**Photogrammetrically Measured Distortions of Composite Microwave
Reflector System in Vacuum at \~90K**

Peter Mulé, Michael D. Hill, Henry P. Sampler

Goddard Space Flight Center, Greenbelt Maryland

# ABSTRACT

**The Microwave Anisotropy Probe (MAP) Observatory, scheduled for a 2001
launch, is designed to measure temperature fluctuations (anisotropy) and
produce a high sensitivity and high spatial resolution (better than 0.3°
at 90 GHz.) map of the Cosmic Microwave Background (CMB) radiation over
the entire sky between 22 and 90 GHz. MAP utilizes back-to-back
composite Gregorian telescopes supported on a composite truss structure
to focus the microwave signals into 10 differential microwave receivers.
Proper position and shape of the telescope reflectors at the operating
temperature of \~90 K is a critical element to ensure mission success.**

**We describe the methods and analysis used to validate the in-flight
position and shape predictions for the reflectors based on
photogrammetric metrology data taken under vacuum with the reflectors at
\~90K. Contour maps showing reflector distortions were generated. The
resulting reflector distortion data are shown to be crucial to the
analytical assessment of the MAP instrument\'s microwave system
in-flight performance.**

**Keywords:** reflectors**,** distortions, and photogrammetry

**1. INTRODUCTION**

The MAP instrument is designed to measure the anisotropy of the Cosmic
Microwave Background (CMB) radiation over the full sky while operating
at a temperature of approximately 90K. The instrument\'s Thermal
Reflector System (TRS) consist of back-to-back Gregorian telescopes with
reflectors manufactured by Programmed Composite Incorporated (PCI) of
Anaheim California, and are constructed of SF-70A-75/RS-12D facesheets
with a shaped Korex core sandwich bonded with a FM-73 film adhesive.
Each reflector has an aluminum honeycomb backing structure with
XN-70A/RS-3 facesheets. The truss structure on which the reflectors are
mounted is constructed of XN-70A/RS-3 and M46J/RS-3 flat laminates
bonded with EA 9394 adhesive.

Figure 1 shows the positions of the primary and secondary reflectors on
the composite truss structure comprising the Thermal Reflector System
(TRS). A flight unit as well as a Reflector Engineering Unit (REU) was
manufactured identical except that the REU included only one reflector
pair and part of the truss on the opposing side was removed. Both the
flight TRS and the REU were instrumental in characterizing the reflector
system.

![](media/image1.pct)

Figure 1: Thermal Reflective System (TRS)

Accurate predictions of in-flight reflector distortion and reflector
position values were necessary to predict the instrument antenna
patterns. Distortion and position values are input into Diffraction
Analysis of a Dual Reflector Antenna (DADRA) code (a product of YRS Inc)
to provide the antenna pattern at the various frequencies. Distortions
were initially derived with finite element analysis by applying flight
temperatures to the structural finite element model. In parallel, we
were investigating photogrammetry as a technique to verify the reflector
shapes during thermal vacuum testing. A close range photogrammetry
system**^1^** used to acquire precise coordinates from photographs was
acquired and initially used during thermal vacuum testing of a Reflector
Engineering Unit (REU. Dramatic differences in Finite Element Model
(FEM) and photogrammetrically (PG) measured shapes were realized (Figure
2). Attempts to make sense of the FEM were unsuccessful. Photogrammetric
measurements were adopted as the method of deriving reflector shape and
point position values to be used for the flight antenna pattern and
beamwidth analysis of the reflectors.

