A test method particularly suited for X-ray telescopes was evaluated experimentally. The method makes use of a focused ring formed by an annular aperture when using a point source at a finite distance. This would supplement measurements of the best focus image which is blurred when the test source is at a finite distance. The telescope used was the Technology Mirror Assembly of the Advanced X-ray Astrophysis Facility (AXAF) program. Observed ring image defects could be related to the azimuthal location of their sources in the telescope even though in this case the predicted sharp ring was obscured by scattering, finite source size, and residual figure errors

Korsch, D.

Zissa, D. E.

English

NASA Technical Reports Server

, ... * 
TEE LIiU'Z EOCDS TEST FCI; X - E B Y  'XEIESCOPES 
USIdG A X B F ' S  iZECHNCLOGP B I G I i C E  ASSEHbLY, 
'I PISEC COLE PRCJECT KO. E20 E i n a l  Report U n c l a s  
NASA 
Technical 
Memorandum 
EXPERIMENTAL EVALUATION OF THE RING FOCUS 
TEST FOR X-RAY TELESCOPES USING AXAF'S 
TECHNOLOGY MIRROR ASSEMBLY 
MSFC Center Director's Discret ionary F u n d  
Final Report ,  Project No .  H 2 0  
B y  D .  E. Zissa and D .  Korsch 
Information and Electronic S y s t e m s  Laboratory 
Science and Engineer ing  Directorate 
October 1986 
(NASA-TN-86  5701 
National Aeronautics and 
Space Administration 
George C. Marshall Space Flight Center 
https://ntrs.nasa.gov/search.jsp?R=19870006483 2020-03-20T12:07:16+00:00Z
REPORT STANDARD TITLE PAGE 
1. REPORT NO. 2. GOVERNMENT ACCESSION NO. 3. RECIPIENT'S CATALOG NO. 
NASA TM-86570 
I 
4. T I T L E  AND SUBTITLE 
Experimental Evaluation of the Ring Focus Test for X-Ray 
MSFC CDDF Final Report, Project No. H20 
7. AUTHOR(S) 
D. E. Zissa and D.  Korsch 
Telescopes Using AXAF's Technology Mirror Assembly 
9. PERFORMING ORGANIZATION NAME AN0 ADDRESS 
George C.  Marshall Space Flight Center 
Marshall Space Flight Center, AL 35812 
12. SPONSORING AGENCY NAME AN0 ADDRESS 
National Aeronautics and Space Administration 
Washington, D .C . 20546 
15. SUPPLEMENTARY NOTES 
5. REPORT DATE 
October 1986 
6. PERFORMING ORGANIZATION CODE 
8 .  PERFORMING ORGANIZATION REPOR r R 
10. WORK UNIT NO. 
1 1 .  CONTRACT OR GRANT NO. 
13. TYPE OF REPOR'I' & PERIOD COVERED 
Technical Memorandum 
1.3. SPONSORING AGENCY CODE 
16. ABSTRACT 
A test method particularly suited for x-ray telescopes was evaluated experi- 
The method makes use of a focused ring formed by an annular aperture mentally. 
when using a point source at a finite distance. This would supplement measurements 
of the best focus image which is blurred when the test source is at a finite distance. 
The telescope used was the Technology Mirror Assembly of the AXAF program. 
Observed ring image defects could be related to the azimuthal location of their 
sources in the telescope even though in this case the predicted sharp ring was 
obscured by scattering, finite source size, and residual figure errors. 
- ~- 
17. KEY WORDS 
ring focus, x-ray telescopes, optics, 
geometrical optics, AXAF, TMA, optical 
testing, x-ray testing, grazing incidence, 
grazing-incidence telescopes , x-rays 
19. SECURITY CLASSIF. (d thh r-part) 120. SECURITY CLA 
18. D I  STRl B UT I  ON STATEMENT 
Unclassified - Unlimited 
Unclassified I Unclassified 15 I NTIS 
~ F C  - Form 3292 (&r 1969) 
TABLE OF CONTENTS 
INTRODUCTION ............................................................. 
4 EXPERIMENTAL APPARATUS AND PROCEDURE .............................. 
RESULTS .................................................................... 
8 
CONCLUSIONS .............................................................. 
REFERENCES ................................................................ 
P a g e  
1 
1 
3 
3 
5 
iii 
LIST OF ILLUSTRATIONS 
Figure 
1. 
2. 
3 .  
4.  
5 .  
6 .  
7. 
Title 
Schematic of image space geometry where spherical aberration 
is due to a finite object distance ................................... 
Diagram of TMA optics ............................................. 
Contour plot of ring image intensity data at predicted position 
of ring focus. One HRI pixel corresponds to 7.5 v m . .  ............. 
Radial profiles of ring annuli with 25 v m  pinhole scan. 
labels indicate distance in front of the best focus ................... Plot 
Variables used to describe correspondence between ring image 
