In this recalibration effort for ASCA, we are attempting to update the physical models for the detectors and the mirrors in the various responses of ASCA to astronomical sources. Part of the motivation is that the physics of the instrument response is just as important as the physics of the sources we are observing, because every photon of information we get from those sources bounces off atleast one mirror surface, survives tranmission through atleast one thermal shield, and must ultimately get detected. The main motivation, however, is to resolve discrepancies between the ground and inflight calibration, and to make sure the latter is physically self-consistent.
Currently, energy dependednt fudge factors are applied to each of the sensors response matrices. There is no physical motivation for any of these fudges, and they may only be fixing the problem for a few narrow situations. If a source is in a nonstandard position, or it is extended, then the fudges will not help, and errors will creep out. In the figure below, see the fudge factors currently applied to the ASCA responses.
This recalibration effort also takes advantage of the latest knowledge of the mirror response including measurements of the optical constants from AXAF and JET-X.
Currently, we have good reason to suspect some of the physics assumed in the released X-ray Telescope (XRT) model. There is also some suspicious pieces in the Gas Imaging Spectrometer (GIS) response model. These are particularly important because the "in flight" calibration of ASCA depends crucially on these. In particular, the SIS is cross calibrated to the GIS assuming that both the XRT and GIS models are correct. Pieces of this cross calibration are in contradiction to the extensive ground calibration. There is also room for the SIS physical model.
Here will outline current efforts and concerns for each of the instruments. We will also discuss the merrits of the in flight calibration. In particular, we will ask "how good is the Crab as a standard candle?"
This is a work in progress. The recalibration effort is expanding. Current recalibration team members are Richard Fink, Richard Pisarski, Keith Arnaud, Keith Gendreau, Ken Ebisawa, Koji Mukai, Tahir Yaqoob, Nick White, and several others.
We have made changes to the optical constants and optical boresights in this recalibration. We have also examined the effects of contamination on ASCA response and point-like approximations to the finite crab nebular.
There has been considerable work by several groups on the optical constants used to compute various x-ray properties. For mirrors, reflectivity demands attention be paid to a real and imaginary optical constant foreach energy. We have looked at 4 sets of optical constants for the ASCA recalibration. We found that the constants used in the release matrices result in several spectral features and that they were physically internal inconsistant, as they violate Maxwell's Laws. We will show that the constants found by Alan Owens and collaborators are the better choice.
The optical constants are often referred to as the atomic scattering factor: f = f1 + if2. They define the ratio of scattered radiation to incident radiation.
When one rigorously follows Maxwell's Laws to compute the scattering of an X-ray from an atom, one finds a distinct relation between the real and imaginary components of the optical constants. This relation is called the "dispersion integral". The real component is a comlicated integral of the imaginary component.
One must change the real an imaginary components in such a way as to conserve the dispersion integral. The currently releasd XRT response uses optical constants which do not follow this rule- as we will show below.
The available Optical Constants
There are five sets of optical constants to consider. These are the "Nagoya Constants", the "old Henke 82 constants", the "AXAF Transmission Grating constants" (also known as "new Henke"), the "old AXAF Constants" (also known as the "PJS Constants"), and the "Alan Owens Constants". I made up the names of these sets of constants- just to make them distinct. There actual identity may be somewhat different.
The "Nagoya Constants" are what are currently used in the officially released XRT response. There are actually 2 versions: the origional and the "tuned". On inspection of the raytracing code used by the XRT team to produce the ASCA response, we discovered that the optical constants are mostly derived from 1982 Henke results. Dotani-san reports that:
In reality, it is not this simple. The above break down represents what nominally was in the "origional" XRT response. It is true that "Beta" came from Henke 82. It is also true that UVSOR syncrotron measurements were made from 2 to 3.5 keV. However, there were complications with the UVSOR data, which we summarise below. In addition, the delta was "tuned" to fit the GIS crab spectrum in the later version of the XRT response.
In the UVSOR experiment, the reflectivity as a function of energy was
measured for five different graze angles off of a typical ASCA mirror foil.
The energy range measured was from 2 to 3.5 keV in roughly 5 eV steps.
A double crystal spectrometer was used. The direct beam and then the reflected
beam were measured to derive reflectivities. The angles measured were 0.3,
0.5, 0.7, 1.0 and 1.2 degrees. The reduced data is here: figure XRT-1:
The energy scale of the spectrometer was first determined using the
Argon K edge from the proportional counter used to make the measurements.
