar transparency should not be an issue: 0.84% of 0th for wavelengths 15-39 Å and 0.76% for 70-82 Å, a 2.1σ difference. It is not clear if this result is significant or not. The SRON report noted differences between Al-K and O-K results but their significance was also questionable.
Possible nonnegligible systematic error sources: nonlinear nonuniformity in QE in the Xdisp direction; nonlinear nonuniform detector background in the Xdisp direction; primary higher order contamination in the Mkn421 5.5-8.4 Å spectrum.
Implications: I think that any errors in Xdisp (and raytrace) modeling would affect our primary 1st order calibration in such a way that errors in EEFRACs would cancel out and yield the same EA. I should study the LSF and Xdisp orders in LETG/ACIS data at some point. Hmmm, this DOES affect the LETG/ACIS EA because it's absolutely calibrated. I'll have to check but I think my EEFRAC work assumed 90.5% in the main order--half a percent error is nothing, and the uncertainty in my Xdisp calib is probably similar.
Last update 5/12/14. Plots below will be updated with improved results.
Data from all 5 continuum sources were binned in few-Å slices to obtain roughly TBD** counts per bin and their tg_d profiles extracted as before. The program contours.f was used to measure cumulative count fractions and blah blah... see Figure 6 (for now, but I need to make a new one). Medians are also shown for uncorrected Archive data from two observations with extreme tilts (ObsIDs 59 and 8274, corresponding to the highest and lowest points in Fig. 4).
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| Fig. 6. Cumulative count fractions of corrected data from combined Mkn421 and combined HZ43 observations. The cross-dispersion 1st order is shown in light gray (also seen with 2nd order as the faint "whiskers" in Fig. 1). Solid black line is the current spectral extraction region. | Fig 7. tgd profiles for HZ43 ObsID59 before correcting tilt. Remake this using composite HZ43 and Mkn421 files, and swap +/- to left/right. |