and best focus image ............................................... 
Parameterization of previously measured best focus image ........... 
Model predictions from parameterized best focus data for 
radial profiles of ring annuli with a 25 p m  pinhole scan. 
Plot labels indicate distance in front of the best focus .............. 
Page 
6 
6 
7 
8 
9 
10 
10 
iv 
TECHNICAL MEMORANDUM 
EXPERIMENTAL EVALUATION OF THE RING FOCUS TEST FOR X-RAY 
TELESCOPES USING AXAF'S TECHNOLOGY n'IIRROR ASSEMBLY 
MSFC Center Director's Discretionary Fund Final Report, 
Project N o .  H20 
INTRODUCTION 
If an axially symmetric system is illuminated by an on-axis point source through 
a narrow annular aperture, then, in the presence of spherical aberration, a sharply 
focused ring is formed in front of or behind the best-focus image plane, depending 
on the amount and the sign of the spherical aberration (Fig. 1). 
circular symmetry as well as changes in the thickness of the ring are indications of 
surface defects and alignment errors in the imaging system and may be  sr,a!yzed as 
sucn. in  an earlier paper [ 11 the test method r2] has been discussed theoretically 
for the telescope design of the Advanced X-ray Astrophysics Facility (AXAF) and 
results were given for a visible light test of a one-sixth scale model of the Hubble 
Space Telescope. The test method is only of limited value for visible light telescopes 
because widening of the ring due to diffraction with the larger wavelength through a 
narrow annular aperture tends to obscure the effect. 
Any deviation from 
In this paper results are given from an experimental test of the method with the 
Technology Xirror Assembly (TMA) of the AXAF program. 
two-thirds scale model of the smallest paraboloid-hyperboloid mirror pair planned for 
the AXAF program. 
ft vacuum tunnel was used for the test. 
The TMA is roughly a 
The Marshall Space Flight Center (XSFC) test chamber and 1000- 
EXPERIMENTAL APPARATUS AND PROCEDURE 
The TMA is a Wolter Type 1 grazing-incidence telescope with one paraboloid- 
hyperboloid pair of mirrors (Fig. 2 ) .  Each element is roughly cylindrical with a 
410 mm length. 
them. 
focal length of 6 m (the measured focal length was 5 . 9 7  m ) .  The entrance annulus 
has a width of about 3.6 mm. 
The actual equations for the mirror surfaces derived from the specifications for the 
system are  of the following form (Fig. 2 ) :  
The elements are lined up along their axes with a 28 mm gap between 
The telescope has an entrance aperture diameter of about 427 m m  and a nominal 
The grazing angle of incidence is about 30 arcmin. 
2 h2 - ho2 = 2kz - (1  + 6 )  z 
where : 
2 h2  = x + y2,  where x , y  are transverse coordinates 
z = axis of symmetry 
(z=O at center of each mirror, z is positive toward the front of each mirror) 
ho = h at z = 0 
k = subnormal at z = 0 
6 = -e where e is the eccentricity 2 
d = 438 mm = distance between mirror centers 
(28 mm mirror gap midway between centers) 
Paraboloid 
hO1 = 211.906860 mm 
kl  = 1.836797 mm 
6 = -1. 1 
Hyperboloid 
hO2 = 204.243289 mm 
k2  = 5.377429 mm 
6 2  = -1.0006122657 
For the 1000-ft source distance used here, the best focus was calculated to be 
120 mm behind the infinite focus. The best focus was calculated to have a 13 pm r m s  
diameter due to the finite source distance. The ring focus was predicted to be 4 1  mm 
in front of the best focus obtained with the 1000-ft source distance. It was calculated 
to have a diameter of 2.8 mm.  
0 .2  p m  r m s .  However the source was effectively about 1 mm by 1 / 2  mm o r  20 p m  
by 10 u m  at the ring focus and at the best focus. 
focus is about 3 p m  between zeros of the sinc function for the x-ray wavelength of 
8.34 8. 
The width of the focused ring geometrically would be 
The diffraction width of the ring 
- 7  m n m ~  L - J  I _ _ _ _  -Y-- I--- 
I I I ~  I L V ~ ~ ~  I I U  all-eauy u e ~ n  plaz-ed in the test chamber cf t h e  IOOO-ft V B C U U ~  
tunnel at PASFC for tests at the best focus position. 
had the facility readied fo r  this experiment. wavelength were used. 
The detectors were supplied by the Smithsonian Astrophysical Observatory (SAO)  and 
were operated by Dan Schwartz of SAO. One 
of the detectors was the High Resolution Imager (HRI)  which is a microchannel plate 
