Initial core scan data of the VETA-I x-ray mirror proved disappointing, showing considerable unpredicted image structure and poor measured FWHM. 2-D core scans were performed, providing important insight into the nature of the distortion. Image deconvolutions using a ray traced model PSF was performed successfully to reinforce our conclusion regarding the origin of the astigmatism. A mechanical correction was made to the optical structure, and the mirror was tested successfully (FWHM 0.22 arcsec) as a result

Bilbro, J.

Freeman, Mark D.

Hughes, John P

Vanspeybroeck, L.

Weisskopf, M.

English

NASA Technical Reports Server

vN93-26190
Image Analysis of the AXAF VETA-1 X-ray Mirror
M. Freeman, J. Hughes, L. Van Speybroeck
Smithsonian Astrophysical Observatory
60 Garden SL
Cambridge, MA 02138
(617)495-7000
J. Bilbro, M. Weisskopf
Space Sciences Laboratory
NASA / George C. Marshall Space Flight Center
ES 65, Huntsville, Alabama 35812
Phone (205)544-5498 FAX (205)544-7754
ABSTRACT
Initial core scan data of the VETA-1 x-ray mirror proved disappointing, showing considerable
unpredicted image structure and poor measured FWHM. 2-D core scans were performed, providing
important insight into the nature of the distortion. Image deconvolutions using a raytraced model PSF
was performed successfully to reinforce our conclusion regarding the origin of the astigmatism. A
mechanical correction was made to the optical structure, and the mirror was tested successfully (FWHM
0.22 arcsec) as a result.
1. INTRODUCTION
The Verification Engineering Test Article - 1 (VETA-1) was a subset of the High Resolution Mirror
Assembly (HRMA), the AXAF flight optics. It consisted of the outer mirror pair (P1/H1) in the
polished but uncut and uncoated state. The goal of the VETA-1 test was to demonstrate the feasability
of polishing grazing incidence x-ray optics to the level required by the stated AXAF mission
requirements. The Congressionally-mandated milestone was a FWHM of 0.5 arcsec for the optic, to be
reported by mid-September. The VETA-1 and its associated test hardware were placed in the X-ray
Calibration Facility (XRCF) at NASA's Marshall Space Flight Center (MSFC) during the last weeks of
August, 1991. Pumpdown of the chamber began on the evening of Friday, Aug. 30. It was found that
2-3 days were required to achieve thermal stabilization at vacuum before running critical tests. Using
the VETA X-ray Detection System (VXDS) and a quadrant shutter placed behind the mirror, relative
alignment of the opical elements was performed, first using the VXDS imaging detector, and then the
VXDS proportional counters and apertures. By Monday, Sept. 2, the alignment and focus adjustments
were complete, and we began detailed pinhole scan measurements of the VETA'i image.
Initial one-dimensional (l-D) core scans through the image center at the best RMS focus showed a
marked bimodal shape in the intensity distribution (Fig. 1). Even after many 1-D scans, the unexpected
shape and large variation of measured FWHM with scan position and direction did not yield the needed
understanding of the image, instead indicating significant two-dimensional (2-D) structure. In addition,
the measured FWHM was not sufficiently better than 0.5 arcsec to avoid concerns of measurement
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error. It was determined that to provide a better understanding of the image, it was necessary to perform
a 2-D raster scan of the entire image core. Weighing image detail against test time, a 19 by 19 raster
pattern using the 10 _tm pinhole was chosen, producing a sampled image of the inner 4 arcsec core of
the point response function (PRF).
2. INITIAL 2-D CORE SCANS ..................
Z _ Z: :
The first complete 2-D scan 0D: 10579) of the image, taken 6 days into the test (Sept. 5), is shown in
Fig. 2, in (a) as an isometric intensity plot, and 0a) as isointensity contours. This pattern of isometric
view followed by contours will be used throughout for image display. The 19 by 19 data were
