The latest modification was to add a section on absolute calibration ( See Also: HRMA/SI encircled energy and effective area (absolute calibration) ) , necessary for the HRMA/SI encircled energy/effective area measurements. This gives requirements for the calibrations at BESSY.
This document gives accuracy allocations for parts of the HXDS (HRMA X-ray Detection System) to be used for prelaunch ground calibration of AXAF at the MSFC XRCF (X-ray Calibration Facility). In many cases, models are used to make these allocations, since calibration accuracy cannot be determined without consideration of data reduction that occurs after the calibration measurements are made at XRCF. When that is true, we include a description
The error budgets described in this document deal with measurements of various properties of the AXAF mirrors and gratings during calibration tests performed at the XRCF. The errors presented here reflect ground based measurements at specific x-ray energies and not the overall on-orbit result interpolated to any energy.
The requirements for the HXDS capability to make these measurements are given in SAO-AXAF-DR-92-017, "Contract End Item (CEI) Specification for the HRMA x-ray detection system (HXDS)," section 3.2.1.1.1, hereinafter referred to as `CEI'.
NOTES ON NOMENCLATURE AND CONVENTIONS USED IN THIS DOCUMENT
Introductory and explanatory material is given in paragraph format.
The data accumulation process for alignment is the same as for focus, so we treat it as one operation. The time required varies: 7 min/shell, for alignment, and 11 or 15 min/shell for focus.
L. Van Speybroeck provides the following equations for each of two independent focus error measurements applicable to a four quandrant shutter system (see SAO-AXAF-90-040, p. 34):
and for the average focus error:
sij represents shutter j of shell i. i,j =1,2,3,4
yij is the centroid y coordinate of a HSI image with shutter j of shell i open.
zij is the centroid z coordinate of a HSI image with shutter j of shell i open.
r is the mirror intersection radius, and f is the focal length of the mirror
Positive x f 's indicate that the correct focus is located at a larger value
The source size ds must be kept as small as possible, ds < FWHM(PSF). By measuring the source distribution, we can only partially correct for its effect on distorting the HRMA PSF.
Focal plane position (for avg. of vertical & horiz. foci) X=+/- 10. x10 -3 mm
Focal length = 10m; mirror radius = 0.6m
To find the error in a measurement of x
f
, we use the uncorrelated error propagation
1
equation.
where 
are the variables on which
x
f depends.
and similarly for y
4
, z
1
and z
3
, if they all have the same errors,
so 
(Note: needs amending to consider all shells)
Conclusion: sensitivity of average between vertical and horiz. focus errors to image centroid error is 13.1
Error due to image centroid error in YZ plane X=+/- 6.42 +/-(corresponds to YZ=+/- 0.49 +/-).
Model: uncertainty = 
N = 10,638 counts
Time to acquire data: assume rate with 10 mm pinhole is 4000 s-1. Then, it takes (2.66 seconds + 2 seconds overhead) x4 shutters x (7x7) image positions = 913 seconds = 15 min for all four shells taken togehter, or each one independently. For all four shells taken independently, multiply x4, to get 60 min..
Misalignment of the shutter blades, and deviation from an ideal quadrant geometry will have an effect. This needs to be calculated.
Focal length = 10m; mirror radius = 0.6m
To find the error in a measurement of x
f
, we use the uncorrelated error propagation equation as for the average focus error above, so 
(Note: needs amending to consider all shells)
Conclusion: sensitivity of vertical or horiz. focus error to image centroid error is 9.3
Model: uncertainty = 
, so N = 5,406 counts
Time to acquire data: assume rate with 10 mm pinhole is 4000 s-1. Then, it takes (1.35 seconds + 2 seconds overhead) x 4 shutters x (7 x 7) image positions = 656 seconds = 10.9 min. for each mirror shell pair, or for all four taken simultaneously. For all four shells done independently, it would be 44 min.
Misalignment of the shutter blades, and deviation from an ideal quadrant geometry will have an effect. This needs to be calculated.
HSI and pinhole scan image centroid position measurements at the focal plane of the HRMA can provide an estimate of the relative lateral displacement between the hyperbola and parabola back foci, dy and dz respectively. The relative displacements can be due to a combination of tilts or decenters of the optical elements. Van Speybroeck provides x-ray alignment formulae applicable to a four quandrant shutter system in Reference 2 of document SAO-AXAF-90-040. He provides the following equations for measuring the lateral displacements from x-ray data:
i = 1,2,3,4 for the four quadrants.
The tilt angles about the y & z axes corresponding to these displacements are:
, 
, where
f
is the focal length.
