The Constellation-X Spectroscopy X-Ray Telescope: Recent Technology
Development

Robert Petre[^1]^1^, John Lehan^1,2^, Stephen O'Dell^3^, Scott Owens^4^,
Paul B. Reid^5^, Timo Saha^4^, Jeff Stewart^6^, William D. Jones^3^,
William Zhang^1^

^1^X-ray Astrophysics Laboratory, Code 662, NASA / GSFC, Greenbelt, MD
20771 USA

^3^Universities Space Research Association

^2^Optics Branch, Code 551, NASA / GSFC, Greenbelt, MD 20771 USA

^4^Space Science Department, NASA / MSFC, Huntsville, AL 35812 USA

^5^Smithsonian Astrophysical Observatory, 60 Garden Street, Cambridge,
MA 02138 USA

^6^Mechanical Systems Branch, Code 543, NASA / GSFC, Greenbelt, MD 20771
USA

# ABSTRACT

We describe recent progress in the technology development program for
the mirror system for the Constellation-X Spectroscopy X-ray Telescope
(SXT). Development of this mirror represents a significant technology
challenge, as it must provide a combination of large effective area (3
sq. m) and modest angular resolution (15 arc second half power diameter
requirement; 5 arc second goal) with a limited mass allocation. The
baseline design incorporates over 200 nested Wolter 1 mirrors. Each of
these in turn is segmented in order to simplify handling of the mirrors
and facilitate mass production. The X-ray reflecting surfaces are
fabricated from thin, thermally formed glass sheets. Production
improvements have yielded mirror segments that approach the performance
requirement without the need for epoxy replication. A mounting and
alignment approach incorporating piezoelectric actuators has been shown
to manipulate mirror segments with the required precision without
introducing significant distortion. Substantial improvements in
metrology methodology have provided insights into the mirror segment
forming and alignment processes. We describe the technical advances made
over the past year and summarize near-term plans.

**Keywords:** X-ray mirrors, Constellation-X

**1. INTRODUCTION**

This paper represents the latest in a series of annual status reports
about the technology development program for the Constellation-X
Spectroscopy X-ray Telescope (SXT) mirror.^1-3^ Constellation-X is
NASA's next flagship X-ray observatory, a key component of the Beyond
Einstein program. The Constellation-X scientific goals can be found in
the paper by Garcia et al. in these proceedings.^4^ The overall mission
implementation, placing the SXT mirror in context, can be found in the
paper by White et al.^5^

The scientific goals of Constellation-X require sensitivity for
high-resolution spectroscopy that is a factor of 25-100 higher than
previous missions. This sensitivity requirement in turn calls for an
X-ray mirror system with ambitious performance goals. Adding to the
challenge are the envelope and mass constraints, which drive the program
toward innovative implementation.

Table 1 summarizes the key performance requirements for the SXT mirror.
These include an effective area of \~3 m^2^ at 1 keV and an angular
resolution of 12.5 arc seconds half power diameter (HPD). The critical
performance requirements listed in have not changed since the inception
of the program, but there is a strong desire to achieve the 5 arc second
angular resolution goal.

A modular design has been adopted for the SXT mirror. This design
incorporates tightly nested, thin glass mirror segments. The glass
segments are shaped by thermal forming, and an X-ray reflecting surface
applied by epoxy replication. This approach maximizes the throughput and
minimizes the areal density. It also facilitates mass production of many
identical mirror elements, thus keeping cost to a minimum.

> **Table 1**
>
> **SXT mirror requirements**
>
> Bandpass 0.25-10.0 keV
>
> Effective area (per mirror)
>
> \@0.25 keV 35,000 cm^2^ Total for mission (1-4 mirrors, depending on
> configuration)
>
> \@1.25 keV 33,000 cm^2^ 0.25 keV area for losses due to grating and
> detector
>
> \@6.0 keV 6,9000 cm^2^ inefficiency
>
> Angular resolution 12.5" HPD Consistent with observatory HPD of 15 arc
> seconds.
>
> 4" HPD goal Consistent with observatory HPD goal of 5 arc seconds
>
> Field of view 2.5 arc minutes Defined by detector field of view
>
> \>90 % of on-axis effective area at 1.25 keV across field of
>
> view

Over the past year, significant developments have occurred both within
the Constellation-X project, and the SXT technology development. One
major change over the past year has been a reconfiguration of the
mission. The baseline mission called for four satellites, launched
pairwise on Atlas V rockets. Each satellite had identical
instrumentation: a single 1.6 m diameter SXT mirror which fed a grating
spectrometer and a microcalorimeter, plus three Hard X-ray Telescope
systems (40 cm mirror plus focal plane detector). After considerable
study of numerous options, Constellation-X was reconfigured into a
single spacecraft, to be inserted directly to L2 via a Delta IV launch
vehicle. This spacecraft will carry four SXT systems and 12 HXT systems,
identical to the ones on the baseline configuration. This
reconfiguration is described in the paper by White in these
proceedings.^5^ The sole implication of this reconfiguration on the SXT
mirror systems is that the angular resolution error budget term
associated with mispointing of four spacecraft is replaced by one
representing misalignment on a common optical structure. The technology
development activities are unaffected.