However, when it was found in the reflectivity data that the gold M edges
appeared at different energies than those tabulated in the 1982 Henke tables.
The experiment notebook listed a 35 eV discrepency. The Nagoya team then
shifted their data to agree with the 82 Henke values and he argon edge.
They appear to have lost the actual correction they employed. Unfortunately,
the discrepency between their uncorrected data and the Henke 82 values
was probably real. Several groups have found this to be the case. See Owens
This error can also lead to more subtle problems. Specifically, when we look at the crab with the XRT-GIS, and we redetermine the gain due to the high counting rate, then the strongest spectral feature drives the gain determination. This strongest feature would be the Gold MV edge. If it is off by 20 eV, then we have introduced a systematic 1% gain error. At the highest and lowest energies, where the response is changing quickly, we will have errors in the effective area.
The next thing to notice in the ground XRT data are the reflectivities below 2.2 keV. In figure XRT-1, notice that the reflectivities for 0.3, 0.5 and 0.7 degrees are all on top of each other at the low energies. If you work the numbers yourself, you will find that this is quite impossible. Use this link to the LLNL Henke page to try out computing reflectivities to convince yourself. The data should be spread out. Larger graze angle should have smaller reflectivities. In fact, if you look at the data very closely, you will notice that the 0.5 degree data slightly- but significantly- exceeds the 0.3 degree data at the lowest energies.
My personal belief is that there was some sort of alignment problem. The X-ray beam size was 200 microns. The typical ASCA foil is 100 mm across. At 0.3 degrees, the ASCA foil is 525 microns in projected size. These are small dimensions- errors are possible. In the section on "Alan Owens Constants" below, I fit the data for an energy independent correction factor with this in mind. In addition, if you look carefully at the data, there is atleast some evidence of a "backlash" like problem. In figure XRT-2, below, I take the data of figure XRT-1 and draw lines between each of the points. Notice at about 3 keV that the data taking was repeated. For the 0.5 degree data there is a large internal inconsistency. For some angles, the mismatch is in a different sense than it is with other angle data. Another possible contributing factor is X-ray beam stability. If the beam is drifting in intensity, then it is not clear how- or if at all- this data is useful. This suggests that we should pay special attention to future reflectivity measurements- particularly for ASTRO-E.
Figure XRT-2 
The Nagoya team contends that the error at low energies may be due to dead time errors. The counting rates were of the 10,000 c/s order. Kamata-san says "...dead time correction is effective at high intensity data, say, < 2.2keV". However, if that is the case, then certainly at higher energies, the data is suspect since the direct beam data must also have a large counting rate. To address this issue, the raw data is required- but, this seems to be missing.
I am also concerned about the calculation of errors in the data. Assuming that the errors are 1 sigma, why are the point to point measurements so discrepant?
Finally, the treatment of the data violates the dispersion relation described above. Specifically, you cannot tune "delta" while keeping "beta" fixed. This is fundamentally a violation of Maxwell's Laws.
In the section below on Alan Owens Optical constants, I take the XRT ground data, attempt to uncorrect the energy scale, and fit for gold density, roughness and an energy independent alignment correction factor.
The old 1982 Henke values are generally unreliable for Gold. Although, they are internally consistant and obey the dispersion relation. You can get the "old" and "new" henke values at the LLNL Henke page
At LLNL Henke page , the default is to give you the latest Henke data. Currently, for gold, you get the results of the AXAF transmission grating calibration, as reported by Nelson et al (1994) in SPIE Volume 2280, Page 191.
When computing the reflectivity, one must use gold densities smaller than that of bulk (19.3 g/cm**3). This is due to gold sputtering effects. AXAF mirror work suggests denities 90% that of Bulk. Peter used 88% for BBXRT and for his own ASCA XRT code. While there are no comments in the code, I believe the Nagoya group uses a larger value here- but then again, they use different constants.
I have computed new ASCA effective area curves for several gold densities.
