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Chapter 4
High Resolution Mirror Assembly (HRMA)

4.1  Introduction

The Chandra X-ray telescope consists of 4 pairs of concentric thin-walled, grazing-incidence Wolter Type-I mirrors called the High Resolution Mirror Assembly (HRMA) [X-ray optics are reviewed by B. Aschenbach (1985)]. The front mirror of each pair is a paraboloid (Pn) and the back a hyperboloid (Hn). The eight mirrors were fabricated from Zerodur glass, polished, and coated with iridium on a binding layer of chromium.

4.1.1  Description and Physical Configuration

The HRMA, shown schematically in Figure 4.1, contains the nested mirrors, center, forward and aft aperture plates, baffles, inner and outer cylinders, mounts, pre- and post-collimators, fiducial light transfer components, mirror support sleeves, forward and aft contamination covers, flux contamination monitors, and thermal control hardware. The outer mirror pair is number 1, and, progressing inwards, 3, 4, and 6. The original design had six mirror pairs; numbers 2 and 5 were eliminated. The pair diameters range from about 0.65 to 1.23 meters. The distance from the center of the Central Aperture Plate (CAP) separating the paraboloid and hyperboloid mirrors to the HRMA focus is 10.0548 meters, with each mirror pair varying slightly about this value. Note that this distance is close to, but not exactly, the focal length . An annular on-axis beam enters each mirror pair, is reflected from paraboloids and hyperboloids and exits to converge to a focus. The angle θ between the direction of the reflected ray and the optical axis lies between two cone angles θc and θd. These and other important HRMA characteristics are listed in Table 4.1.
./images/hrma-config.png
Figure 4.1: The four nested HRMA mirror pairs and associated structures.
Link to postscript file for Figure 4.1
Table 4.1: Chandra HRMA Characteristics

    Optics Wolter Type-I
    Mirror coating Iridium (330 Å, nominal)
    Mirror outer diameters (1, 3, 4, 6)1.23, 0.99, 0.87, 0.65 m
    Mirror lengths (Pn or Hn) 84 cm
    Total length (pre- to post-collimator) 276 cm
    Unobscured clear aperture 1145 cm2
    Mass 1484 kg
    Focal length 10.070 ±0.003 m
    Plate scale 48.82 ±0.02 μm arcsec−1
    Exit cone angles from each hyperboloid:
      θc (1, 3, 4, 6)3.42°, 2.75°, 2.42°, 1.80°
      θd (1, 3, 4, 6)3.50°, 2.82°, 2.49°, 1.90°
    f-ratios (1, 3, 4, 6)8.4, 10.4, 11.8, 15.7
    PSF FWHM (with detector) < 0.5′′
   
Effective area:
@ 0.25 keV 800 cm2
@ 5.0 keV 400 cm2
@ 8.0 keV 100 cm2
    Ghost-free field of view 30′ diameter

4.1.2  Sub-assembly Calibration

Extensive measurements of the mirror shapes and of the surface characteristics were made at Hughes-Danbury Optical Systems (HDOS) during fabrication of the mirror segments and during assembly at Eastman-Kodak Co. HRMA throughput depends critically on the coating of the individual mirror elements carried out at Optical Coating Laboratory, Santa Rosa, California. Mirror flats were present in the coating chamber and coated with iridium at the same time as the HRMA mirror elements. Reflectivity of X-rays from these witness flats was measured with the X-ray beam from the synchrotron at the Brookhaven National Laboratory [Graessle, D. E., et al., 1998, 2004].

4.1.3  Operating Environment

Insulation and heaters maintain the HRMA temperature at 70°F (21°C) on-orbit to minimize changes from the assembly, alignment environments, and to minimize molecular contamination.

4.1.4  Heritage

The Chandra mirrors represent a logical progression from those of the Einstein (HEAO-2) [Giacconi et al. 1979] and Rosat [Trümper 1983; Aschenbach 1991] missions. Each of these previous X-ray observatories utilized nested Wolter Type-I optics with about 4 arcsec angular resolution. The Einstein mirror assembly had considerably less geometric area than Chandra, while Rosat had comparable area (1100 cm2) at low energies ( < 1 keV).
To verify the technology required for the spatial resolution of Chandra, a Validation Engineering Test Article-I (VETA-I ) was constructed and tested in 1991. VETA-I contained the P1H1 proto-flight mirror shells constructed to final tolerances, but uncoated and with ends uncut. The VETA-I tests included the image full-width-half-maximum, encircled energy, effective area, and ring focus properties (for azimuthal and low spatial-frequency figure). Many of the results of these tests appear in SPIE Proceedings 1742. A good overview of the VETA tests is given by Zhao et al. 1994, in SPIE Proceedings 2011.