A second major change is a substantial scaling back of technology
development funding. The reduced funding forced the SXT mirror team to
emphasize component development, largely using existing facilities, over
prototype development or system studies. This has proven extremely
beneficial in that a number of fundamental technical issues regarding
mirror fabrication and mounting have been solved.

**2. Mirror SEGMENT fabrication**

The mirror segment fabrication process now consistently yields segments
with surface quality approaching the requirement. This process is
described in the paper by Zhang in these proceedings^6^ and previous
publications.^7-9^ Figure 1 shows the progress that has been made since
the start of the program toward the angular resolution requirement and
goal, for typical segments and for the best ones.

In Figure 2 the power spectral density (PSD) needed to meet the angular
resolution requirement is plotted along with the measured PSD from one
of the best segments. The spatial frequency range in Figure 2 has been
divided into three regions. These are the low order terms with size
scale 2-20 cm, the mid-frequency range, with size scale 0.1-2.0 cm, and
the high frequency range, shorter than 0.1 cm, which is also known as
microroughness. The causes of errors in these three spatial frequency
domains are largely decoupled, and errors in them are dominated by
different factors. Minimizing the errors in each is the path toward
achieving the required or desired angular resolution.

In low order, distortions are largely determined by the quality of the
thermal forming, and not correctable by epoxy replication. This is the
regime where distortions arising from gravity and mechanical stresses
manifest themselves.

![](media/image1.png){width="5.375in" height="3.838888888888889in"}

![](media/image2.pct){width="4.875in"
height="3.707638888888889in"}**Figure 1:** Improvement of
Constellation-X SXT mirror segment surface quality over time. Typical
substrate quality approaches the Constellation-X requirement, while the
best surfaces exceed it.

**Figure 1:** The smooth curve represents the power spectral density
(PSD) distribution required for mirror segments to meet the SXT mirror
angular resolution requirement. The PSD can be divided into three
regimes as indicated by the dashed lines. The jagged curve represents
the PSD of one of the better segments, with no epoxy replication. The
power excess at low spatial frequencies is the result of known figure
errors in the forming mandrel.

This spatial frequency range largely dictates the figure and smoothness
requirements on the forming mandrels.

Mid-frequency surface errors are imparted to the substrate during
forming. We have demonstrated the very sensitive dependence of the
roughness in this domain on the physics of the forming process. This is
also the frequency range in which distortions appear due to the presence
of particulates between the forming mandrel and the substrate. The
mid-frequency errors can be substantially suppressed or removed by epoxy
replication.

The raw substrate material (Desag D263 borosilicate glass) has low
microroughness. This is largely preserved during forming, despite the
contact between the optical surface and the forming mandrel. Thus the
forming mandrel surfaces do not need to be highly polished. Epoxy
replication introduces an entirely new microsurface, imparted from the
replication mandrel. Thus when epoxy replication is performed, stringent
requirements are placed on the replication mandrel microroughness,
requiring expensive superpolishing.

Three factors drive our efforts at developing a mirror segment
production process that does not require epoxy replication. First is the
elimination of a second, expensive set of superpolished mandrels. Second
is removal of undesirable mechanical properties introduced by the epoxy
layer. Mechanical stress between the epoxy and the substrate introduced
by epoxy shrinkage during curing could manifest itself as another source
of low frequency error. The different coefficients of thermal expansion
of substrate and epoxy also lead to much tighter temperature constraints
on the mirror. Third is the obvious simplification of the segment
manufacturing process resulting from the deletion of a major step. While
epoxy replication remains in the production baseline, production cost
and risk can be significantly reduced if it becomes unnecessary. The key
to elimination of the need for replication is the improvement of the
mid-frequency roughness. We fully expect that identified process
improvements will allow us to drop replication from the baseline within
the next year.

Recent forming work has demonstrated that the formed substrates
consistently and faithfully reproduce the forming mandrel surface at low
spatial frequencies. Shown in Figure 3 are axial profiles from four
segments formed consecutively and the forming mandrel. The vertical
scale is greatly exaggerated. In general, deviations between the mandrel
and a substrate have an RMS height difference on the order of 50 nm
after large scale (2^nd^ order and lower) terms are ignored.