Here, I simply replace the new optical constant data within the official
raytracing code. I have taken the new ASCA effective area curves for gold
densities 88% and 90.7% that of bulk gold, and compared them with the effective
areas computed with the Nagoya optical constants. The ratio of the New
areas to the Old areas is in figure XRT-3: 
Note the bumps at 2.2 keV and 3.8 keV as well as the hard tails. This alone may explain many of the residuals seen in the ASCA data before people started fudging the response by adding 2.2 keV gaussian features. Compare this to figure 2 of Yaqoob et al in PASJ 46 L49, 1994. Currently, ASCAARF adds a gaussian at 2.2 keV for the SIS data and the GIS team adds a gaussian at 2.2 keV in their GIS response.
Alan Owens
Alan Owens and collaborators published results of their measurements of the optical constants of gold at the Daresbury Syncrotron (Owens et al , ApJ, September 1996). Alan Owens kindly provided tables of the measurements for me.
The tables include measurements and theoretical values. The values appear consistant with the new AXAF constants described above. However, the measurements were done at a higher energy resolution and unveiled additional structure near several of the gold M edges. See the figure below, were two sets of the optical constants are compared. In the figure, the top two curves show the f1 constants from the New Henke and Alan Owens tables (Green and black curves, New Henke and Owens, respectively). The lower two curves are the f2 values from the same tables (red = Owens, blue=new Henke). The curves are actually lines between measured points, which are indicated in the figure. Clearly, the higher resolution Owens data reveals sharper structre than the new Henke tables can. Apart from that, these constants seem remarkably similar.
I have taken the XRT ground data- shown above under the section on Nagoya Optical Constants- and tried to fit for the gold density and surface rougness using the Owens optical constants. The energy scale of the ground calibration data needed to be uncorrected, but the XRT team did not have the correction they used recorded. I did a simple 35 eV shift.
The other correction to the data I made was an energy independent scale factor for each angle. I actually fit for this in parallel with fitting for the physical parameters. The motivation here was as described above. Namely, the low angle data had reflectivities at low energy which did not make any physical sense. Also, in the experiment, the x-ray beam was about 200 microns in diameter. The foil samples being measured were 10 cm long. At the low graze angles, the 10 cm foil would have a projected size of 500 microns and wider- dependent on angle. Thus there would have to be alignment at the 100s of micron level. While possible, it would be difficult.
In the figure below, is the best fit. The gold density is 18.4 g/cc. The roughness is 8 angstroms. The correction factors (applied to the data in the figure) are 0.89, 0.91, 0.93, 1.02, and 1.09 for the 1.2, 1.0, 0.7, 0.5, and 0.3 degree data respectively. The reduced chi sqaure on the fit is large (45 for 1450 degrees of freedom). However, as I note above in the section on Nagoya constants, I am suspicious of what angles are actually being measured and if they are constant (note the inconsistant data around 3 keV). Also, it would be nice to have the correct energy scale for the data.
As mentioned above, the new Henke data and the Alan Owens constants are very similar except for resolution. In the fitting of the ground data, the Owens constants differ from the new Henke constants in that they can fit the small bump peaked at about 2.3 keV in the 1.2, 1.0, and 0.7 degree data above ( the red, blue, and pink data points). The new Henke constants completely miss this feature., due to their poorer resolution. This may be an important consideration for the AXAF grating.
Peter Serlimitsos- Old AXAF
Peter Serlimitsos was given constants for gold by members of the AXAF teams several years ago. The details of where these constants came from is not clear. It is also not clear if these are still in use by the various AXAF teams.
These are what were used in BBXRT and in Pete's code for the ASCA mirrors. These constants have the M edges at energies very close to those found in the new Henke and Owens tables. However there are several differences. See the figure XRT-5. Most notably there are Gold N edges in these constants. The N14 Gold edgeis very close to the oxygen K edge and may lead to low energy problems. However, after several years of using gold coated reflectino grating spectrometers, I have never seen an N edge- which makes me suspicious. Infact, there is very little published data at these energies.
Another interesting thing to ask is: Given that the XRT boresight has an error of about +/- 0.5 arcminutes, what is the effect on Spectral fitting?
I have computed ratios of the Effective Area vs Energy curves for adjacent off axis angles at a fixed phi pf 45 degrees. Specifically, I look at the effective area curve for phi=45 degrees and theta=XX arcminutes and compare it to the effective area curve for phi=45 degrees and theta=XX+1 arcminutes. The ratio of these gives you some idea of what the effect of this uncertainty is on your spectral fitting. Interesting off axis angles to consider are: 0-1 arcminutes, 5-6 arcminutes, and 8-9 arcminutes. The "standard" (eg 1 CCD mode position) positions are 5-6 arcminutes for some detectors and 8-9 arcminutes for others.