4.2  Calibration and Performance

4.2.1  Calibration and Model

Before launch, the HRMA underwent extensive ground calibration tests at the X-Ray Calibration Facility (XRCF) at Marshall Space Flight Center (MSFC), Huntsville, AL, from September 1996 through May 1997. The full HRMA XRCF Calibration Report is accessible at http://cxc.harvard.edu/cal/Hrma/XRCF_Report. During these tests, the mirror assembly was mounted horizontally in a vacuum chamber and irradiated with X-rays from various electron-impact sources located at a distance of 524.7 meters. The data taken at the XRCF include the effective area and image distributions as a function of incident energy and angle. The mirror performance during these tests differs from that expected in space because of gravity distortions and the finite source size and distance; consequently, the calibration data cannot be directly compared to flight observations. The approach taken was to develop a model based upon surface and assembly measurements taken before the X-ray calibration activity. The X-ray calibration data then were used to validate this model and to make minor adjustments in model parameters to achieve satisfactory agreement with the observations. Further minor modifications were made as a result of flight experience. A series of papers in SPIE Proceedings 3113 report the results of the HRMA ground calibration.
The HRMA characteristics illustrated in this chapter were generated by a ray-trace program using this model. Note that this chapter typically gives characteristics of the HRMA only; unless otherwise indicated, blurring caused by the detector and the aspect solution is not included. These effects are very important for on-axis sources, and are included in the instrument chapters (Chapters 6 and 7). See also section 4.4.

4.2.2  HRMA Effective Area

The unobstructed geometric aperture of the HRMA is 1145 cm2. The obstruction of the HRMA aperture by supporting struts is less than 10%. Since the reflectivity of the mirror optics depends on photon energy as well as grazing angle, the HRMA throughput varies with X-ray energy.
The HRMA effective area is derived from the the predictions of the raytrace code discussed above along with empirical corrections based on the XRCF ground-based calibration data. The initial XRCF correction (i.e., the correction used to calculate the HRMA effective area prior to CALDB 4.1.1) was derived assuming that there was an insignificant layer of molecular contamination on the mirrors. Subsequent in-flight gratings observations of blazars showed evidence for systematic effects near the Ir-M edges of the coating on the mirror as shown in Figure 4.2. Using these data and raytrace simulations, it was estimated that a 22Å layer of hydrocarbon was present on the mirror optics. An updated HRMA effective area was released in CALDB 3.2.1 on Dec. 15, 2005 based on the predictions of the raytrace code now with a uniform 22Å layer of molecular contamination on all 8 optics.
Subsequently, inconsistencies in the measure of cluster temperatures derived by two different methods (line and continuum measures) led to a re-analysis of the data taken at the XRCF. This reanalysis provided evidence that molecular contamination was already present on the mirrors at XRCF. Thus, since the initial, ad-hoc, empirical correction of the HRMA model had already corrected for most of the effects of the molecular contamination, the addition of another 22Å of contamination in the raytrace model post-launch (CALDB 3.2.1) was an over-correction .
During XRCF testing, a system of shutters was placed behind the HRMA so that the effective area of the 4 shells could be measured independently. These tests were essential since the gratings intercept X-rays from different shells. Two focal plane instruments were used during XRCF: 1) a flow proportional counter (FPC) and 2) a solid state detector (SSD). Both of these instruments were non-imaging detectors and were used in conjunction with a number of different pin hole apertures. Using the data obtained from each mirror pair, the thicknesses of the contaminant on shells 1, 3, 4 and 6 were determined to be 28, 18, 20 and 27Å  respectively. Thus a new version of the HRMA effective area (CALDB 4.1.1) is being released at this time (Jan 2009), based on the predictions of the raytrace code with the, as-measured, contamination depths on each shell. In addition, an energy independent correction is applied to the predictions of the raytrace code for each shell to determine the absolute effective area. The correction factor is calculated by averaging the averaged FPC emission line data with the SSD continuum data for that shell. Note that, while a gray correction is applied to each shell, the overall empirical correction for the full HRMA absolute effective area is not energy-independent, since different shells contribute a different fraction of the total effective area at different energies (see Figure 4.3).
Several HRMA effective area models have been generated with different methods for calculating the gray corrections for each shell (e.g., no gray correction or gray corrections with unequal weighting between the FPC and SSD data) to determine the systematic effect of the gray corrections on the gas temperatures derived from ACIS observations of clusters of galaxies. For cool clusters (kT < 4 keV), the derived gas temperatures are essentially independent of the method used to calculate the gray correction. For hotter clusters, the derived temperatures vary by ± 2% depending on the algorithm used to determine the gray correction
The combined HRMA/ACIS and HRMA/HRC effective areas released in CALDB 4.1.1 are shown in Figure 4.4 and the effect of off-axis vignetting on the HRMA  effective area is shown in Figure 4.5 at several different photon energies. Note that this change in the effective area also serves to bring Chandra and XMM-Newton continuum measurements of cluster temperatures into closer agreement.
./images/hrma_ea_irm.png
Figure 4.2: Combined residuals from power law fits to 18 blazar observations (Marshall, H.L., 2005). The residuals in the upper panel are based upon models of contaminant free optics, while those in the lower are based upon a model of the mirror surfaces which includes a thin (22Å) hydrocarbon layer.
Link to postscript file for Figure 4.2
 