A fundamental problem we have encountered is determining the true
three-dimensional shape of the formed segment. While every recent
measurement we have performed suggests that the segments conform to the
mandrel on all scales, our ability to demonstrate this is limited by the
mechanical flimsiness of the segments, coupled with the difficulty of
mounting them in a way that minimizes stresses and removes the effect of
gravity. An example of the difficulty of measuring the segment figure is
illustrated in Figure 4. The two curves are PSD plots from the same
segment. The curve with the better overall PSD is the result of
measuring the surface profile with the segment mounted nearly vertically
in a three point metrology mount (the segment rests on a pair of soft
pads and is constrained at a single mounting point at the top. The worse
PSD in figure 4 was derived from the same segment held upside down in
the three-point mount. Distortions due to the inverted mounting
propagate to 11^th^ order of a polynomial fit, corresponding to a
spatial frequency of \~ 1 cm. This is the crossover point to
mid-frequency; thus the entire low frequency domain is distorted by the
metrology mount.

**3. Segment mounting and Alignment**

The challenge in measuring the low order figure is exactly the same
challenge associated with mounting and aligning the substrates. The
substrates must be held as stress free as possible, and with minimal
introduction of gravity-induced deformations. Finite element analysis
suggested that the optimum number of points at the entrance and exit
apertures necessary to hold the segment with minimal distortion is five.
The conceptual design of a module housing implementing this approach is
shown in Figure 5.

![](media/image3.pct){width="3.30625in" height="3.30625in"}

![](media/image4.pct){width="3.4305555555555554in"
height="3.4305555555555554in"}**Figure 3:** Axial profiles of a forming
mandrel (black trace) and four segments formed consecutively. Note that
the tick marks on the vertical scale represent 01 nm. The segment
profiles trace that of the mandrel nearly identically. The RMS height
difference between the mandrel and any segment is 50 nm or less.

**Figure 4:** Measured PSDs for one segment, held upright in a
three-point metrology mount, and held upside down. The profile
difference is introduced by the mounting. Significant differences on all
scales above \~1 cm are introduced. This experiment demonstrates the
sensitivity of the global figure of the mirror segments to the manner in
which they are mounted

![](media/image5.pct){width="2.4541666666666666in"
height="2.7527777777777778in"}

**Figure 5:** Schematic of a mirror module. The mounting scheme
incorporates five pairs of mounting points at the entrance and exit
apertures of each of the two reflection stages.

To verify that this mounting scheme will work, we have constructed a
simplified housing. This housing is composed of titanium, and has been
made much stiffer than a flight like housing so that mirror alignment
could be studied without worrying about structural distortions. The
housing can accommodate one or two pairs of mirrors; it is our
expectation that if we can demonstrate that a small number of mirror
segment pairs (i.e., two) can be coaligned to the required accuracy,
then it will be possible to successfully coalign all the mirror segments
comprising a module. This simplified housing, known as the Optical
Alignment Pathfinder 2 (OAP2) is shown in Figure 6. Each of the ten
mounting points consists of a bidirectional piezoelectric actuator. One
crucial aspect of the OAP2 unit is the cutout on the side facing the
segment reflecting surface. This opening affords normal incidence
viewing of over 90 percent of segment reflecting surface. This opening
makes possible normal incidence surface interferometry simultaneously
with focusing the mirror.

The alignment setup and procedure is described in detail in the paper by
Owens et al. In these proceedings.^10^ Briefly, the Centroid Detector
Array (CDA) is used to bring all azimuths along the segment to a common
focus.^11^ Simultaneously, approximately two-thirds of the surface is
imaged at normal incidence by a combination of a large aperture
interferometer and a cylindrical null lens. The interferometic image is
used to detect and minimize surface distortions introduced by actuator
movement.

Figure 7 shows the scatter of CDA points in the focal plane and the
simultaneous interferometer image for the secondary (hyperboloid) mirror
segment only. (Once the secondary mirror has been aligned and bonded,
the same procedure will be followed for the primary mirror segment.) For
the secondary segment mounted in the OAP2, we have found that the best
alignment represents a compromise between the best focus as determined
by the CDA and the least distorted surface as determined by the
interferometer. This is likely the consequence of intrinsic azimuthally
dependent slope errors in the segment originating on the mandrel
(delta-delta-R error).

The data in Figure 7 lead to an image quality prediction for the segment
of 5.1 arc seconds half power diameter (HPD). Combining this prediction
with several assumptions leads to an image quality prediction for the
aligned mirror pair. The assumptions are that the PSD of the secondary
mirror is represented by that inferred from the half of the segment
illuminated by the interferometer; that the primary segment surface has
an identical PSD to that of the secondary; and that alignment errors are
negligible. In that case, the geometric HPD is 11 arc seconds. Adding
scatter from the known mirror microroughness leads to an HPD at 1 keV of
14.6 arc seconds. Figure 8 shows a ray tracing simulation of the image
from the simulated segment pair, and the inferred point spread function.