detector with a resolution of about 30 p m  and of a size that could image the whole 
ring. The other detector was a proportional counter with a 25 u m  pinhole placed in 
front. 
Cary Reily of the Test Laboratory 
X-rays of 8.34 
Dan Schwartz also supplied the data. 
Data were taken at four positions in front of the overall best focus position. 
The best focus image had been measured by S A 0  in an earlier experiment in the same 
test chamber [3 ,4 ] .  The four positions were 15.672, 28.372, 41.072, and 53.772 mm 
in front of the best focus with the 41.072 mm point being the predicted ring focus 
position. (The best focus position was experimentally determined by closing off all 
but one quadrant of the exit aperture at a time. The separate images produced by 
I 2 
this procedure were forced to overlap.) 
in order to see the overall ring. Then the 25 p m  pinhole detector was scanned across 
the width of the ring at 12 p m  intervals at the same orientation on each ring. 
scan was made along the coordinate axis in which the source was narrower. 
that the scan was actually made at a point on the ring 11 deg above the narrow axis 
has negligible effect here. 
scans. 
H R I  data were taken at each axial position 
The 
The fact 
The background rate was measured for the 25 v m  pinhole 
RESULTS 
First, an overall picture of the ring was obtained with the H R I  detector with a 
resolution of 30 p m .  
the ring focus is shown in Figure 3 .  
was. 
A contour plot of these data at the predicted axial position of 
This plot gives an idea of how uniform the ring 
Figure 4 shows radial profiles of the ring annulus made with the 25 p m  pinhole 
detector at intervals of 12 px ar?d i~ tegra tzd  ~ v e r  200 sec except fer the 53 .772  iiiiii 
curve which was integrated for 100 sec and those counts were multiplied by two. 
Increasing values on the horizontal distance scale indicate motion from outside toward 
the inside of the annulus. 
been excluded from Figure 4. The 
intensities decrease as  the ring radius increases with distance in front of the best 
focus. 
scattering, the finite source size, and residual figure errors in the mirrors. 
Background counts of 62 per 200 sec integration time have 
The widths of the profiles are all about 100 u r n .  
Evidently the narrowing predicted for the ring focus has been obscured by 
Since the best focus image had a full width at half maximum of about 1 4  ~ . l m  i 3 ]  
in the direction of the scan across the ring annulus, it seemed surprising at first that 
the ring distributions of Figure 4 were much wider and of constant width. This would 
not be the case if spherical aberration due to the finite source distance were the only 
image degrading cause. Since in this case scattering is predominantly responsible for 
the image spread, the appearance is  quite explicable. The best focus is formed where 
the central ring of the annular image collapses to a point. 
the intensities from around the annulus overlap in a small area. 
intensity grows sharply towards the center of the best focus spot. 
quantitative explanation of the effect, a simple computer model was developed. 
Actually, the procedure was carried out in reverse by using previously measured best 
focus image data, and convolving the results with a 25 1 ~ m  pinhole. 
of Figure 5 ,  the energy in radial increment rtdr77 at radius ffAr7v in the best focus 
image would be mapped in equal parts to radial increments rrdrrr at radii Orn + A r ? '  and 
"r - Art' in the annulus. For the best focus image distribution, a parameterization 
(Fig. 6) of the measured distribution was used from Reference 4. Even though that 
parameterization assumed circular symmetry, the results still should give some idea of 
what the ring data should look like. The results are shown in Figure 7. The shape, 
width, and relative intensities from the model are similar to those of the measured data 
shown in Figure 4. 
Only at this location do 
To give a more 
Therefore, the 
In the notation 
- 
0 
CONCLUSIONS 
The ring focus test method provides a most sensitive procedure to measure 
surface defects of telescopes, in particular grazing-incidence telescopes with narrow 
3 
entrance annuli. 
ing diffraction effects) generally sma l l  compared to the best focus image, errors can 
be detected that would normally be obscured by the presence of spherical aberration 