./images/hrma_ea_xrcf_data_raytrace_olvd.png
Figure 4.3: The HRMA Effective area: The raytrace prediction (top panel) and the ratio (bottom panel) of the XRCF measurements to the raytrace simulation are shown as a function of energy. The raytrace includes the effects of molecular contamination of variable thickness on the mirrors. The dotted line (to emphasize that these measurements were taken simultaneously) with error bars shows the data taken with a solid state detector (SSD) with a C-K continuum source. Data obtained from spectral line sources with a flow proportional counter (FPC) are shown as diamonds; obtained with a solid state detector (SSD) are shown as triangles. All the line measurements are circled for clarity. The dashed (green) line in the bottom panel shows the XRCF empirical correction to the raytrace based on the XRCF data. The dashed (green) line in the upper panel shows the absolute HRMA effective area with the XRCF empirical correction.[Note that the color is viewable only in the electronic version.]
Link to postscript file for Figure 4.3
 
./images/hrma_ea_onaxis_qe.png ./images/hrma_ea_onaxis_qe_log.png
Figure 4.4: The HRMA/ACIS and HRMA/HRC effective areas versus X-ray energy in linear-linear (top) and log-log (bottom) scales. The structure near 2 keV is due to the iridium M-edge. The HRMA effective area is calculated by the raytrace simulation based on the HRMA model and scaled by the XRCF calibration data. The HRMA/ACIS effective area is the product of the HRMA effective area and the Quantum Efficiency (QE) of ACIS-I3 (front illuminated) or ACIS-S3 (back illuminated). The HRMA/HRC effective area is the product of HRMA effective area and the QE of HRC-I or HRC-S at their aimpoints, including the effect of UV/Ion Shields (UVIS). [Note: the colored lines are viewable in the electronic version]
Link to postscript file for Figure 4.4
./images/hrma_ea_offaxis.png
Figure 4.5: The HRMA  effective area versus off-axis angle, averaged over four azimuthal directions, for selected energies, normalized to the on-axis area for that energy.
Link to postscript file for Figure 4.5

4.2.3  Point-Spread-Function and Encircled Energy Fraction

The Chandra HRMA point-spread function (PSF ) has been simulated with numerical ray-trace calculations based upon the mirror model previously discussed. A most useful parameter is the encircled energy fraction (the two-dimensional integral of the PSF) as a function of radius from the image center. The PSF and the encircled energy fraction for a given radius depend upon off-axis angle and energy. The HRMA optical axis is defined for practical purposes, and calibrated in flight, as the direction of the sharpest PSF. The PSF broadens, and the encircled energy fraction decreases, as (1) the off-axis angle increases because of mirror aberrations; and (2) the X-ray energy increases because of increased X-ray scattering.