The variances of these two angles in terms of the uncertainties in image positions are:
, and if all the 
and 
are equal to 
, 
. Since
= 0.1 arcsec = 4.85 x 10-7, then 
arcsec and 
= +/- 4.4 x10-3 mm. Therefore, we have the result for the allowed error in focal plane position measurements by the HXDS:
Model: uncertainty = 
, so N = 277 counts
Time to acquire data: assume rate with 10 mm pinhole is 4000 s-1. Required exposure time for each point is 69 msec. Minimum incremental time for accumulation is 20 msec. Therefore, it takes (0.08 seconds + 2 seconds overhead) x 4 shutters x (7 x 7) image positions = 408 seconds = 6.8 min for each mirror shell pair, or for all four taken simultaneously. For all four shells done independently, it would be 27 min.
Centroid uncertainty, fitting errors YZ=+/- 0.1 +/-Stage accuracy over 50 +/- range YZ=+/- 1. +/-Reserve YZ=+/- 2. +/-Fitting errors YZ=+/-Reserve YZ=+/-Non-HXDS YZ=+/-These are such things as motion of the HRMA and/or the XSS relative to the HXDS, normally detected by the MDS, finite XSS source size, and problems arising from incorrect focus of the HRMA image on the HXDS detector. We consider all these to be negligible under normal XRCF operating conditions.
This is a measurement of the Full Width Half Maximum of the point response function, consisting of a one-dimensional scan across the peak of the PRF.
We use a simple model for the FWHM measurement. We assume that we make measurements in three bins, at the peak and one bin on either side. Suppose that we spend appropriate integration time so that the total number of counts in the two side bins is equal to the number in the central bin. The FWHM is then the ratio of the heights of the two composite bins, times the bin size. If we take a typical bin size of 0.2 arcsec, then the statistical error =
arcsec times the% error in the single bin. This implies 99,000 counts in each of the two bins. At a peak rate of ~5000 s
-1
, that means an accumulation time of ~40 s.
For example, due to drift of gain, shifting counts out of the pulse height region of interest.
For example, due to buildup of ice on the window of the SSD.
This is the contribution of uncertainties in the beam monitor counting rate to FWHM measurement. In the previous entry, only the statistical errors due to the focal plane counts were accounted for. When we take into account that each count measurement will be divided by the BND counts, additional statistical uncertainty is introduced. The BND-H detectors have 200 cm 2 area. Their effective area vs. E follows that of the focal plane counters, since they are nominally identical. Therefore, the counting rate in BND-H at low energies will be about the same as in the focal plane with one shutter open. At higher energies, it will be necessary to increase the incident flux to achieve 5000 s -1 in the focal plane. This will mean that the BND-H rates will be even higher, so the BND-H will make the largest contribution to Poisson errors at low energies. At equal rates in BND-H and focal plane, the BND will contribute equally with the focal plane to the Poisson errors.
With a focal plane scale of 50 +/-/arcsec, this angular tolerance corresponds to +/- 1.67 +/- within ~ 50 +/- FWHM scan. Capability is +/- 1 +/- per SAO-AXAF-DR-93-055.
This corresponds to an increase in beam size away from best focus of 0.5 +/-. With our expected focus accuracy of 10 +/-, the HXDS detector should always be well within the focus waist, which should extend for about 120 +/-. The budgeted value allows the image diameter to increase by 0.5 +/-...(could use a more careful analysis)
This error contributor is due to the XSS source having a finite size.Let us assume that the source size adds in quadrature, and that we will account for this effect in data analysis, since we will have measured the brightness distribution of XSS. Then this contributor represents the residual uncertainty after correction for XSS size. The magnitude of this contributor corresponds to 27 +/- at the XSS source, which is about 5% of the specified size of the XSS sources. So this is a requirement on the accuracy of measuring the XSS brightness distribution, and of performing the modeling to eliminate source size effects.
This contributor can be thought of as arising from uncorrected motion of the type normally measured by the Motion Detector System (MDS). we estimate that MDS could have residual errors of 0.5 +/-, which equals this allocation.
We define the region from 0 to 1 arcsec diameter in the focal plane as the inner PRF. Because of the limited spatial resolution of the HSI (~20 mm), we will map out the region from 0-1 arcsec with a 5 mm dia. pinhole apertured proportional counter or SSD detector.
Errors in the area, or effective area carry over directly to errors in point response, since the BND data are used to normalize all the focal plane aperture measurements. Capability was reported as +/- 0.02% (Podgorski et. al. 1992. Proc. SPIE 1742, 49), but is probably not that good, since not all error sources were identified there.