resampled in the following images by 4 in each axis for visualization. An aluminum anode target,
which produces characteristic line radiation at approximately 1.488 keV, and the flow proportional
counter (FPC) were used. Note that the intensity corresponds the the number of counts accumulated
from the FPC spectra in an operator defined region-of-interest (ROD. No corrections were made for
deadtime, since the deadtime was dominated by the Beam No_allzati0n Detector (BND) Count rate,
making the relative deadtime Correction over the image only of order a few percent. Pulse pile-up
Energy: 1.49 keV
E
E
N
0.05
0.00
-0.05
(a) Isometric intensity plot
Full image span 190/_ (3.8 orcsec)
I I " -" I
0.__
-0.05 0.00 0.05
Y (ram)
(b) Isointensity Contours
' Contour
Levels:
Each 0.1
Normalized
Intensity
Figure 2. 19 x 19 Scan with 0.010 mm Pinhole
File: 1000AL1057g.scn
SAO_D$ 31Julg2
corrections were also ignored for these analyses, but are expected to be of order a few percent, since the
source intensity was controlled to limit the maximum count rate.
The image showed a significant "cross" structure. The alignment of the cross with the gravity vector
provided an indication of the origin of the distortion (the y-axis of the images shown [labelled Z] is the
anti-gravity direction). Although it was known that gravity produced ovalization of the optics, no
raytrace predictions of the most recent Kodak finite element model of the optics in the test configuration
had been performed by SAO. Work began immediately to perform these analyses. In addition, we
compared the focal position measured using only the top and bottom mirror quadrants to that of only the
left and right, and found them to differ by approximately 600 ttm.
3. MODEL POINT SPREAD FUNCTION
A NASTRAN Finite Element Analysis (lEA) model of the VETA-I in the test configuration was
obtained by SAO from Eastman Kodak, the load in this case being the body forces due to gravity. The
resultant predicted distortion, after removal of the rigid body effects, was primarily ovalization with a
magnitude of 4.95 I_m (zero to peak) for the paraboloid (P1) and 3.43 lain for the hyperboloid. SAO
produced an independent ANSYS model, with predicted values within 20% of the EKC model. Using
SAO-developed software and OSAC, a raytrace code developed by Perkin-Elmer (P. Glenn et. al.), the
FEA model data was fit with Legendre-Fourier poiyng__a!s _d _ytraced.ilIn_uded in the raytrace
model and the subsequent post-processing were the following effects_i _ _ _:_ - :_i _ _
1. Finite Source Distance (518.16 m)
2. Finite Source Size (.22 arcsec dia.)
3. P1-H1 Despace (109.03 mm)
4. Calculated Gravitational Distortion (above)
5. Zerodur Reflectivity at 1.488 keV
6. AAR errors (RMS = 0.098 arcsec, from HDOS)
7. Circumfrential slope errors: 6.446 grad (P1) and 9.745 grad (HI)
8. Sag errors: 1585 _ (P1) and 447 ,_ (HI)
9. Axial slope errors:
a. Low frequency gaussian core: 0.158 arcsec
b. Mid-frequency PSD term: 25 ,_ (18 mm correlation length)
c. Upper Mid-frequency PSD term: 10 _ (0.35 mm correlation length)
d. High frequency PSD term: 7 _ (0.018 mm correlation length)
The first four will be referred to as 'Facility Effects': Inclusion of just these terms is equivalent to
assuming a perfect mirror in the test configuration. No residual rnisalignment of P1 to the X-ray
Calibration Facility (XRCF) or PI to HI was assumed. Excellent relative positional stability of the
source, optics, and detectors was realized based on inspection of the Motion Detection System (MDS)
data. For this reason, we decided to ignore the effects of vibration in the simulation. Finally, the focal
plane ray file was sampled to simulate the actual 10 circular pinhole scan.
The results are shown in Fig. 3 (a) and (b), exhibiting good qualitative agreement with the measured
image. An algorithm was created to perform a simple image subtraction by scaling the simulation to the
peak of the measured image, then aligning them for minimum RMS difference. This resulted in an