On-axis PSF

Figure 4.6 shows the encircled energy fraction as a function of image radius for an on-axis point source and for different energies. The resulting increase in image size with energy is apparent. Figure 4.7 shows the radii of selected encircled energy fractions as functions of energy for an on-axis point source. Table 4.2 lists the encircled energy fraction contained within one and ten arc seconds diameters for an on-axis point source at different energies.
./images/hrma_psf_guide_fp.png
Figure 4.6: The Fractional encircled energy as a function of angular radius, calculated for an on-axis point source, at selected X-ray energies. The curves are the combined response and centered at the common focus of the full HRMA, i.e. four nested mirror pairs. For higher energies (8.638 keV and 9.700 keV), the curves are broadened at small radii. This is because the focus of higher energies does not coincide with the the HRMA common focus, but is offset by about 0.2′′, due to a slight tilt of the HRMA mirror pair 6.
Link to postscript file for Figure 4.6
./images/hrma_ee.png
Figure 4.7: The radii of selected encircled energy fractions as functions of X-ray energy for an on-axis point source, calculated from the mirror model derived from ground-based calibration data.
Link to postscript file for Figure 4.7
Table 4.2: HRMA Encircled Energy Performance

X-ray:Encircled Energy Fraction
EλDiameter
keVÅ1′′ 10′′
0.1085 114.2712 0.7954 0.9979
0.1833 67.6401 0.7937 0.9955
0.2770 44.7597 0.7906 0.9929
0.5230 23.7064 0.7817 0.9871
0.9297 13.3359 0.7650 0.9780
1.4967 8.2838 0.7436 0.9739
2.0424 6.0706 0.7261 0.9674
2.9843 4.1545 0.6960 0.9560
3.4440 3.6000 0.6808 0.9479
4.5108 2.7486 0.6510 0.9319
5.4147 2.2898 0.6426 0.9300
6.4038 1.9361 0.6365 0.9344
8.0478 1.5406 0.5457 0.9185
8.6389 1.4352 0.5256 0.9151
10.0000 1.2398 0.4971 0.8954
Pre-flight measurements and images taken at the XRCF show that there is a slight ( ≈ 500 μm) offset between the optical axes of the paraboloids and hyperboloids, and that pair 6 is slightly tilted with respect to the other three. Consequently, the image from mirror pair 6 is not as symmetrical as the images produced by the other shells. The effect of this asymmetry on images depends on energy because of the different relative contribution of mirror pair 6.
./images/hrma_hrc_onaxis_image_bw.png
Figure 4.8: Simulated on-axis HRMA/HRC-I images of on-axis mono-energetic point sources with aspect blurring. The grayscale is a linear stretch; surface brightness contours are at 90%, 80%, 60%, 40%, and 20% of the peak brightness. The 8 keV image core is asymmetric and off-center due to the shell 6 misalignment.
Link to postscript file for Figure 4.8
Figure 4.8 shows simulated HRMA/HRC-I images at several energies. The effect of the mirror pair 6 alignment errors can be seen in the higher energy images as then mirror pair 6 becomes the dominant contributor to the total effective area. Note the movement of position of the core as well as the asymmetric flaring. The  ∼ 0.2′′ core motion is comparable to other factors of image degradation encountered in flight, such as uncertainties in the aspect solution.
The HRMA PSF has a faint halo extending to large angles, resulting from X-rays scattering from micro-roughness on the mirror surfaces. This scattering is energy dependent; the spectrum of the scattered X-rays hardens significantly with increasing angle from the source. An empirical model was generated based on the ground calibration measurements; a number of systematic effects remain to be accounted for, and the uncertainties in the flux in the wings are probably at least 30-50%. This model is described more fully in http://cxc.harvard.edu/cal/Hrma/psf/XRCF_PSF_wing_profile/. A deep calibration observation of Her X-1 (obsid 3662) was obtained in order to improve the understanding of the PSF wings. The SIM was shifted to move the optical axis to  ∼ 1′ from the edge of the S3 detector furthest from the frame store; a Y-offset moved the image  ∼ 1′ into node 0 of the detector. The resulting pointing is  ∼ 45′′ off-axis, effectively on-axis with regard to the mirror scattering properties. The analysis is discussed in more detail in http://cxc.harvard.edu/cal/Hrma/psf/wing_analysis.ps; see also http://cxc.harvard.edu/cal/Hrma/users_guide
Radial profiles of the Her X-1 scattering wings are plotted for energy bands 1.0-2.0 keV and 3.0-4.0 keV in Fig. 4.9. These are surface brightness profiles normalized by the source count rate estimated from the transfer streak spectrum. The units of the normalized profiles are in arcsec−2. A fit (powerlaw plus exponential cutoff) is overplotted, and the fit applies for θ > 15′′. Inside 15′′, the profiles are increasingly depressed because of the effects of pileup in this very bright source. The shape of the wing profile is well represented (beyond 15′′), but the overall normalization may be off up to a factor of two.
./images/hrma_wings_both_rev2.png
Figure 4.9: Normalized radial profiles (units arcsec−2) of the Her X-1 scattering wings. The shapes are well determined beyond 15′′, but the overall normalization may be uncertain by a factor of 2. The lower curve shows the 1.0-2.0 keV profile and the upper curve shows the 3.0-4.0 keV profile. In each case, the heavy solid line is a powerlaw plus exponential cutoff fit to the Her X-1 data. The overall normalizations are uncertain by up to a factor of two.
Link to postscript file for Figure 4.9
Because the mirror scattering is in part diffractive, the diffuse mirror scattering halo is energy dependent. Spectra extracted from the diffuse mirror scattering wings of the PSF are significantly modified from the spectrum of the incident source X-rays. Generally, the scattering halo spectrum becomes harder with increasing angle from the source Fig. 4.10 shows the ratio of diffuse spectra extracted from annuli centered on the specular image (Her X-1) to the corresponding spectrum extracted from the ACIS transfer streak; the transfer streak spectrum is thought to be  ∼ 4% piled up in this case. To make the variations more evident, the ratios have been normalized to 1 at 2 keV.
./images/hrma_ann_over_xfrstreak_rev2.png
Figure 4.10: Hardening of the diffuse mirror scattering halo with distance from the image. The ratio of spectra extracted for a number of annuli centered on the specular image to the spectrum extracted from the ACIS transfer streak. The legend indicates the annular radii in arcsec.
Link to postscript file for Figure 4.10