I have put these ratios in figure XRT-4 
Notice that:
1) even 1 arcminute errors can give 8% uncertainties in normalization
2) 1 arcminute errors can EASILY give you the hard tail seen in the data. But this effect competes/ compliments the effects of using the new optical constants.
Now consider the fact that the crab is actually a 3 arcminute extended object- AND even in Makeshima-senseis thesis there is evidence that the spectrum changes with position across it.
In previous versions of the ASCA response, more than 12 crab pointing were used to get the boresight positions on the GIS detectors. Since the crab is too bright for the SIS, 4 N132D pointings were used to get boresight positions for the SIS.
Both the Crab and N132D are extended object ( about 1-3 arcminutes ). This gives one some feel of possible systematic errors. In fact, no errors are quoted for the SIS, and the errors quoted for the GIS are about +/- 0.5 arcminutes.
Given this, we have designed a new method to extract the boresights of each of the telescopes. This new method requires a minimum of three observations (4 observations give somewhat more information) of any point source(s) at different positions in detector coordinates. The sources may vary with time. Also, we need not know their absolute fluxes.
THE METHOD:
Consider two sensors for which the XRT boresight positions are at unknown but fixed relative positions. See figure XRT-FIG bore.
If a point source is positioned to be somewhere on a sensor, then there is a set of possible boresight positions which will yield ARF response files which will result in a fit with a given unfolded flux. For example, a power-law point source observation will have a set of possible boresight positions which will have ARFS which with XSPEC will yield a flux of X ergs/s/cm**2. These constant flux curves will be closed figures around the point source- nearly circular.
Now imagine an observation where you have data from two sensors/XRT pairs. On sensor 1, you can make an ARF file assuming any boresight position (eg. "1" on the figure). For this observation and boresight position, you use XSPEC , fit a model, and extract an unfolded model flux using the "flux" command. Take this flux, and compute a constant flux curve of possible boresight positions on the other sensor. This involves the generation of an incredibly huge grid of ARF files. For the work here, about 60,000 ARFs were generated. In the figure for observation 1, the red arc is the set of possible boresight positions on sensor 2 which yield the same flux as the flux derived by assuming that the boresight on sensor 1 is at position "1".
On another observation, take the same fixed position on sensor 1, compute the unfolded flux for that observation/boresight position, and produce a different constant flux curve of possible boresight positions for sensor 2. In the figure, the green arc is the set of possible boresight positions on sensor 2 which yield the same flux as the flux derived by assuming that the boresight on sensor 1 is at position "1" for observation 2.
Do this with more observations.
If the position on sensor 1 which you are assuming is the correct boresight position is, infact, the correct boresight position, then the constant flux contours on sensor 2 from all the observations should intersect at one point. If this does not happen, then the assumed boresight position on sensor 1 is incorrect, and a new possible boresight position must be considered.
To adjust the sensitivity, you can adjust the tolerence in the flux agreement you should have between the two sensors.
Figure XRT-FIG-bore: 
We did this for the 4 observations of 3c273 which centerd the object on each of the 4 CCDs for each SIS.
SIS0 to SIS1: Agreement to 0.85%
GIS2 to GIS3: Agreement to 0.85%
|
Sensor |
X |
Y |
Delta From Current Release |
|
SIS-S0 |
675 |
595 |
1.03 mm |
|
SIS-S1 |
632.5 |
790 |
0.58 mm |
|
GIS-S2 |
132.25 |
132.0 |
0.32 mm |
|
GIS-S3 |
120.25 |
133.0 |
0.42 mm |
We used this new method assuming two different values of the gold density in the mirror response (17.5 g/cc and 18.0 g/cc). The boresight shifted less than 0.1 mm with this change.
Something which may need to be done in the future is to consider the possibility that there are different boresight positions (and focal lengths) for each of the 14 sectors. The working model here, is that the sectors are defined by comb-like alignment bars which define the radii of curvature for all the foils azimuthally. If these comb alignment bars shifted during launch, then distinct features would appear in the PSF and different sectors would have different focal points.