RMS residual of 3.7%, a peak residual of 33.5%, and a correlation coefficient of 0.961. These data and
the measured focus difference pointed more strongly to the lg ovalization as the source of the image
distortion, although work continued to determine if there were reasonable alternate hypotheses. At this
point, engineering personnel from the Eastman Kodak Co. (EKC), the designers of the mirror support
structure, began to consider possible ways to corr_t the problem. SAO, TRW and MSFC staff desired
even more concrete evidence that this was ind_d _e cause, since the solution would most likely
involve breaking vacuum, making mechanical changes to the VETA-1 assembly, and another
pumpdown. With only days left before the _ needed to be reported, such a significant loss of test
time could only be contemplated if the confidence that it would correct the problem was very high.
4. DECONVOLUTION AND SUPPORTING DATA
Given that the fit to of the model to the data was reasonable, deconvolution of the facility effects from
the raw data was attempted. The assumption was made that the superposition of the facility effects (F),
such as the gravitational distortion or the finite source distance (see above), and the "true" imaging
performance of P1/H1 (P) could be represented as a two-dimensional convolution to yield the test data
(D):
D =F ®P -L F(R-r)P(r)dr.
The ultimate aim of the restoration was to restore the 'true' imaging performance of P1/H1, ie. remove
the 'facility effects'.
The general approach entailed resampling the 10 gm pinhole 19x19 point raster scan image onto 1 gm x
1 gm pixels, to yield D. The convolution kernel F was defined by running a raytrace of a perfect mirror
(i.e., without AAR, circumferential slope, sag, or axial slope errors) in the test configuration, including
only the facility effects as enumerated above. This was output as a FITS image with 1 gm x 1 gm
pixds. This image is shown in Figure 4. Two standard techniques for deconvolution were then used:
Wiener filter deconvolufion and a nonlinear recursive restoration scheme described by Richardson and
for astronomical use by Lucy [1112].Note that both of these deconvolution techniques are available under
IRAF (package: stsdas.playpen). The Richardson-Lucy (R-L) technique has been heavily employed for
deconvolution of HST images TM.
Wiener filter deconvolution is a simple Fourier quotient technique which uses estimates of the noise and
signal power spectrum (PS) to obtain an optimally-filtered result. In our application the noise PS was
assumed to be white and was computed from the input image. The PS of the convolution kernel F was
assumed to be noiseless, which is only approximately correct since the raytrace which produced this
function used a finite number of rays. A low pass filter (4 pixel sigma) was applied in the frequency
domain. The results are shown in Figure 5. The technique restores a point image with a full width half
maximum (FWHM) of 0.24 arcsec. However there is a significant amount of "ringing" in the image,
which appears as ripples in the zero level. This is often the case with this type of deconvolution
technique and arises because of the sharp digital filter and the lack of a constraint requiring the
restoration of positive counts only.
Energy: 1.49 keV
E
E
N
0.05
0.00
-0.05
(a) Isometric intensityplot
Full image span 190/_ (3.8 orcsec
, • i | | • i i | I , , , • 1
-0.05 0.00 0.05
Y (ram)
(b) IsointensRy Contours
Contour
Levels:
Each 0.1
Normalized
Intensity
Figure 3. SAO Raytroce Prediction of VETA-I Performance
EKC Structural Model of 19 Deformation
s_Dxos 31J_2
Energy: 1.49 keV
E
E
v
N
0.05
O.O0
-0.05
(e) Isometric intensity plot
Full imoge spon 190/_ (3.8 orcsec)
° ' I I ' " ' " " !
• • • I I , i , i | i i • • I •
-0.05 0.00 0.05
Y Cram)
(b) Isointensity Contours
• Contour
Levels:
Eoch 0.1
Normalized
Intensity
Figure 4. Facility Effects PSF
(Grovity(EKC), FinTte Source Size & Distance, end Despoce)
SAO/VXD$ 3 IJ.192