These are errors in the ratio of QE between the BND and the FP detector.
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Sensitivity to temperature is also +/-0.368, so dT/T= +/- 0.38° C. Capability is +/- 0.1° C (SAO-AXAF-DR-94-102). |
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This effect is highly dependent on energy. Scholze 2 has shown that large uncertainties occur in the range from 0.5 keV downward, due to a varying amount of ice condensing on the detector window. The HXDS has a system to reduce this effect by placing a barrier between the detector and the external environment, which is the source of water vapor. We do not yet know how well that works (needs more analysis, and lab tests). We are also considering the possibility of adding a radioactive source mounted within the SSD500 on the aperture wheel, observing the FeL a counting rate to monitor ice thickness. |
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Based on lab work by Chartas, this is not a problem (quote results).
This is to account for variations in the angular distribution of the flux traversing the guide tube during the period between beam map measurements. We do not yet know whether this is a problem. The solution would be to map the beam often enough.....
This is the error introduced by uncertainties in the livetime. Studies by Chartas (see CDR presentation, SAO-AXAF- DR-94-???) indicate that we can obtain livetime to at least this accuracy at 9000 Hz and lower rates. We are still investigating how accurately we can make this correction at higher rates. This error may actually turn out to be significantly smaller, since we are dividing one livetime by another, and many of the sources of livetime error may cancel out.
To convert counts to line flux we must estimate how many counts in the pulse height spectrum come from the monochromatic line. Errors come from spectrum separation errors : uncertainties in estimating how many of the observed counts are from the monochromatic line, and how many photons impinging on the detector are not counted, due to quantum efficiency .
Errors in estimating how many of the observed counts are from the monochromatic line come from
Errors in quantum efficiency come from uncertainties in
which were treated earlier, and from
Sensitivity of measured flux to change in gain is a result of errors from subtraction of continuum from under a line peak. The broader the peak, the more continuum is under it, and the larger the error we make in subtracting out the continuum (see See Also: Continuum Subtraction Errors ). If the FWHM broadens to 250 eV, the error goes to +/- 0.25%.
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Continuum subtraction error 3 |
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For the SSD at 10 keV, the FWHM is ~200 eV, or +/-E/E = 2%. This will result in a continuum subtraction error of ~ +/-+/-since the line-to-continuum ratio for K lines at ~10 keV in the SSD is about the same as in the FPC at 1.49 keV+/-A gain shift of 150 eV, or 1.5%, added in quadrature with the original detector resolution gives the budgeted 0.15% added counting rate error due to increased uncertainty in continuum subtraction.
For FPC, the worst case would be at its highest energy, since that is where the ratio of FWHM to energy is the smallest, and the contribution from continuum is largest(?). If we assume the highest FPC energy is 2.04 keV, Zr-L, because the SSD will be used at higher energies, the FWHM is 32%. Now, we RSS the existing 0.25% error with the additional budgeted amount of 0.15% to get RSS: (.25 2 +.15 2 ) 0.5 = 0.29; the resulting additional FWHM due to gain shift is x =
(1 2 +(x/32) 2 ) 0.5 =.29/.25; 1 2 +(x/32) 2 = 1.36; x = 19%. The sources of gain change in the FPC are as follow, with the allocated allowances for each, to add up to 19% RSS:
We can keep a reserve of 16.8% to achieve the overall requirement of 19% FPC gain stability.
see See Also: Spectrum separation errors %=+/- ..46
Corresponds to accumulating 105 counts.
This includes relative intensity of K,L lines, x-ray source high voltage, target contamination, continuum to line ratio and source filter thickness.
These are relative errors between the monitor detector and the focal plane detector.
Many of the errors in See Also: Counts-to-line flux conversion during (RBND)max measurement %=+/- 0.47 will cancel out when determining the ratio of BND counting rates, so we believe that including them all for (R BND ) max and none for (R BND ) i is a conservative approach.
Here, we need to account for the differences in QE between the BND and FP detectors. There are at least two cases: BND-H FPC with either FPC or SSD in the focal plane.
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The window transmissions will be calibrated as a function of YZ position. This error allocation is for the residual errors after calibration. |
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We need sensitivity and derived rqmts for mesh placement/measurement. |
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See HXDS CDR analysis 6 : window slopes for transmission, and gas depth variations. Treat both local bubbling of window and global bending of wires |
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QE differences due to p,T differences. Variations in counter depth, especially the Be insert. |
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The error breakdowns are shown in See Also: Relative FP QE Errors .