Wandering of Satellite
An additional complication comes in when one considers that the pointing stability of ASCA is somewhat limited. Given our sensetivity to the position of the boresight (shown above), if the satellite wanders during an observatino by a few tenths of an arcminute, then the assumption that the alignment is fixed will yield errors in the assumed response. In addition to telescope issues described above, there are more complications when one considers the GIS window grids.
The typical ASCA pointing stability is about 0.5 arcminutes. As an example, consider the figure below which indicates the typical pointing positons during the long observation of the crab made on september 28 1994.
For this long crab pointing, I divided the data based on the Z_ALPHA, and Z_DELTA point information in the MKF files. I extracted spectra for the different event files and then compared the spectra. Notice that the source is the same and I am actually looking at how the nature of the data changes; no response models are assumed.
Here is a comparsion of two other regions.
Notice that in these two graphs, there is a bump at around channel 475. Could this indicate an error in the linearization of the PHA to PI? (I am using "rev1" data.). This is small compared to other obvious trends, but I note it anyhow.
What is dangerous is that it was this crab pointing which was used to make the "ARFFILTER". The ARFFILTER was the energy dependent fudge factor introduced by thje GIS team to force the GIS crab spectrum to a particular power law. Later on, this effect propogates to the SIS during the forced cross calibration of the SIS and GIS during the 3c273 observations.
On a related issue to telescope wander ing and boresight uncertainty, I present here some concerns and analysis of the effects of a finite sized crab nebula when one assumes it is a point source.
Since the Crab is actually about 3 arcminutes across and not a point source, its use as a calibrator with conical mirrors is somewhat compromised. The GIS team uses a point source XRT response to the crab to do its fitting. They then make an energy dependent fudge called the "arffilter" to smooth out the wiggles. I have simulated two possible crab distributions: a uniform brighness 3 arcminute disk and a disk which falles like 1/r to a cut off radius of 3 arcminutes. These simulations were done for the crab at 5 arcminutes off axis. Next a standard point source response for the central position was used to produce a ratio of the extendedn response to the point source response. In both the extended and pointsource response, the nerw optical constants were used. The results are in below:
Note that there are wiggles of the same order of size as the arffilter fudge. The wiggles are at different energies, but recall that:
1) the arffilter still needs to correct for optical constant problems
2) The crab distribution is not quite round and may have an energy dependent figure.
Scattering Function
Rich Fink, Please include your analysis here.
Incomplete
My origional motivation in checking out the XRT mirror reflectivity code was to address contamination effects at low energies. We know that there is some "low energy calibration problem" for the ASCA SIS/XRT system. Currently, the belief is that the CCD deadlayer/ thermal+optical blocking filters are incorrectly modeled. This implies an absorption effect. An alternative solution to the "low energy calibration problem" would be that the telescope effective area is inaccurate. This would be a reflection effect.
After all this work, I believe that contamination is at most a minor effect for ASCA. In anycase, I present it here for your consideration.
AXAF mirror calibration has included a study on the effects of contamination on the effective area of grazing incidence optics. They have put out many papers including:
Elsner et al, SPIE Vol 1742 page 6.
Elsner et al, SPIE Vol 2279 page 332.
Graessle et al, SPIE Vol 2279 page 12.
Principle results of the AXAF study are:
1) a contamination layer increases the area in the 0.5 to 6 keV range. principly around 2.2 keV. The enhancement near 2.2 keV looks VERY similar to the "gold bump" in the asca data...even with as little as 75 angstroms of a carbon based contamination.
2) a contamination layer produces a downward goiing effective area going from 1 towards 0.277 keV which is the opposite of the expected mirror energy dependence. This may look like absorption similar to the effect of increasing the CCD dead layer- but with a somewhat different energy dependence. Infact in many cases, the contamination results in a HIGHER area at low energies.
3) the effect of adding a gaussian to the mirror effective area near 2.2 keV coupled with some of the enhance area due to the mirror contamination is to make a bump roughly where the XRT people have been working to "tune" the constants.
The contamination make the mirror effectively a single layer multilayer- which is why the reflectivity is enhanced. There is constructive interference between reflections on the top of the contamination and from the contamination/metal interface.
I have made an additional modification to the raytracng code which allows one to enter a chemical compound formula (eg. H2O, H8C20N4, and so on...), a density, and a film thickness. This film is then added on top of the gold and the reflectivity is computed for the resulting bilayer.
