New types of holographic optical elements, combining the flexibility of computer generated holograms with the large space bandwidth product and high diffraction efficiency of interferometrically recorded volume phase holograms, are demonstrated. The optical elements are recorded by subdividing a volume hologram film surface into numerous small areas (facets), each of which is individually exposed under computer control. Each facet is used to produce a portion of the desired final wavefront. Three different optical elements are demonstrated

Case, S. K.

Haugen, P. R.

English

NASA Technical Reports Server

t MULTI-FACET HOLOGRAPHIC OPTICAL ELEMENTS 
Steven K. Case and Pau l  R. Haugen 
E lec t r i ca l  Engineering Department 
University of Minnesota 
Minneapolis, Minnesota 55455 
SUMMARY 
New types of  holographic op t i ca l  elements a r e  demonstrated which combine some of 
t h e  f l e x i b i l i t y  of computer generated holograms with the  la rge  space-bandwidth pro- 
duct and high d i f f rac t ion  eff ic iency of interferometr ical ly  recorded volume phase 
holograms. The opt ica l  elements are recorded by subdividing a volume hologram f i lm 
surface in to  numerous small areas ( f a c e t s ) ,  each of which i s  individually exposed 
under computer control. 
f i n a l  wavefront. Three d i f fe ren t  op t ica l  elements are demonstrated. 
Each facet is  used t o  produce a portion of the  desired 
INTRODUCTION 
Holographic opt ica l  elements a re  a n  a t t r a c t i v e  a l t e rna t ive  t o  conventional opti-  
c a l  elements i n  systems using coherent l igh t .  The a t t r i b u t e s  of holographic op t i ca l  
elements include the capabi l i ty  of producing low f-number di f f rac t ion  l i m i t e d  
op t i c s ,  and the a b i l i t y  t o  generate a rb i t r a ry  wavefronts. They are  a l so  poten t ia l ly  
easy t o  rep l ica te  and have low weight and compact size.  Unfortunately, not a11 of 
these  a t t r i b u t e s  are  shared by a l l  hologram types. 
W e  could categorize holograms a s  computer generated, interferometr ical ly  
generated, or generated by a hybrid technique as described i n  t h i s  paper. 
generated holograms ( C G H )  o f f e r  t he  grea tes t  f l e x i b i l i t y  i n  t h e  production of 
a r b i t r a r y  wavefronts. C G H ' s ,  however, usually have l i m i t e d  space-bandwidth products 
and d i f f rac t ion  efficiency, Volume phase holograms, on the  other hand, can have 
near ly  100% di f f rac t ion  eff ic iency in to  a s ingle  order and very large space- 
bandwidth products (necessary for  low f-number op t i ca l  e lements ) ,  but o f f e r  l i m i t e d  
f l e x i b i l i t y  i n  the  production of  a rb i t r a ry  wavefronts. 
Computer 
The new type of hologram described here combines t h e  best  features of t he  pre- 
vious hologram types: high eff ic iency,  large space-bandwidth product, and greater  
f l e x i b i l i t y  i n  wavefront generation. The pr inciple  used t o  design the new hologram 
i s  straightforward. While the  interference pat tern required t o  record a n  en t i r e  
"arb i t ra ry  wavefront" volume hologram i s  quite complex, t h e  required pat tern within 
a small area on t h e  hologram i s  r e l a t ive ly  simple such t h a t  it can be approximated 
by planar, spherical ,  o r  cy l indr ica l  waves. Thus our new holographic op t i ca l  ele- 
ment i s  recorded by individually exposing numerous, small volume hologram facets. 
The wavefronts used t o  record each facet can be d i f f e ren t  but a re  produced by con- 
vent ional  op t i ca l  elements which a r e  positioned v i a  computer control. 
t This work supported by the  University of Minnesota and by AFOSR/ARO Grant 
Dm9-81-K-0033. 
319 
https://ntrs.nasa.gov/search.jsp?R=19820008047 2020-03-21T09:50:37+00:00Z
WAVEFRONT TRANSFORMATION OPTICAL ELEMENTS 
The f i r s t  type of o p t i c a l  elements t h a t  we describe a r e  used f o r  wavefront 
transformations. For t h i s  system we start with a Gaussian i n t e n s i t y  p r o f i l e  l a s e r  
beam which we wish t o  transform i n t o  another shape i n  order t o  optimally i l luminate 
some object  ( f o r  interferometric t e s t i n g  or materials processing ). 
w e  assume t h a t  we must i l luminate the  periphery of a hollow, square box. Such a 
transformation requires  two holographic o p t i c a l  e lements  as shown i n  Fig. 1. The 
f i r s t  hologram a c t s  t o  s p a t i a l l y  r e d i s t r i b u t e  the  input l i g h t  beam and t h e  second 
hologram produces a desired phase front  on the redis t r ibuted l i g h t  so t h a t  it can 
