Review of calculations of plane grating mosaic for photon energ

Fisher, P. C.

English

NASA Technical Reports Server

1. Review of Calculations f o r  Plane Gratings 
A thorough re-examination of about e igh ty  percent  of t h e  previous 
g ra t ing  mosaic ca lcu la t ions  w a s  completed during t h i s  quarter. 
po r t ion  of t h e  ca lcu la t ions  includes a l l  results dbtained f o r  mosaiaa 
This 
made of plane g ra t ing  elements and t h e  f i rs t  f e w  results found using 
curved g ra t ing  elements. Because of  our own d i f f i c u l t y  i n  g e t t i n g  
reacquainted, and the  f e w  mistakes found, a new and hopeful ly  more 
understandable terminology i s  introduced here. Henr? fo r th ,  a q u m t i t y  
propor t iona l  t o  t h e  r e so lu t ion  of t h e  g ra t ing  mosaic f o r  a photon of 
energy E w i l l  be used. This quant i ty  i s  a r b i t r a r i l y  def ined as E/DE, 
when DE i s  t h e  ful l -width a t  half m a x i m u m  on a p l o t  of t h e  number of 
photons i n  a given energy in t e rva l  (which reach a given po in t  i n  t h e  
image plane)  versus  energy. The goa l  of the  ca lcu la t ion  e f f o r t  then 
amouftts t o  t r y i n g  t o  design a mosaic wi th  a t h e o r e t i c a l  value of a t  
least 200 f o r  E/A E, i n  hopes o f  a t t a i n i n g  a value of 100 i n  a c t u a l  
p rac t i ce .  
The essence of t he  results from t h e  plane g ra t ing  ca lcu la t ions  
i s  given i n  Figures 1-3. The curves i n  Figure 1 show E/AE f o r  a given 
source-grating-image-plane configuration as a funct ion o f  t he  p a i r s  of 
wavelengths se l ec t ed  f o r  optimizing reso lu t ion .  All mosaics had 32 
elements NEL, each ruled with s i x  d i f f e r e n t  l i n e  spacings NSUB, t h e  
i n i t i a l  spacing do being 12,000A between grooves. 
d i d  not exceed 60, gra t ing  curvature w a s  eventual ly  introduced (see 
Because E/aE values  
sec t ion  2 below). L1 N65-32192 
0 
/(THRul 
93 
(ACCESSION NUMBER1 : 6 
GPO PRICE $ c (PAGES1 
(CATEGORY1 
[?&fLWK3-< 
CSFTI PRICE(S1 $ ( N A S A  CR OR TMX OR AD N J M D E A J  
LOCKHEED MISILES & SPACE COMPANY Hard copy (HC) 
Microfiche (M F) 
/+ 
. 5  i, c/ 
ff 653 July 65 
-~ - ~ 
https://ntrs.nasa.gov/search.jsp?R=19650022591 2020-03-17T00:57:55+00:00Z
, 
I 
6 
e Figure 1 i s  based on r e s u l t s  l ike. thos& shown i n  Figure 2,'which 
I 
i nd ica t e s  t h a t  a v a r i e t y  of photon energies  kay be assoc ia ted  w i t h a  
given poin t  i n  the  image plane, the d e t a i l s  depending upon t h e  p a i r  
of wavelengths s e l e c t e d  f o r  optimum reso lu t ion .  The two histograms 
apply t o  the-8A r a d i a t i o n  for  mosaics designed t o  b e s t  handle the  p a i r s  
of 5 and 40A and 8 and 16~. 
ca lcu la t ing  t h e  wavelength d i f f r a c t e d  t o  a given poin t  i n  the  image 
plane by each of t h e  192 elemental g ra t ings  i n  the  mosaic. 
depic t s  t h e  change i n  reso lu t ion  produced by a 3' change i n  x-ray input  
angle, and by halving the  number (from 6 t o  3) of d i f f e r e n t  g r a t i n g  
spacings used. 
be wasted construct ing a mosaic whose response has values of E/ fS  < 100. 
The results were obtained by simply 
Figure 3 
The l i n e  drawn i n  a t  E/AE = 100 means t h a t  no time should 
Because appropriately ruled g r a t i n g s  of t he  desired l a r g e  radius  
of  curvature are not ava i lab le ,  the i n i t i a l  mosaic mockup w i l l  be made 
from off- the-shelf  plane elements. 
2. Improvement from Curved Gratings 
It i s  c l e a r  from Figure 3 t h a t  E/AE of t h e  gra t ing  mosaic i s  not 
p a r t i c u l a r l y  dependent on the  exact angle of incidence or t he  number of 
subelements i n  t h e  mosaic. The lack of dependence a r i s e s  because the  
g r a t i n g  elements considered i n  Figure 3 were not curved. 
i nd ica t e s  t he  considerable improvement r e a l i z e d  i n  one of t he  Figure 3 
cases when t h e  mosaic i s  subdivided i n t o  gra t ings  which possess one of 
t h r e e  d i f f e r e n t  curvatures.  U s e  of a parabol ic  surface may produce 
even b e t t e r  r e s u l t s .  
Figure 4 
F 
- 2- 
LOCKHEEC MISSILES & SPACE COMPANY 
L 
Ln . 
I 
I 
I 
(%> 3 m  
rl cu ;f 
I 
1 
I 
I 
I 
I 
0 
Ln 
rl 
0 
0 
rl 
0 
Ln 
3 
Ln 
m 
m 
In 
cu 
cu 
Ln 
r( 
r l  
Ln 
0 
-3- 
LOCKHEED MISSILES & S P A C E  C O M P A N Y  
L c 
t 
0 
3 
& 
L n  
L 
I I I 
M a i- 
w UT U o T C p R q  
-4- 
LOCKHEED MISSILES & SPACE COMPANY 
0 
Ln 
=t 
c 
0 
L n  
(u 
Ln 
(%I 3 m  
rl cu 3 
4 
0 
0 
0 
(u 
rl 
I I  
.\ 
do 
I I  I I  I I  
.a .a .a 
4 4 4  
I I 
0 0 
0 cu 
0 
L n  
rl 
-5- 
0 
0 
rl 
0 
Ln 
Ln 
cr) 
cu w 
si 
0 
Ln -P 
0 
rl # 
rl 
0 
LOCKHEED MISSILES & SPACE COMPANY 
0 
In cu 
In 
0 
V 
rl 
4 
0 
0 
0 
rl 
I I  
cu" 
do 
cv) 
( u c u  0 0  
I ' I  
/ 
/ 
/ 
I I 
0 
0 cu 
(u 3 
/ 
/ 
/ 
/ 
/ 
/ 
0 
0 
d 
0 
L n  
=f 
L n  
M 
M 
Ln 
ai 
cu 
Ln 
4 
rl 
In . 
0 
0 
- 6- 
LOCKJ3EED MISSIUS & SPACE COMPANY 


Calculations for mosaics with plane and curved grating elements quarterly progress report no. 4

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server