Figure 2: REU Primary Reflector FEM vs Photogrammetry Deformations from
Ideal at ≈90K

(Plots are of z-axis deformation in the reflector coordinate system)

![](media/image2.jpeg){width="6.4944444444444445in"
height="4.208333333333333in"}

The desired surface figures (ideal) were defined for a cold reflector by
Princeton U., and actual surface figures were verified at room
temperature by the REU and TRS manufacturer. They performed a continuous
surface scan with an SMX ^TM^ laser tracker prior to coating the
surfaces and subsequent integration of the reflectors as a telescope
unit. Tooling balls located on ears extending from each reflector were
measured and valued at this time. The coordinates of the reflector
tooling balls with warm offsets were used to align the reflectors in a
local instrument reference frame during integration at room temperature.
Tooling hole boss (THB) targets on the TRS truss structure were also
added and valued in the local reference frame of the instrument to
provide a means of reestablishing the reference frame after removing the
tooling ball targets on ears extending from the reflectors. A
combination of the warm (atmospheric pressure) and cold (vacuum) PG
measurements, the defined ideal surface figure, and a knowledge of the
warm surface positions with respect to ideal (from the TRS
manufacturer), allowed us to describe the reflector positions under
flight-like conditions. DADRA code was then used to analyze the effects
of the relative positions and distortions of the reflectors on the
optical performance (beamwidth and antenna pattern).

**2. Photogrammetry Measurements**

The target and point position measurements reported here were acquired
from retro-reflective photogrammetry targets designed to be placed in
the THBs and from stick-on photogrammetry retro-reflective targets
placed on the front surfaces of the reflectors (two primaries -35
targets each, 2 secondaries-13 targets each). Measurements were
performed at ambient temperature at atmospheric pressure and in vacuum
at ambient temperature and when cold (Table 1). The photogrammetry
camera used to make the measurements was mounted in a thermally
controlled canister on a carousel mounted atop a helium shroud
surrounding the TRS. The carousel itself was remotely operated to
position the camera in 42 locations and 2 orientations to allow for
triangulation and resection of target coordinates and camera positions
in the photographs taken. PG target positions were measured with a
precision of 0.002 inches.

Table 1: TRS Photogrammetry Test Conditions

  ------- -------------- -------- ----------------------------------------
  PG Run  Pressure       Temp (K) Comments

  1       Atmospheric    290      Established reflector target baseline
                                  values

  2       Vacuum         290      Identified effects of vacuum (none)

  3       Vacuum         91       First cold deformation case

  4       Vacuum         95       Second cold deformation case

  5       Atmospheric    294      Identify residual effects of thermal
          (N2)                    vacuum cycling (none)
  ------- -------------- -------- ----------------------------------------

To verify the precision of the PG system measurements, ambient
temperature and pressure PG measurements of the TRS THB targets were
compared with measurements made with a Leica Laser Tracker (LT) system
and measurements made using a theodolite network system (the Analytic
Industrial Metrology System (AIMS)). The three-metrology systems agreed
to within 0.007 inches (0.178 mm) worst case. The PG system measurements
when compared to each other were repeatable to 0.002 inches (0.051 mm)
and agreed with the values established in the final Laser Tracker
measurements performed by the telescope\'s manufacturer.

Analysis of the deformations of the TRS in thermal vacuum required only
minor changes in the methods of establishing the local instrument
coordinate reference frame. The low coefficient of thermal expansion
(CTE) and symmetry of the truss structure allowed the use of room
temperature THB coordinates measured on the truss when performing a
transformation of coordinates into the local coordinate reference frame.
The truss THB targets were located symmetrically such that no biasing
would occur in their alignment when cold. Vertical translations of the
truss at its Titanium flexure interface due to flexure contraction
(0.0046 inches (0.117 mm)) were noted. The final coordinates when cold
were established by least squares fitting the truss THB target
measurement to the room temperature measurement values. Then scaling
back using scale-bars of known CTE and temperature (the scale factor was
very near 1 confirming a low CTE for the truss), together with applying
predicted flexure contraction translation.