![](media/image6.pct){width="4.43125in" height="3.4125in"}

![](media/image7.pct){width="3.2430555555555554in"
height="3.2819444444444446in"}**Figure 6:** The Optical Alignment
Pathfinder 2 (OAP2) assembly undergoing alignment. The mirror surfaces
can be seen through housing openings.

**Figure 7:** Output from alignment of secondary mirror in OAP2. The
left frame shows the scatter of return beams from the CDA in the focal
plane. The right frame shows a 2D interferometric image of the central
two thirds of the segment. The peak-to-valley level of distortions from
the nominal mirror shape is 3 µm.

![](media/image9.pct){width="3.05625in"
height="2.785416666666667in"}**Figure 7: P**redicted focal plane image
and point response function of the OAP2, assuming based on the measured
performance of the secondary. The performance of the primary is assumed
to be identical to that of the secondary, and alignment errors are
assumed to be negligible compared with the figure errors. The HPD at 1
keV is predicted to be 14.6 arc seconds, including scattering.

**5. SUMMARY**

Over the past year significant progress has been made in SXT mirror
technology despite a substantial funding reduction. The key results
include:

-   We have demonstrated that the thermal forming process consistently
    yields mirror segments that reproduce the mandrel figure with high
    fidelity.

-   We have shown that our knowledge of the quality of the global
    segment figure is limited by metrology.

-   The quality of the substrates is limited by the figure of the
    forming mandrels.

-   The mirror mounting and alignment scheme embodied by the OAP2,
    coupled with CDA focal plane measurements and normal incidence
    interferometric mapping is a feasible approach for meeting the SXT
    angular resolution requirement.

**6. Near term plans**

The significant funding reduction experienced in February 2006 is
expected to persist for the next several years. While the milestones
along SXT mirror technology development roadmap have not changed, the
speed at which they are being reached has been substantially reduced.
The next major milestone is the completion of the mirror segment pair
alignment in the OAP2 housing. It is anticipated that sometime within
the next year this assembly will be subjected to an X-ray imaging test
at the Marshall Space Flight Center Stray Light Facility. The X-ray
performance test results will be compared with the predictions based on
the extensive metrology data collected during the OAP2 alignment and the
results of finite element analysis. While the goal of this process is to
demonstrate that a mirror pair performs in X-rays consistent with the
Constellation-X requirement, it is more important at this stage of the
technology development to show consistency between measurements and
predictions so that we can improve mirror performance in future assembly
and alignment experiments.

Looking ahead beyond the X-ray test, we hope to:

-   Refigure a pair of mandrels close to the specifications for
    producing segments that meet the Con-X angular resolution goal. This
    will both prove that current segments are limited by mandrel
    quality, and allow us to explore the limits of the thermal forming
    process.

-   Introduce more stringent cleanliness controls and a smoother release
    layer into the thermal forming. Doing so will reduce the
    mid-frequency roughness to the degree that replication is no longer
    necessary. The elimination of replication and a dedicated set of
    replication mandrels will translate into substantial cost and risk
    reduction.

-   Modify the OAP2 housing to accommodate multiple reflector pairs.

-   Continue refinement of metrological techniques so metrology does
    limit our knowledge.

## ACKNOWLEDGEMENTS

Numerous talented and dedicated individuals from the SXT mirror team
member institutions have contributed to the progress toward the SXT
mirror goals. Special mention must be given to our key technical support
staff. These include Dave Content, Diep Nguyen and Geraldine Wright
(GSFC); Jim Mazzarella, Marton Sharpe, Melinda Hong, Charlie Fleetwood,
Theo Hadjimichael and Dave Colella (Swales Aerospace; and Josh Schneider
and Thomas Meagher (USAF PREST), The SXT mirror is a collaboration led
by NASA / GSFC, with critical contributions from SAO and NASA / MSFC.

## REFERENCES

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Stewart, W. D. Jones, and W. Zhang, Technology Development for the
Constellation-X Spectroscopy X-ray Telescope, Proc. SPIE, 5900, 59000V,
2005

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J. Stewart, W. Zhang, The Constellation-X spectroscopy x-ray telescope,
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9\. W. W. Zhang et al., Development of mirror segments for the
Constellation-X mission, Proc. SPIE, 5168, 168, 2004.

10\. S. M. Owens, T. Meagher, J. Schneider, J. P. Lehan, T.
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[^1]: ^\*^ [robert.petre-1@nasa.gov](mailto:Robert.petre-1@nasa.gov);
    phone 301-286-3844; fax 301-286-0677