Off-axis PSF

The PSF broadens for off-axis sources, and there is considerable distortion in the image even if the HRMA were perfect. This distortion is due to the aberrations of Wolter type I optics and to the different focal surfaces (Figure 4.11) for the four mirror pairs. The increase in image size with off-axis angle is greatest for the inner shell, and hence is larger for higher X-ray energies.
./images/hrma_focal_surface.png
Figure 4.11: The HRMA focal surface (from simulations), indicating its dependence on energy and off-axis source position.
Link to postscript file for Figure 4.11
Figure 4.12 shows the dependence of encircled energy radii on off-axis angle on the HRC-I with the HRMA focus at the HRC-I aimpoint. Because the HRC-I is axially symmetric with respect to the HRMA optical axis, the off-axis encircled energy radii are almost azimuthally symmetric, except some small asymmetry due to the imperfect HRMA as mentioned above. The figure gives the averaged radii for 1.49 keV and 6.40 keV at 50% and 90% encircled energy. The blurs due to the HRC-I spatial resolution and the aspect solution, estimated to be FWHM: 0.22′′, are included.
./images/hrma_ee_offaxis_hrci.png
Figure 4.12: The HRMA/HRC-I  encircled energy average radii for circles enclosing 50% and 90% of the power at 1.49 and 6.40 keV as a function of off-axis angle. The HRC-I surface is a flat plane perpendicular to the optical axis, which does not follow the curved Chandra focal plane. These curves include the blurs due to the HRC-I spatial resolution and the Chandra aspect error.
Link to postscript file for Figure 4.12
The ACIS-I surface is not axially symmetric with respect to the HRMA optical axis, because the HRMA aimpoint is located near the inner corner of one of the four ACIS-I chips - I3. Thus the off-axis encircled energy radii are not azimuthally symmetric. Figure 4.13 shows the dependence of encircled energy radii on off-axis angle on the four ACIS-I chips. The figure gives the encircled energy radii for 1.49 keV and 6.40 keV at 50% and 90% encircled energy in four azimuthal directions - from the aimpoint to the outer corners of the four ACIS-I chips. The blurs due to the ACIS-I spatial resolution and the Chandra aspect error are included.
./images/hrma_ee_offaxis_acisi.png
Figure 4.13: The HRMA/ACIS-I encircled energy radii for circles enclosing 50% and 90% of the power at 1.49 and 6.40 keV as a function of off-axis angle. The ACIS-I surface is composed by four tilted flat chips which approximate the curved Chandra focal plane. The HRMA optical axis passes near the aimpoint which is located near the inner corner of chip I3. Thus the off-axis encircled energy radii are not azimuthally symmetric. The four panels show these radii's radial dependence in four azimuthal directions - from the aimpoint to the outer corners of the four ACIS-I chips. These curves include the blurs due to the ACIS-I spatial resolution and the Chandra aspect error.
Link to postscript file for Figure 4.13
Figures 4.14 and 4.15 illustrate the effect of aberrations on images of off-axis point sources at 1.49 keV and 6.4 keV. The images are simulations of the HRMA alone, projected to the HRC-I detector plane. The degradation in image quality is primarily due to the separation between the detector plane and the effective focal plane, which is a strong function of both energy and off-axis angle (see Figure 4.11). Cusps in the HRMA images are due to a slight misalignment of the parabolic and hyperbolic mirrors. The signal in these figures is much higher than what might be expected in an actual observation. Figure 4.16 shows how the morphology of an off-axis image varies with the number of counts in the image. It is very easy to mistakenly conclude that an off-axis source is extended or has several components, even with a large number of counts.
./images/hrma_offaxis_image_1_49.png