**3. Reflector Distortions**

Figure 3 shows the placement scheme of the PG targets on the surfaces of
the TRS primary and secondary reflectors. Contamination concerns as well
as line of sight concerns restricted the number and location of surface
targets. Target locations were chosen to best describe the overall
distortion based on the distortion pattern identified during Reflector
Engineering Unit (REU) testing. Targets were not placed on the upper
portion of the secondary reflector due to the camera could not view it
in the test configuration.

Figure 3: PG Target Positions on Primary Reflector 2R and Secondary
Reflector 2

![](media/image3.jpeg){width="6.675694444444445in"
height="4.470833333333333in"}

To develop a description of the distortions of the primary reflectors
when cold and due to the DADRA code requiring a specific input format,
the following process was used:

1.  The measured coordinates of the reflector targets when cold were
    least squares fit to their warm positions. This placed the cold
    surface of the reflector in a position known with respect to the
    ideal surface figure.

2.  Knowledge of the reflector warm surface position with respect to an
    ideal surface figure, (from telescope manufacturer data) allowed us
    to transform positions from step 1 to their locations for ideal
    surface figure. Steps 1 and 2 provided knowledge of the measured
    reflector cold positions with respect to an ideal surface figure.

3.  The target positions were then compared with the ideal surface
    figure using Imageware surface fitting software where a shift in the
    standing axis direction was allowed to partially correct for the
    0.010-inch (0.254 mm.) target thickness.

4.  Residuals from the least squares fit) from step 3 were used to
    develop distortion values in the reflector local coordinate
    reference frame (the format required for DADRA code).

5.  Fine grid interpolation was performed using NASTRAN modeling. DADRA
    requires a x, y, and dz input so that an interpolation of dz could
    be done using a flat plate model with enforced displacement.

We compared the distortions measured with the photogrammetric camera
(PG) with the warm distortions measured with the PCI laser. Table 2 is a
summary of LT and PG based surface distortions for the TRS primary
reflectors. This comparison highlighted differences in the outer annulus
that has the largest unsupported areas and the least stiff backing
structure. These differences are likely due to relaxation of the
reflector material between the initial LT measurement and the PG
measurement. LT measurements were made prior to the surface coating and
integration of the reflectors onto the truss structure.

Table 2: TRS Primary Reflector RMS Distortion Summaries ~(i)~

  -------------- --------- --------- --------- --------- --------- ---------
                 Primary                       Primary 3           
                 2R                                                

                 r \< 9.8  9.8\< r   r \> 19.7 r \< 9.8  9.8\< r   r \> 19.7
                           \<19.7                        \<19.7    

  Requirement    0.0015    0.0020    0.0030    0.0015    0.0020    0.0030

  LT Warm +      0.0024    0.0021    0.0034    0.0018    0.0017    0.0031
  ^(ii)^                                                           

  PG Warm        0.0024    0.0024    0.0052    0.0022    0.0037    0.0060
  ^(iii)^                                                          

  PG Cold        0.0069    0.0053    0.0117    0.0047    0.0064    0.0111
  ^(iii)^                                                          
  -------------- --------- --------- --------- --------- --------- ---------

(i) Values represent surface normal errors. Distortion contour plots
    represent z component error of the optical coordinate system.

(ii) LT measured points and additional derived points included for more
     uniform and complete distribution.

(iii) PG measured points and additional derived points included.

Table 3 below is a summary of surface target residuals for a secondary
reflector in the local coordinate reference frame of the TRS after least
squares fitting to the warm data. The small residuals agree with
measurements made on the REU.

Table 3: TRS Secondary Cold Fit to Warm PG Residuals ~(\*)~

  ----------------- ----------- --------- --------- ----------- --------- ---------
                    Secondary                       Secondary             
                    SN 2                            SN 3                  

  No. of Targets    9                               8                     

                    dX          dY        dZ        dX          dY        dZ

  Standard          0.0012      0.0015    0.0009    0.0021      0.0008    0.0010
  Deviation                                                               

  Minimum           -0.0025     -0.0027   -0.0010   -0.0040     -0.0010   -0.0018

  Maximum           0.0015      0.0022    0.0015    0.0030      0.0013    0.0011
  ----------------- ----------- --------- --------- ----------- --------- ---------

(\*) Three upper targets on the secondary reflectors were at extreme
angles and are included in a limited number of photos. These targets
were not included in summary.

