4. High Resolution Mirror Assembly (HRMA)

The Chandra telescope consists of 4 pairs of concentric thin-walled, grazing-incidence Wolter Type-I mirrors. [X-ray optics are reviewed by B. Aschenbach (1985).] The front mirror of each pair is a paraboloid (

) and the back a hyperboloid (

). The eight mirrors were fabricated from Zerodur glass, polished, and coated with iridium on a binding layer of chromium.

The High Resolution Mirror Assembly (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 Gaussian focal point 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.. Some other characteristics are given in Table 4.1 and in section 4.5

Table: Chandra HRMA Characteristics
HRMA

    Optics Wolter Type-I

    Mirror coatings Iridium

    Nominal coating thickness 330 Å

    Mirror outer diameters (1, 3, 4, 6) 1.23, 0.99, 0.87, 0.65 m

    Mirror lengths ( or ) 84 cm

    Total length (pre-collimator to post-collimator) 276 cm

    Unobscured clear aperture 1145 cm

    HRMA mass 1484 kg

    Focal length $10.070 \pm 0.003$ m

    Plate scale $48.82 \pm 0.02\,\mu\rm m\,arcsec^{-1}$

    PSF FWHM (with detector) 0.5 arcsec

    Effective area:

        @ 0.25 keV 800 cm $^{2}$

        @ 5.0 keV 400 cm $^{2}$

        @ 8.0 keV 100 cm $^{2}$

    Ghost-free field of view 30 arcmin dia

**Table:** *Chandra* **HRMA** Characteristics
HRMA
Optics	Wolter Type-I
Mirror coatings	Iridium
Nominal coating thickness	330 Å
Mirror outer diameters (1, 3, 4, 6)	1.23, 0.99, 0.87, 0.65 m
Mirror lengths ( or )	84 cm
Total length (pre-collimator to post-collimator)	276 cm
Unobscured clear aperture	1145 cm
HRMA mass	1484 kg
Focal length	$10.070 \pm 0.003$ m
Plate scale	$48.82 \pm 0.02\,\mu\rm m\,arcsec^{-1}$
PSF FWHM (with detector)	0.5 arcsec
Effective area:
@ 0.25 keV	800 cm $^{2}$
@ 5.0 keV	400 cm $^{2}$
@ 8.0 keV	100 cm $^{2}$
Ghost-free field of view	30 arcmin dia

**Figure:** The 4 nested **HRMA** mirror pairs and associated structures.
$\begin{figure}\centering \scalebox{0.5}{\includegraphics{../../ogplots/hrma-config.eps}} \end{figure}$

4.2 Calibration and Performance

4.2.1 Calibration and Model

VanSpeybroeck (1997), Weisskopf (1997), and Zhao et al. (1997), describe the ground calibration of the HRMA and present some preliminary results. During these tests, the mirror assembly was mounted horizontally in a vacuum chamber and irradiated with X-rays from a source located at a distance of approximately 500 meters. The data taken in the XRCF (the X-Ray Calibration Facility at MSFC ) include the effective areas 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.

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 unobscured geometric clear aperture of the HRMA is 1145 cm

. The obstruction of the HRMA clear aperture by supporting struts is less than 10%. Since reflectivity depends on energy as well as grazing angle, the HRMA throughput varies with X-ray energy.

Figure 4.2 shows the HRMA effective area as a function of X-ray energy, in linear scale, as well as the HRMA /ACIS and HRMA /HRC effective areas. Figure 4.3 shows the same curves with log-log scale.

Figure 4.4 shows the effects of off-axis vignetting on the effective area for various energies; the plotted results are averages over the azimuthal angle.

The above predictions are based upon the mirror model discussed previously and scaled by the HRMA ground calibration data. The agreement between the effective area predicted for the ground calibration using this model and the actual measurement, as well as the scaling function used for the on-orbit prediction, are shown in Figure 4.5.