See See Also: Ratio of livetimes (RBND)max and (RBND)i measurements %=+/- 0.2
Capability +/- 0.02% (Podgorksi et. al., op. cit)
See See Also: (RBND) max/(RBND)i %=+/-Relative detector quantum efficiency %=+/- 0.1
Capability +/- 0.02%, (Podgorski et. al., op. cit.)
See See Also: (RBND) max/(RBND)i %=+/-Relative detector quantum efficiency %=+/- 0.1
See See Also: Ratio of livetimes (RBND)max and (RBND)i measurements %=+/- 0.2
See See Also: Ratio of livetimes (RBND)max and (RBND)i measurements %=+/- 0.2
This measurement is planned with the SI in the focal plane.
The HXDS only monitors the beam. We consider its accuracy not to be a strong contributor, for the relative normalization of the wing PRF.
See See Also: (RBND) max/(RBND)i %=+/-Relative detector quantum efficiency %=+/- 0.1
The fractional Encircled Energy (EE) is expressed as:
qi is the angular diameter of the focal plane pinhole aperture i, where i=1,2,...max.
f(qi) is a correction factor for the deviation of the aperture i from an ideal circular hole of radius r i.
R FP , RBND are the x-ray line fluxes incident on the focal plane (FP) and beam normalization detectors (BND) respectively.
The Effective Area Aeff of the HRMA is expressed as:
where 
is the angular diameter of the largest pinhole aperture
f(
) is a correction factor for the deviation of the largest focal plane pinhole aperture from an ideal circular hole of angular diameter 
.
Focal plane measurements will be performed with an apertured flow proportional counter ora solid state detector (SSD). The x-ray beam incident on the mirror will be monitored with four flow proportional counters at the BND-H location and a flow proportional counter and a SSD at the BND-500 location. The beam will be mapped with a flow proportional counter at both BND-H and BND-500 locations.
We consider the case of the largest pinhole aperture q i , at an energy for which the EE( q i ) obtains its largest value. This case places the tightest accuracy requirement on the encircled energy, +/- 0.99%.The CEI requirement 3.2.1.1.1.6 states that the error of measuring the fractional EE within an aperture qi shall be:
or +/-10% of the measured value, whichever is smaller.
f(+/- i )/f(+/- max ) %=+/- 0.10
See See Also: (RBND) max/(RBND)i %=+/-Relative detector quantum efficiency %=+/- 0.1
See See Also: Ratio of livetimes (RBND)max and (RBND)i measurements %=+/- 0.2
We consider the case of the largest pinhole aperture +/- i at an energy for which the EE(+/- i ) obtains its largest value. This case places the tightest accuracy requirement on the encircled energy of 9.9%.
f(+/- i )/f(+/- max ) %=+/- 1.0
The accuracies here do not determine the requirements, being 10x looser than See Also: f(+/-i)/f(+/-max) %=+/- 0.10
See See Also: (RBND) max/(RBND)i %=+/-Relative detector quantum efficiency %=+/- 0.1
See See Also: Ratio of livetimes (RBND)max and (RBND)i measurements %=+/- 0.2
See See Also: Ratio of livetimes (RBND)max and (RBND)i measurements %=+/- 0.2
See See Also: Ratio of livetimes (RBND)max and (RBND)i measurements %=+/- 0.2
This refers to the absolute calibration of HXDS beam monitor detectors (BND), which will serve as the primary standard to determine the absolute x-ray flux in the beam at XRCF, thereby giving a calibration of the absolute effective area of the combined HRMA and focal plane SI effective area.
This will be measured at the PTB white beam line at BESSY. The energy resolution will be that of the detector. The input x-rays will be the undisturbed beam from the synchrotron ring, with no intervening optical elements, or filters, etc. We use the white beam as a standard source, whose intensity is calculated from special relativity and Maxwell's equations.
BESSY magnetic field 7 %=+/- 0.0080 |
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BESSY beam energy See Also: T. Lederer et al, Proc. SPIE 1995 2519 xxx. %=+/- 0.0075 |
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BESSY beam current See Also: T. Lederer et al, Proc. SPIE 1995 2519 xxx. %=+/- 0.001This will vary depending on the value of the beam current, which will be < 1000 electrons for these measurements 8 .