in the focal plane. 
almost perfect optical system, and a source the ideal image of which should be s m a l l  
compared to the aberrations caused by the finite source distance. 
presence of a significant amount of near angle scattering, as in the present case, 
observations in the neighborhood of the ring focus can yield valuable information. 
By radially unfolding the best focus image into a ring pattern it becomes possible to 
relate an observed image defect to the azimuthal location of its source in the tele- 
scope. This information is obtained by carrying out radial scans at different azi- 
muthal angles, whereby the theoretical image of the source should be small compared 
to the measured image spread, and preferably of circular shape. The measurements 
performed on the TMA and discussed here excellently demonstrate this property of 
the test. 
Since the width of the ring focus of a perfect telescope is (neglect- 
To measure defects of this magnitude, however, requires an 
But even in the 
4 
REFERENCES 
1. Griner, D. B . ,  Zissa, D.  E . ,  and Korsch, D. : Test Method for Telescopes 
Using a Point Source at a Finite Distance. NASA Technical Memorandum 86523, 
Marshall Space Flight Center CDDF Project No. H 2 0 ,  September 1985. 
2 .  Korsch, D.  : Design and Analysis in Support of AXAF. Final Report to 
Marshall Space Flight Center, Contract NAS8- 35622, April 1985. 
Schwartz, D. A . ,  et al. : 
Assembly (TMA) Mirror. 
Astronomy," J. L.  Culhane, ed., Vol. 597, 1986, p. 10. 
3 .  X-ray Testing of the AXAF Technology Xirror 
In SPIE Proceedings "X-ray Instrumentation in 
4. Van Speybroeck, L . ,  et al.: 
formance and hcodels Based upon Mechanical and Visible Light Measurements. 
In SPIE Proceedings "X-ray Instrumentation in Astronomy, 'I J .  L . Culhane, ed. , 
Vol. 597, 1986, p .  20. 
Correspondence Between AXAF TMA X-ray Per- 
5 
FOCAL PLANE PLANE OF IMAGE PLANE 
FOR INFINITE RING FOCUS FOR FINITE 
OBJECT DISTANCE OBJECT DISTANCE 
(BEST POINT FOCUS) 
Figure 1. Schematic of image space geometry where spherical 
aberration is due to a finite object distance. 
PARABOLOID HYPER BOLO I D 
Figure 2 .  Diagram of TMA optics. 
180C 
z 2000 
rn 
K 
W 
K 
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2200 
2400 
ORIGINAL PA= CS 
.w POOR QuALnr 
. 
0 
. 
0 
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0 
0 
. 
0 
. 
0 '  . 
- 
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0 - 0 
I 
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. 
1 
b 
. 
0 
. .  
I 
. 
. 
1 
Y 
I 
2400 2600 2800 
(HRI PIXEL NUMBERS) 
3000 
Figure 3 .  Contour plot of ring image intensity data at predicted 
position of ring focus. One H R I  pixel corresponds to 7.5 u r n .  
7 
0 8 co 
N 
8 
Q, 
p3 
SlNf l03 A W - X  
x 
p3 
9 
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a - 
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k 
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a, 
a, a 
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> 
k 
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t 
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z 22.0 
.o I 
-102.0 -61.2 -20.4 20.4 61.2 102.0 
POSITION ( p MI 
Figure 6 .  Parameterization of previously measured best focus image [ 41 . 
 120.0 
I 
I I I , I . -. .o 40.8 81.6 1 ~ 2 . 4  163.2 204.0 
POSITION ( p MI 
Figure 7.  Kodel predictions from parameterized best focus data for 
radial profiles of ring annuli with a 25 p m  pinhole scan. 
labels indicate distance in front of the best focus. 
Plot 
APPROVAL 
EXPERIMENTAL EVALUATION OF THE RING FOCUS TEST FOR X-RAY 
TELESCOPES USING AXAF'S TECHNOLOGY MIRROR ASSEMBLY 
MSFC Center Director's Discretionary Fund Final Report, 
Project No .  H 2 0  
By D.  E.  Zissa and D.  Korsch 
The information in this report has been reviewed for technical content. 
of any information concerning Department of Defense or  nuclear energy activities or  
programs has been made by the MSFC Security Classification Officer. 
in its entirety, has been determined to be unclassified. 
Review 
This report, 
/ 
W .  C .  BRADFORD 
Director, Information and Electronic 
Systems Laboratory 
t 
11 


Experimental evaluation of the ring focus test for X-ray telescopes using AXAF's technology mirror assembly, MSFC CDDF Project No. H20

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