Contour maps were created to visually represent the distortions of the
reflectors. The contours represent actual surface as compared to ideal
surface deviations in the z axes direction in the reflector coordinate
system. The local coordinate axes for the reflectors can be seen in
Figure 4**.** DADRA code requires the x, y, and delta z format**.**
Figure 5 shows the relations between the surface normal and the
reflector z translation direction for a single point. An Ideal reflector
would appear as a flat disc of uniform color. Images are orientated such
that we are looking at the reflective surface along an axis nearly
parallel with the individual reflector z-axis (a slight x-axis rotation
is applied to provide view of distortion). The offset angles are used in
the images to give a better idea of the distortion patterns and do not
show reflector shape.

Figure 4: Reflector Coordinate Systems

![](media/image4.png){width="3.4in" height="3.3986111111111112in"}

Figure 5: Relations between Surface Normal and Reflector dZ for a single
point in the local area of the point

![](media/image5.jpeg){width="6.5in" height="3.921527777777778in"}

The contour maps in figure 6 show warm (as-built) distortions of primary
reflector 2R as derived from laser tracker and photogrammetry
measurements. The 35 PG targets produce a relatively good representation
of the distortion over the entire surface. LT data consisted of
approximately 1000 points distributed over the entire surface.
Differences in these images, and those for reflector SN 3, are mainly
near the outer perimeter and are likely due to extrapolation in areas of
high distortion gradient and minor changes in the reflectors shape
during the surface coating and integration process following the initial
LT measurements.

Figure 6: Primary Reflector 2R Laser Tracker and PG Camera Comparisons
(Warm)

![](media/image6.jpeg){width="5.950694444444444in"
height="4.358333333333333in"}

The contour maps in figure 7 show warm (as-built) distortions of primary
reflector 3 as derived from laser tracker and photogrammetry
measurements. There is an apparent difference in the lower section of
the contour maps. Later THB measurements show the balls in this area to
be out of position by approximately 0.010 inches when compared to the
baseline data measured prior to delivery of the reflector system.

Figure 7: Primary Reflector 3 Laser Tracker and PG Camera Measurements
(Warm)

![](media/image7.jpeg){width="5.950694444444444in" height="4.35in"}

The contour maps in Figure 8 shows the primary reflector distortions
based on the cold PG data. The distortions when cold are nearly
identical for the two reflectors. These images reflect the DADRA
distortion input values used to predict flight performance.

Figure 8: TRS Primary Reflectors PG Measured Distortions at 90K

![](media/image8.jpeg){width="6.05in" height="4.414583333333334in"}

The contour maps in figure 9 were created from the PG measurements
performed on the REU in a cold vacuum environment. These are included to
show the similarity to TRS distortions and how a reduced number of
targets were able to create a good shape. When compared to the TRS cold
images it revealed that a hat ring stiffener added to the outer
perimeter of the TRS reflectors slightly reduced the distortion along
the outer rim, especially in the middle and upper rim areas where the
ring properties were the stiffest. The primary reflector back rib
pattern is apparent in this cold distortion image.

Figure 9: PG Camera Measurements at Room Temperature and at 90K

![](media/image9.jpeg){width="5.950694444444444in"
height="4.597916666666666in"}

The secondary reflector contour maps of figure 10 are based on the REU
measurements. The secondary reflector surface was completely targeted
(81 PG target positions marked) for the REU testing. The images show
that the overall distortion of the secondary after the cold transition
is negligible supporting the limited TRS secondary reflector
measurements.