Energy: 1.4g keV
(a) Isometric intensity plot
E
E
v
N
0.05
0.00
-0.05
Full image span 190/_ (3.8 orcsec)
• ' ' ..... ' ' Contour
Levels:
-0,05 0.00 0.05
Y (ram)
(b) Isointensity Contours
Each O. 1
Normalized
Intensity
lmJgure 5. Wiener Deconvolution of 19x19 Scan 10579
using F'ocility Effects PSF
sao/v_s 31_2
The R-L image deconvolution requires that the restored data be non-negative everywhere. Furthermore
it insists on statistical agreement between the observed data and the rectified estimate, instead of exact
agreement and employs Z2 as the figure of merit. One well-known shortcoming of this approach is the
lack of a built-in stopping rule. We found that during the first 10 or so iterations the change in Z2 was
rapid, while after about 50 standard iterations the change in Z 2 from iteration to iteration became very
small. During the test period, we used this to indicate convergence. Figure 6 shows the restored image
from this technique after 8 accelerated (equivalent to - 50 standard) iterations. The FWHM of the
imaged point source is 0.21 arcsec.
5. MIRROR GRAVITY OVALIZATION CORRECTION AND RESULTS
All indications were that we had a correct hypothesis for the source of the image distortions. EKC had
determined that a force could be applied to the mirror support rings which would correct the majority of
the ovalization and related distortion. The data and a correction plan were presented to appropriate
project management personnel on Monday, Sept. 9. Approval was given to implement the correction,
and repressurization was begun as soon as the necessary hardware had been fabricated by EKC. After
the required 3 days of stabilzation, realignment of the optics began on Sept. 15. Two days later, on
Sept. 17, the first 19 x 19 scan after the lg correction had been applied was performed. The results are
plotted in Figure 7, showing a much improved PRF. Later that same day we measured the FWHM with
1D scans using the 5_tm pinhole to be 0.22 arcsec, the figure reported to the Congress and announced
publicly.
The corresponding OSAC raytrace model PSF of the new facitity effects is shown in Figure 8. Using
the same R-L deconvolution technique, we obtained the deconvolved image (after 8 accelerated
iterations) shown in Figure 9.
6. DISCUSSION OF THE R-L DECONVOLUTION RESULTS
It was noted during the test work, and in subsequent processing of test images, that the Richardson-Lucy
algorithm would produce continuous improvement in the estimated mirror performance for many
iterations, albeit at a decreasing rate. Although the deconvolution work during the test was used
primarily to establish correlation between the measured image and a model, it would be desirable to
develop a "stopping rule" such that an estimate of the true mirror performance (ie. removing the facilty
effects) might be made.
To investigate more completely the behavior of the restoration as a function of the number of iterations,
we employed the Accelerated R-L algorithm I41 in an IDL/PV-WAVE TM implementation available from
the ST-ECF. In our application, we saw an improvement in convergence rate of 5-8 over the standard
R-L algorithm. This allowed us to quickly "push" the restoration to the equivalent of hundreds of
standard iterations. Figure 10 shows the the FWHM plotted for both the pre- and post-correction
restorations, as well as the measured value and that produced by the Wiener filter. As noted, the
restoration continued to improve the image well beyond the measured value, although no direct
comparison can be made since the measured FWHM includes all facility effects, most significant in this
case being the source size effect. Although not evident in the restorations shown at 8 iterations, the
effects of 'over-restoring' the image can be seen in Figure 11, the restoration of scan 20057 after 32
accelerated R-L iterations. Here the data variations in the_ outer regions of the image are beginning to be
restored as separate "sources". This is inconsistent with our physical situation, and emphasizes the