**Figure:** The **HRMA** **HRMA** /ACIS and **HRMA** /HRC effective areas versus X-ray energy in linear scale. 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 areas are the products of **HRMA** effective area and the Quantum Efficiency (QE) of ACIS -I3 (front illuminated) or ACIS -S3 (back illuminated). The **HRMA** /HRC effective areas are the products of **HRMA** effective area and the QE of HRC-I or HRC-S at their aimpoints, including the effect of UV/Ion Shields (UVIS).
$\begin{figure}\centering \scalebox{1.0}{\includegraphics{../../ogplots/hrma_ea_onaxis_qe.ps}} \par \end{figure}$

**Figure:** The **HRMA** **HRMA** /ACIS and **HRMA** /HRC effective areas versus X-ray energy in log-log scale. 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 areas are the products of **HRMA** effective area and the Quantum Efficiency (QE) of ACIS -I3 (front illuminated) or ACIS -S3 (back illuminated). The HRMA/HRC effective areas are the products of **HRMA** effective area and the QE of HRC-I or HRC-S at their aimpoints, including the effect of UV/Ion Shields (UVIS).
$\begin{figure}\centering \scalebox{1.0}{\includegraphics{../../ogplots/hrma_ea_onaxis_qe_log.ps}} \par \end{figure}$

**Figure:** The **HRMA** effective area versus off-axis angle, averaged over azimuth, for selected energies, normalized to the on-axis area for that energy.
$\begin{figure}\centering \scalebox{0.5}{\includegraphics{../../ogplots/hrma_ea_offaxis.ps}} \par \end{figure}$

**Figure:** The **HRMA** effective area measured at the XRCF. In the upper panel: the solid line is the raytrace simulation of the **HRMA** effective area within a 2 mm diameter aperture at the focus; the dashed line with error bars shows data taken with a solid state detector (SSD) with a C-K continuum source; the diamonds and triangles show data taken with a flow proportional counter (FPC) and SSD data with spectral line sources. The lower panel shows deviation of data from the raytrace: the dashed line with error bars is the ratio of SSD C-K continuum data vs. the raytrace; the diamonds and triangles show the ratio of FPC and SSD spectral line data vs. the raytrace; the solid line is a polynomial function, which gives equal weight to the deviations of the continuum and line measurements, for scaling the raytrace simulation to provide the predicted **HRMA** effective area.
$\begin{figure}\centering \scalebox{0.6}{\includegraphics*{../../ogplots/hrma_ea_data_wfpc.ps}} \vspace{-0.2in} \par\end{figure}$

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 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 narrowest PSF . The PSF broadens, and the encircled energy fraction decreases, as the off-axis angle increases because of mirror aberrations. The performance also degrades as the X-ray energy increases because of larger X-ray scattering.

4.2.3.1 On-axis Response

Figure 4.6 shows the encircled energy fraction as a function of image radius for on-axis rays and for different energies. The resulting increase in image size with energy is apparent. The fraction contained within one and ten arc seconds diameters for on-axis rays is shown as a function of energy in Figure 4.7 and in Table 4.2.

**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 of the four nested mirror pairs.
$\begin{figure}\centering \scalebox{0.55}{\includegraphics{../../ogplots/hrma_ee_pointsource.ps}} \end{figure}$

Table: HRMA Encircled Energy Performance
X-ray: Encircled Energy Fraction

$\lambda$ Diameter

kev Å $1^{\prime\prime}$ $10^{\prime\prime}$

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

**Table:** **HRMA** Encircled Energy Performance
X-ray:	Encircled Energy Fraction
	$\lambda$	Diameter
kev	Å	$1^{\prime\prime}$	$10^{\prime\prime}$
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

**Figure 4.7:** On-orbit performance prediction for encircled energy, calculated from model derived from ground-based calibration data.
$\begin{figure}\centering \scalebox{0.5}{\includegraphics{../../ogplots/hrma_ee.ps}} \end{figure}$

Pre-flight measurements and also images taken at the XRCF show that there is a slight ( $\approx 500 \mu$ m) 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 from the other shells. The effect of this asymmetry on images depends on energy because of the different relative contribution of mirror pair 6.