Figure 10: REU Secondary Reflector PG Measurement Distortion Contour
Maps

![](media/image10.jpeg){width="5.951388888888889in"
height="4.317361111111111in"}

**4. Photogrammetry Based Performance Predictions**

To derive the flight beamwidth predictions and antenna patterns for the
MAP optical system (feedhorns and reflectors), the TRS reflector shape
and position data were incorporated in the DADRA code input. Secondary
reflector warm distortions were used for flight predicts since
negligible distortions were measured for the Secondary and their full
surface shapes could not be obtained. Flight performance predictions
were within the criteria set by MAP systems engineering analysis. A
comparison with ground test results was made to give confidence in
combining the PG measured shape, position predictions, and DADRA code.
For the integrated telescopes and feed horns, the comparison showed
excellent agreement between test measurements and analytic predictions
at the various feed-horn positions. [Results are]{.underline} shown in
Table 4 where the X-Beam FWHM is the lateral beam width and Y-Beam FWHM
is the vertical beam width.

Table 4: Comparison of Test and Analytical Performance at Ambient

  ----------- ---------- ---------- ----------- ---------- --------- ---------- ------ -------- ---------- -------- ---------- ---
                         Pointing                                               Beam                                           
                         ^(1)^                                                  Size                                           

  Frequency   Feed Horn             Elevation              Azimuth                     X-Beam              Y-Beam              
              Position              (°)                    (°)                         FWHM (°)            FWHM (°)            

                                    Test        Analysis   Test      Analysis          Test     Analysis   Test     Analysis   

  30 GHz      Ka1A                  -22.26      -22.28     -2.34     -2.34             0.551    0.561      0.684    0.672      

  40 GHz.     Q2A                   -17.77      -17.77     1.97      1.97              0.569    0.543      0.491    0.469      

  60 Ghz      V2A                   -19.66      -19.69     2.04      2.03              0.304    0.317      0.307    0.313      

  90 GHz.     W2A                   -19.04      -19.04     -0.56     -0.56             0.190    0.205      0.187    0.191      

  90 GHz.     W4A                   -20.14      -20.16     0.60      0.61              0.202    0.210      0.201    0.208      

  30 GHz.     Ka1A                  -22.26      -22.27     -2.42     -2.43             0.549    0.560      0.690    0.672      

  40 GHz.     Q2A                   -17.72      -17.72     1.95      1.92              0.573    0.541      0.491    0.465      

  60 GHz.     V2A                   -19.65      -19.64     2.00      2.03              0.293    0.313      0.304    0.306      

  90 GHz.     W2A                   -19.05      -19.01     -0.61     -0.62             0.189    0.201      0.189    0.193      

  90 GHz.     W4A                   -20.13      -20.11     0.55      0.55              0.193    0.205      0.199    0.207      
  ----------- ---------- ---------- ----------- ---------- --------- ---------- ------ -------- ---------- -------- ---------- ---

(1) Test pointing values correct for approximated offset in chamber
    boresight

**5. Conclusions**

Photogrammetric measurements have allowed us to obtain the shape and
position values of our reflectors in vacuum at cryogenic temperatures.
Empirical data of the shape when cold was a significant improvement over
analytical predictions and also highlighted shape errors due to
fabrication where analytical predictions assume a perfect initial shape.
When compared to Laser Tracker metrology, photogrammetric measurements
captured the as built distortions of the reflectors and identified a
possible relaxation of the reflector material. Photogrammetry together
with beam mapping and DADRA code enabled us to quantify and qualify the
ground and on-orbit characteristics of the microwave reflectors.

**ACKNOWLEDGMENTS**

The authors would like to thank Acey Hererra (Swales and Associates),
John Brown (Geodetic Services, Inc.), Programmed Composite, Inc., and
John Beggs (Goddard Space Flight Center).

## REFERENCES

1.  Automation in Digital Close-Range Photogrammetry, Clive S. Fraser,
    First Trans Tasman Surveyors Conference, 12-18 April, 1997, New
    Castle