Figure 4.14: Simulated 1.49 keV images, for the HRMA only. Images are shown with a linear stretch, as they would appear on the sky, at three off-axis angles (5′, 10′, and 15′ and various azimuths. The images are all to the same scale, illustrated by the scale bar. The spacing between images is arbitrary. The surface brightness of the images at 10′ and 15′ has been enhanced to show structure. Spokes in the images are due to shadowing by mirror support struts. Cusps are due to a slight misalignment of the parabolic and hyperbolic mirrors. These simulations are at an effective roll of zero - observations should be "de-rolled" before comparison to these images.
Link to postscript file for Figure 4.14
./images/hrma_offaxis_image_6_4.png
Figure 4.15: Simulated 6.4 keV images, for the HRMA  only. Images are shown with a linear stretch, as they would appear on the sky, at three off-axis angles (5′, 10′, and 15′ and various azimuths. The images are all to the same scale, illustrated by the scale bar. The spacing between images is arbitrary. The surface brightness of the images at 10′ and 15′ has been enhanced to show structure. Spokes in the images are due to shadowing by mirror support struts. Cusps in are due to a slight misalignment of the parabolic and hyperbolic mirrors. These simulations are at an effective roll of zero - observations should be "de-rolled" before comparison to these images.
Link to postscript file for Figure 4.15
./images/hrma_offaxis_image_1_49_confusion.png
Figure 4.16: A simulated 1.49 keV point source at an off-axis angle of 5′, binned to ACIS pixels. The panels show what the source would look like with a varying number of counts. Note how the apparent morphology is a strong function of the number of counts, and how even with a large number of counts one might mistake it for an extended source or even for multiple sources.
Link to postscript file for Figure 4.16

4.3  Ghost Images

Baffles prevent non-reflected or singly reflected photons from impinging on the focal plane within the central 30′ diameter region of the field of view. Outside of this region, however, singly reflected photons from strong off-axis sources may appear. The spray of singly reflected photons is faint relative to the direct image, but can be quite complex. Each individual paraboloidal or hyperboloidal mirror can generate its own single-reflection ghosts. These form loops sweeping in toward the center of the focal plane as the source off-axis angle increases. The ghost loops from the smallest mirrors are the first to approach the central regions as source off-axis angle increases. With increasing source off-axis angle, the large mirrors come into play. As a loop approaches the central 30′ diameter region of the field of view, the inner parts of the loop fade and break up.
These single-reflection ghosts can impinge on the detector even if the source itself does not fall within the detector field of view. These ghosts mainly affect the outermost portions of those detectors which extend to large off-axis angles: HRC-I, and the spectroscopy arrays, HRC-S and ACIS-S. Figure 4.17 shows simulated ghost images on the ACIS-S array. Point sources were simulated at a range of off-axis angle θ and at a fixed off-axis azimuth (φ = 5°). The effects discussed above (e.g. fading of the loops as they approach the central field) can be seen in comparing the ghosts in the 30′-32.5′-35′ sequence, or in the 50′-52.5′ sequence.
Imaging observations with HRC-I or spectroscopy observations with HRC-S or ACIS-S which are near very bright sources can be checked using ChaRT/Marx raytraces do determine whether single-reflection ghost images are likely to be a problem.
./images/hrma_ghost_aciss_mosaic_150dpi.png
Figure 4.17: Simulated images of off-axis sources. The off-axis angle, theta (θ, in arcmin), is indicated, and all simulations were performed for the same value of φ (5°). The rectangle indicates the footprint for one end of the ACIS-S detector. These simulations illustrate how singly reflected photons can hit the detector even when the specular image is well outside the field of view. The surface brightness of these ghosts is low relative to the brightness of the X-ray sources, but could be relevant in planning observations near extremely bright X-ray sources.
Link to postscript file for Figure 4.17