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Distance from ring tangent point to detector @BESSY See Also: T. Lederer et al, Proc. SPIE 1995 2519 xxx. %=+/- 0.025 |
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Detector aperture size error %=+/- 0.08This assumes we can measure the 5 mm diameter aperture to 1 +/-m. |
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BESSY electron beam source size and divergence, +/- y* See Also: T. Lederer et al, Proc. SPIE 1995 2519 xxx. %=+/- 0.15This quantity varies with x-ray energy, and is worst at about 2.5 keV, the value quoted here. |
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Alignment error in angle +/- to storage ring plane See Also: T. Lederer et al, Proc. SPIE 1995 2519 xxx. %=+/- 0.04 |
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Pileup component subtraction %=+/- 0.05 |
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Background %=+/- 0.05 |
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Poisson errors, 10 6 counts in peak %=+/- 0.10 |
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Incomplete charge collection %=+/- 0.01This represents our error in correcting for the counts that are not in the main photopeak, but appear in lower channels of the pulse height spectrum, due to incomplete charge collection in the SSD. There will be small amounts of counts that do not end up in the photopeak, for example, about 1% of the counts from the peak go into a "shelf" of incomplete charge collection events. About 10% of the shelf cannot be directly calibrated, because it is below the lower level threshold of the MCB. Although we may be able to model this, we cannot directly measure it, so we assume it is all error, so 10% of 1% = 0.1%! |
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Incomplete charge collection %=+/- 0.01 (TBR)This represents our error in correcting for the counts that are not in the main photopeak, but appear in lower channels of the pulse height spectrum, due to incomplete charge collection in the FPC. There will be small amounts of counts that do not end up in the photopeak, for example, about 1%(TBR) of the counts from the peak go into a "shelf" of incomplete charge collection events. Some fraction 10%(TBR) of the shelf cannot be directly calibrated, because it is below the lower level threshold of the MCB. Although we may be able to model this, we cannot directly measure it, so we assume it is all error, so 10% of 1(TBR)% = 0.1(TBR)%! |
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Systematics of fit %=+/- 0.05This includes any additional fitting errors in the spectral fit program, i.e. XSPEC. There will be little or no background or continuum, so we are not aware of any such factors, but this term allows for them. |
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Livetime. See See Also: Ratio of livetimes (RBND)max and (RBND)i measurements %=+/- 0.2 %=+/- 0.2 |
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Detector Window condensation, %=+/- 0.07 |
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gain shift %=+/- 0.15 |
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Window mesh modeling corrections %=+/- 0.1 |
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Window thickness variations %=+/-0.2We know that the FPC windows bulge through the wire mesh, and that the wire mesh bulges 10 . This results in variations of effective window thickness that modify the x-ray transmission. This effect is worst at the lowest energies, where the x-ray absorption in the window is the greatest. The number quoted here is for energy from 0.2-0.28 keV, and above 0.5 keV. At the lowest energy, 0.108 keV, we will probably not do better than 5%. |
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Reserve %=+/- 0.1 |
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These will be measured at various monochromator beam lines. Since there are intervening optical elements, we cannot calculate the x-ray flux from first principles. Rather, a standard detector is used to calibrate the x-ray flux incident on our detector. The primary standard detector is an electrical substitution radiometer (ESR).
Measured at PTB's SX700 grating monochromator, which operates from 0.1-1.5 keV. We will only calibrate at energies above 0.7 keV, because the SSD will not be reliable at lower energies.
The primary standard will be PTB's liquid He Electrical Substitution Radiometer (ESR), at a power level of order 10 +/-W. This will be transferred to photodiodes, which then provide a linearity scale down to the nW level needed for our detectors to count at reasonable rates.
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At 0.8 nA - 1 mA , a system of windowless highly linear calibrated photodiode detectors is used to monitor the white light synchrotron flux See Also: G. Ulm et al, 1989 Rev. Sci. Instrum. 60 1752. . %=+/- 0.6 |
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This includes any fitting errors in the spectral fit program, i.e. XSPEC. In this case, there will be small amounts of counts that do not end up in the photopeak. There will be little or no background or continuum. |
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We will most likely use the larger apertures, such as 5 mm down to ~1 mm diameter, so that we achieve adequate counting rates(?). |
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Measurements 1.1-5.9keV %=2.1 (SSD), same for FPC, 5% for FPC at 0.108 keV
At the BESSY KMC (Krystall MonoChromator)
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At 0.8 nA - 1 mA , a system of windowless highly linear calibrated photodiode detectors is used to monitor the white light synchrotron flux See Also: G. Ulm et al, 1989 Rev. Sci. Instrum. 60 1752. . %=+/- 0.6 |
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This includes any fitting errors in the spectral fit program, i.e. XSPEC. In this case, there will be small amounts of counts that do not end up in the photopeak. There will be little or no background or continuum. |
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We will most likely use the larger apertures, such as 5 mm down to ~1 mm diameter, so that we achieve adequate counting rates(?). |
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This value is not well corroborated; only a verbal estimate from Ulm. |
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, 
.
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.