Cool plots
First, trying to add a uniform thickness of carbon with density 0.75 g/cm**3 ontop the gold for 3 carbon thickness, you get the figure below. Note the enhance area- even at low energies. Note that compared to a clean mirror, the slope of the effective area is different for contaminated mirrors. This may look like absorption in a model, but the area is infact bigger than one would expect.
Second, for a fixed thickness, I varied the carbon density from 0.25 to 1.75 g/cm**3. The resulting areas are in the figure below .The dotted green line is the clean mirror effective area.
The increasing density tends to increase the area. The figure below shows the ratio of dirty to clean for the same contamination levels.
Third, I started looking a contamination composition effects. By this I mean, what if it was H2O or some other molecule instead of pure carbon. I made area curves for the same contamination thickness and unit density contaminated mirrors for several different contaminating compounds. See the figure below. Notice that at edges for elements contained in the contaminate, there is a notch. Then just to the low energy side of the edge, the reflectivity is greatly enhance. For Oxygen, this may look like a bigger oygen edge in the CCD response- since we do not see this, I conclude that the contaminate must have very little oxygen (eg water is unlikely).
Having mentioned all of this contaminatino study, I will end with saying that this is probably not a mjaor effect in ASCA now.
We have used a new method to redetermine optical boresights. We are in the process ofseeing how this affects the predicted PSF. We are also starting an investigation of changing radii of curvature in the foils due to alignment bar shifts.
We have investigated new optical constants and are releasing to instrument teams new ASCAARF XRT calibration files appropriate to the Owens constants for the following gold densities (17.5, 18.0, and 18.5 g/cc).
We have investigated the effects of wandering pointings, extended crab emmision, and contamination.
We now wait for an evaluation from the instrument teams.
This section is incomplete, but I will post a few graphs with some short remarks.
Below is a figure (merely schematic) of what I expect the Pulseheight to Energy Relation to look like in a typical Xenon counter. The figure is derived from reading papers by the Portugal group (eg. see Santos et al, Nuclear Instruments and Methods in Physical Research A307 1991, page 347.), other papers, and talking with XTE PCA calibration experts (Keith Jahoda). I'll put a complete reference list here- later.
While the details may be vague (eg. what is the magnitude of any of these jumps), I believe thatwe should see:
1) a jump at the Xenon MV edge-- this would be at the edge of the GIS response and may infact look more like a zero offset. The magnitudes of the other M edges seem small in the liturature.
2)Jumps at the L1,2, and 3 edges.
3) Piecewise linear relations between the jumps. I should be explicit here. The linearity should hold BEFORE the application of the low pulseheight tail (Inoue et al). The application of the low pulsehieght tail would tend to lower the pulseheight at a given energy.
Below is a schematic of what the Released GIS response assumes for the Pulseheight to energy relation.
Note:
1) there is no Xenon M edge jump...
2) There is a Xenon L edge jump, but it curves back to the extrapolation of the pulseheight to energy relation derived before the jump. Note that the nature of the curve is in the opossite sense to that which would happen due to the low pulsehight tail. This seems very unphysical.
Below is a plot of the Energy-pulseheight vs energy from the actual GIS response code. Notice the jump over the L edges of xenon at about 4.6 keV. Note that after the jump, the pulseheight tends back toward the origional energy. These seems questionable and is unlike anyother xenon counter response I have seen. This plot comes from the section of the GIS code which describes the physical situation prior to the application of the low pulseheight tail or any other physical gain distortions.
The attenuation coefficients for Xenon and Beryllium seem suspicious in the current GIS response matrix. First look at the Beryllium window attenuation. In the figure below, I show the computed transmission through a 10 micron thick beryllium window (typical thickness for the GIS) using both the published Henke Values and the GIS values.
Below is a comparison of the mass attenuation coefficients for Xenon in the published Henke 1993 tables and in the GIS code. Note the differences in the M edge energy and in the values of the constants around the M edges and around the L edges. I am not sure which is correct, but I do know that the current Henke tables have been closely examined recently.
Low Energy Tail
The low energy tail treatment in the GIS response seems similar to that of the XTE PCA and the Inoue et al paper. However, they do not apply a low energy tail to the escape lines.
Incomplete...
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