Figure 4.8 shows simulated HRMA /HRC-I images at four energies. The effect of the mirror pair 6 alignment errors can be seen in the 8.6 keV image; note that the core of this image is not centered in the distribution. This $0.2^{\prime\prime}$ effect is not important compared to other sources of image degradation encountered in flight such as uncertainties in the aspect solution.

**Figure:** Simulated on-axis **HRMA** /HRC-I on-axis images of mono-energetic point sources without aspect blurring. Energies are 1.49, 4.51, 6.40, and 8.63 keV. Surface brightness contours are logarithmic and spaced in factors of 3. The innermost contour is at 90% of the peak brightness. The 8.6 keV image core is off-center due to the shell 6 misalignment. Each panel is $3^{\prime\prime}$ square.
$\begin{figure}\centering \scalebox{0.75}{\includegraphics[1.3in,3.2in][7.2in,9.5in]{../../ogplots/hrma_hrc_onaxis_image_bw.ps}} \end{figure}$

4.2.3.2 Off-axis Response

The PSF broadens for off-axis sources, and there is considerable distortion in the image even for a perfect mirror set. This distortion is due to the aberrations of Wolter type I optics and to the different focal surfaces 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.

Figure 4.9 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 Chandra aspect error (FWHM: 0.22 $^{\prime\prime}$ ) are included.

The ACIS-I surface is not axially symmetric with respect to the HRMA optical axis, because the HRMA aimpoint is located at the inner corner of one of the four ACIS-I chips - I3. Thus the off-axis encircled energy radii are not azimuthally symmetric. Figure 4.10 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.

**Figure 4.9:** 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.
$\begin{figure}\centering \scalebox{0.7}{\includegraphics{../../ogplots/hrma_ee_offaxis_hrci.ps}} \par \par \end{figure}$

**Figure:** **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 at 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.
$\begin{figure}\centering \scalebox{0.75}{\includegraphics{../../ogplots/hrma_ee_offaxis_acisi.ps}} \par \par \end{figure}$

Figure 4.11 contains simulated HRMA images of point sources $5^{\prime}$ and $10^{\prime}$ off-axis, on the flat HRC-I surface, with and without the HRC-I detector effects. At $10^{\prime}$ off-axis the separation between the flat detector surface and the curved focal surface is significant. Cusps in the HRMA images are due to a slight misalignment of the parabolic and hyperbolic mirrors.

**Figure:** Simulated 1.49 keV images, for the **HRMA** only (at left, the pure mirror effects) and the **HRMA** /HRC-I combination (at right, mirror effects plus the HRC-I blur and pixelization), of a point source $5^{\prime}$ (at top) and $10^{\prime}$ (at bottom) off-axis. Panels are $11^{\prime\prime}$ and $22^{\prime\prime}$ square for $5^{\prime}$ and $10^{\prime}$ off-axis, respectively, much larger than the panels in figure 4.8. Spokes in the images are due to shadowing by mirror support struts. Cusps in the **HRMA** images are due to a slight misalignment of the parabolic and hyperbolic mirrors.
$\begin{figure}\centering \scalebox{0.75}{\includegraphics[0.7in,3.0in][6.9in,9.5in]{../../ogplots/hrma_offaxis_image_bw.ps}} \par \end{figure}$

4.2.4 Effective Area in Flight

There was a concern that the effective areas might change between ground calibration and flight due to accumulation of contaminants or degradation of the reflecting surfaces. A Flux Contamination Monitor (FCM) was added to evaluate these effects. The FCM consisted of radioactive sources embedded in the forward contamination cover. The ACIS response to these sources was measured in the XRCF at the end of ground calibration, and again in orbit before the forward contamination cover was removed. No change in performance was detected.

The FCM is described in Elsner et al., 1998. The Chandra detectors are not exposed to the FCM now that the forward contamination cover has been opened.

4.3 Ghost Images

Baffles prevent non-reflected or singly reflected rays from impinging on the focal plane within the central $30^{\prime}$ diameter of the field of view. Outside of this region, however, singly reflected rays from strong off-axis sources may appear. Figure 4.12 shows a simulated ghost image in which the off-axis angle was chosen to give the closest approach of singly-reflected rays to the focal point. In this situation, the outermost ray could extend into the HRC field of view. The area extending from the optical axis to a diameter of about 30 $^{\prime}$ is free from ghost images.