importance of exercising caution in the use of this technique.
Energy: 1.49 keV
E
E
v
N
0.05
0.00
-0.05
(a) Isometric intensity plot
Full image span 190/_ (3.8 arcsec)
T , , " I | "," ' " I
• L , , | i • , • | • _ i | i | ,
-0.05 0.00 0.05
Y (ram)
(b) Isointensity Contours
• Contour
Levels:
Each 0.1
Normalized
Intens;ty
Figure 6. R-L (accel) Deconvolutlon of 19x19 Scan 10579
using Facility Effects PSF (8 iterations)
SAO, NXD$ 31Jura2
Energy: 1.49 keV
E
E
v
N
0.05
0.00
-0.05
(a) Isometric intensity plot
Full image span 190/_ (3.8 orcsec)
I I ' ,' " " I
I • . , i I 1 i l | I
-0.05 0.00 0.05
Y (mm)
(b) IsointensityContours
' Contour
Levels:
iEoch 0.1
Normalized
Intensity
Figure 7. 19 x 19 Scan with 0.010 mm Pinhole
File: O02AL2OO57.scn
SAO/VXDS 3 t Julg2
Energy: 1.49 keY
E
E
v
N
0.05
0.00
-0.05
(o) Isometric intensity plot
Full imoge spon 190/_ (3.8 orcsec)
I I ' -' " " I
i * ' " I , , • • 1 , • , • I • • •
-0.05 0.00 0.05
Y (mm)
(b) Isointensity Contours
Contour
Levels:
Each 0.1
Normalized
Intensity
Figure 8. Focility Effects PSF with Modeled 19 Correction
(Grov]ty(EKC), Finite Source Size & Distonce, end Despoce)
S,AO/VX:DS_t_m2
Energy: 1.4g keV
E
E
v
N
0.05
0.00
-0.05
(a) Isometric intensity plot
Full image span 190p (3.8 arcsec)
I ! ' -' ' " I
, • , • 1 , • , , I • • , • | • • •
-0.05 0.00 0.05
Y (me)
(b) IsointensityContours
Contour
Levels:
Each 0.1
Normalized
Intensity
Figure 9. R-L (eccel) Deconvolution of 19x19 Scan 20057
using Facility Effects PSF (8 iterations)
._AO,_ .._1Jut02
in
o
v
t-
oo
t_
"6
-r
1.0
0.8
0°6 --
0.4-
0.2--
0.0
0
R-L Restorotion of 10579
""-_ __rot;o. of IO579
R-L Restoration of 20057
kfimuur_l FWHM
I l I [ I l I
20 40
No. of Iterations (Lucy_occel)
Figure 10. FWHM of Image during Restoration
7. CONCLUSIONS AND FUTURE WORK
The measurement of the VETA-1 FWM within specification and on time was accomplished through
hard work by the test and analysis personnel of SAO, TRW, Eastman Kodak, and MSFC. The
information necessary to make the important real-time correction to the optic was derived in large part
from analysis work, especially the R-L deconvolution, performed in parallel with the test. We believe
this method of application, where certain known ofr modeled effects are deconvolved from measured
data to produce a more useful representation of the system performance, is applicable to many
measurement problems.
More work is necessary in the development of a R-L %topping rule" for this application. We intend to
pursue investigations of image frequency content and the statistics related to the knowledge of the
model PSF as possible avenues for the development of such a rule. This work will be an important part
of providing definition for the test of the HRMA.
Energy: 1.4g keV
E
E
N
0.05
0.00
-0.05
(a) Isometric intensity plot
Full image span 190p, (3.8 orcsec
• ' I I " .' " I " "
6
I . • • = I • • • I
-0.05 0.00 0.05
Y (ram)
(b) Isointensity Contours
' Contour
Levels:
Each O. 1
Normalized
Intensity
Figure II. R-L (accel) Oeconvolution of 19x19 Scan 20057
using Facility Effects PSF (32 iterations)
SAO_n(OS 3 t Ju192
ACKNOWLEDGEMENTS
We are grateful to H.-M. Adorf of the ST-ECF for providing the new implementation of the accelerated
R-L algorithm, a useful interpolation scheme for supsampling images, and many helpful suggestions
related to the application of the R-L technique.
REFERENCES
3.B. H. Richardson,J.Opt.Soc.America 62,55,1972.
3.L. B. Lucy, "An iterativetechniqueforthe rectificationof observeddistributions",
Astron.J.79-6,745-754,June 1974.
3.H.-M. Adorf,J. R. Walsh, and R. N. Hook, "RestorationExperiments at the ST-
ECF", Proc. Workshop The Restorationof HST Images and Spectra,R. L.White
and R. J.Allen (eds.),Space TelescopeScienceInstitute,BaltimoreMID, 21-22 Aug.
1990.
4.H.-M. Adorf, J. R. Walsh, R. N. Hook, and F. D. Murtaugh, "Acceleratingthe
Richardson-LucyAlgorithm",1992 (unpublished).


Image analysis of the AXAF VETA-I x ray mirror

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