4.4  Effects of Aspect and Instrument Uncertainties

The HRMA performance discussed in the previous sections will be slightly degraded by uncertainties in the aspect solution and the details of the imaging detector spatial response function. The ground software system also deliberately adds a small random position error to reduce image artifacts which result from instrument and data system integer location values. The randomization may be turned off in data processing if desired. These effects are illustrated for the HRC-I and HRC-S instruments in Figures 4.18 and 4.19 respectively. These figures also show the fractional encircled energy as a function of radius actually observed in flight compared to model calculations at 0.277, 1.496 and 6.403 keV. An aspect error of 0.22′′ (FWHM) was included in the model calculations. The observed encircled energy curve most resembles that calculated for a monoenergetic source at 1.5 keV because this is typically the energy of the average detected photon.
Similar calculations have been performed for the ACIS-S(S3) over a wider range of energies; the results are shown in Figure 4.20. The simulation accounted for the typical spacecraft jitter, so the location of the instrument pixel boundaries has little effect. There is, however, a small effect of the location of the source compared to the data system pixel boundaries. These particular calculations were performed for a point source centered on the boundary between two data system pixels. The ACIS-I instrument response is similar.
Figures 4.18, 4.19, and 4.20 may be compared with Figure 4.6 to estimate the image performance degradation due to non-HRMA effects.
./images/hrma_ee_aspect_hrc_i_point_obs_guide.png
Figure 4.18: The HRMA HRC-I on-axis fractional encircled energy as a function of angular radius from a point source (Ar Lac) observed in flight compared to raytrace simulations for an on-axis point-source at selected X-ray energies, including the aspect uncertainties and the HRC-I pixelization effects.
Link to postscript file for Figure 4.18
./images/hrma_ee_aspect_hrc_s_point_obs_guide.png
Figure 4.19: The HRMA/HRC-S on-axis fractional encircled energy as a function of angular radius from a point source (LMC X-1) observed in flight compared to raytrace simulations for an on-axis point-source at selected X-ray energies, including the aspect uncertainties and the HRC-S pixelization effects.
Link to postscript file for Figure 4.19
./images/hrma_ee_aspect_acis_s_01_point_guide.png
Figure 4.20: The fractional encircled energy as a function of angular radius expected for in flight ACIS-S(S3) measurements for an on-axis point-source at selected X-ray energies. The curves are the combined response of the four nested mirror pairs, typical aspect uncertainties, and the ACIS response function.
Link to postscript file for Figure 4.20

4.5  References

Aschenbach, B. 1985, Rep. Prog. Phys. 48, 579
Aschenbach, B. 1991, Rev. Mod. Astron. 4, 173
Boese, F.G. 2000, Astron. Ap. Suppl. 507, 141
Edgar, R.J., et al. 1997, SPIE Proceedings, 3113, 124
Elsner, R.F., et al. 1998, SPIE Proceedings, 3444, 177
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Postscript copies of various aspects of the HRMA calibration can be obtained from the CXC Optics Calibration Group at http://cxc.harvard.edu/cal/Hrma/XRCF_Report/
A detailed guide to using and understanding the HRMA is available at http://cxc.harvard.edu/cal/Hrma/users_guide
Further information can be obtained from the MSFC Chandra calibration page at http://wwwastro.msfc.nasa.gov/xray/xraycal/
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