**Figure 4.12:** Calculated image of a source on the HRC-I at $53^{\prime }$ off-axis. The aimpoint is at position (0,0) at bottom center of the figure. The horizontally elongated bright region at (0,150) is the image produced by doubly reflected rays. The other curved lines in the figure are due to single reflections from different mirror segments. These lines comprise the ``ghost image''. If the HRC-I detector were centered on (0,0) with diagonal vertical, the upper corner of the field would be at (0,64). As this figure shows the ghost ray can be as close as (0,44) which is within the HRC-I field of view.
$\begin{figure}\centering \scalebox{0.5}{\includegraphics{../../ogplots/hrma_ghost.ps}} \par\end{figure}$

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 (these can be removed if desired.) These effects are illustrated for the HRC-I and HRC-S instruments in Figures 4.13 and 4.14 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 and 6.403 keV. A aspect error of 0.22 $^{\prime\prime}$ (FWHM) was included in the model calculations. The agreement between the observations and the lower energy model predicted curve is quite good. The HRC efficiency and typical spectral photon number densities both decrease with energy, so the higher energy response curve would not be expected for most sources.

**Figure 4.13:** The fractional encircled energy as a function of angular radius observed in flight compared to model calculations 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 HRC-I response function.
$\begin{figure}\centering \scalebox{0.7}{\includegraphics{../../ogplots/hrma_ee_aspect_hrc_i_point_obs_guide.ps}} \end{figure}$

**Figure 4.14:** The fractional encircled energy as a function of angular radius observed in flight compared to model calculations 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 HRC-S response function.
$\begin{figure}\centering \scalebox{0.7}{\includegraphics{../../ogplots/hrma_ee_aspect_hrc_s_point_obs_guide.ps}} \end{figure}$

Similar calculations have been performed for the ACIS-S (S3) over a wider range of energies; the results are shown in Figure 4.15. 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.

**Figure 4.15:** 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.
$\begin{figure}\centering \scalebox{0.7}{\includegraphics{../../ogplots/hrma_ee_aspect_acis_s_01_point_guide.ps}} \end{figure}$

The curves of this section, Figures 4.13, 4.14, and 4.15 may be compared with Figure 4.6 to estimate the image performance degradation due to non-HRMA effects.

4.5 HRMA Background Material

4.5.1 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 ( $1100\,\rm cm^2$ ) at low energies ( $<1\,\rm keV$ ).

The Validation Engineering Test Article-I (VETA-I) was constructed to verify the technology required for the spatial resolution of Chandra . VETA-I contained the

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, e.g. Hughes et al. 1992. Zhao et al. 1993, give a good overview of the VETA tests. A series of papers in SPIE Proceedings 3113, e.g. Zhao et al. 1997, report on the XRCF calibration of the HRMA assembly.

4.5.2 Exit Cone Angles

Table 4.3: Exit cone angles for each hyperboloid.
Hyperboloid $\theta_c$ $\theta_d$

Mirror [rad] [deg] [rad] [deg]

1 0.05961 3.42 0.06115 3.50

3 0.04795 2.75 0.04923 2.82

4 0.04223 2.42 0.04237 2.49

6 0.03144 1.80 0.03232 1.90

**Table 4.3:** Exit cone angles for each hyperboloid.
Hyperboloid	$\theta_c$	$\theta_d$
Mirror	[rad]	[deg]	[rad]	[deg]
1	0.05961	3.42	0.06115	3.50
3	0.04795	2.75	0.04923	2.82
4	0.04223	2.42	0.04237	2.49
6	0.03144	1.80	0.03232	1.90

4.5.3 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, and some results have been described in the 1997 July/Aug SPIE meeting proceedings.

4.5.4 Operating Environment

Insulation and heaters maintain the HRMA temperature at $70^\circ$ Fahrenheit on-orbit to minimize changes from the assembly and alignment environments.