propagate toward a d i s t a n t  object. 
In t h i s  example, 
The f i r s t  hologram i s  recorded by subdividing the hologram surface i n t o  
numerous, small squares ( f a c e t s )  each of  which i s  individually exposed as i n  Fig. 2. 
The s p a t i a l  frequency of the  grat ing recorded within each face t  i s  var ied by 
su i tab ly  adjusting the object beam incidence angle before recording. The grat ing 
frequency within each facet  i s  chosen such t h a t  the input beam i n  Fig. 1 w i l l  be 
su i tab ly  deflected t o  be s p a t i a l l y  rearranged when it reaches the  plane of Hologram 
#2. Design considerations for  the  hologram a r e  given i n  Ref. 1 and w i l l  not be 
repeated here. 
The redis t r ibuted l i g h t  from Hologram #1 and a plane wave a r e  used as the 
recording waves for  Hologram #2. I n  t h i s  manner, Hologram #2 can r e d i f f r a c t  the 
l i g h t  a r r iv ing  from Hologram #1 t o  produce a f i n a l  output wave with t h e  desired 
i n t e n s i t y  d is t r ibu t ion  and a planar wavefront. Because both holograms a r e  recorded 
i n  dichromated g e l a t i n ,  they have nearly 100% di f f rac t ion  eff ic iency so t h a t  the  
r e d i s t r i b u t i o n  process i s  l i g h t  e f f i c i e n t .  I n  Fig. 3 w e  have photographed the l i g h t  
pa t te rn  i n  f ive  equally spaced planes t o  show t h e  gradual red is t r ibu t ion  of  l i g h t  
v i a  our process. 
SPACE-VARIANT LENS 
The multi-facet hologram technique i s  also useful f o r  t h e  production of custom- 
ized holographic lenses  with very l a r g e  space-bandwidth products. A s  a demonstra- 
t i o n ,  we constructed a space-3ariant cy l indr ica l  l ens  capable of producing a l i n e  
focus on a spherical  surface. The construction of a conventional l e n s  t h a t  would 
perform t h i s  task  would be extremely d i f f i c u l t  i f  not impossible. Without m u l t i -  
f a c e t  hologram approach, however, we divide the  hologram f i lm i n t o  a s e t  of horizon- 
t a l  zones ( f a c e t s )  and s p e c i e  the focal  length t h a t  a cy l indr ica l  l e n s  wihin each 
f a c e t  would need i n  order t o  bring a plane wave t o  a l i n e  focus on the  object sur- 
face ( s e e  Fig. 4). 
For recording, a t h i n ,  s ta t ionary,  f l e x i b l e  mask containing a horizontal  s l i t  
aper ture  i s  a g a i n  pressed l i g h t l y  against  the film. Exposure i s  with a planar 
reference wave incident a t  approxiately 35" with respect t o  the f i l m  normal and a 
c y l i n d r i c a l  wave. The cy l indr ica l  wave i s  produced by focusing a plane wave with a 
conventional cy l indr ica l  lens. The distance between t h e  fi lm plane and the  focal 
plane f o r  the cy l indr ica l  wave ( ? . e . ,  t h e  focal  length of t h e  holographic l e n s  
being recorded) i s  selected by moving t h e  cy l indr ica l  l e n s  r e l a t i v e  t o  the film. 
Both the fi lm and the cy l indr ica l  l ens  a r e  mounted on mini-computer control led 
t r a n s l a t i o n  stages. A facet  i s  exposed v i a  a computer cont ro l le r  shut ter .  To 
record the  next f a c e t ,  the  fi lm i s  t rans la ted  by one facet  height and t h e  cy l indr ica l  
320 
l ens  repositioned t o  achieve the prescribed focal length for t h i s  facet.  The pro- 
cess  i s  repeated u n t i l  a l l  face ts  are exposed. The f i n a l  hologram consis ts  of 13 
f ace t s  each approximately 19x3mm i n  size. 
The experimental results i n  Figs. 5 and 6 show t h e  u t i l i t y  of our system. 
Figure 5 shows the  focal pat tern obtained when a conventional cy l indr ica l  l ens  i s  
used t o  focus a l i n e  on a 5.4cm diameter sphere. The top of the sphere is  located 
one focal length from the cy l indr ica l  lens. 
when our multi-facet op t ica l  element i s  used. The focal l i ne  i s  now sharp and the 
segmenting barely vis ible .  
Figure 6 shows the improved r e su l t s  
IMAGE FORMATION 
Our last  demonstration i s  i n  the use of  multi-facet holograms f o r  the  formation 
o f  images. The hologram surface i s  again subdivided in to  numerous s m a l l  f ace ts ,  
each of which contains a grat ing of a specified s p a t i a l  frequency. When illuminated 
by a plane wave as i n  Fig. 7, t he  l i g h t  i s  d i f f rac ted  t o  specif ic  locat ions i n  the 
image plane which i s  located a short  distance (20cm) a f t e r  t h e  hologram plane. 
image i s  thus b u i l t  up of a number of s m a l l  patches of l i gh t .  
The 
A s  before,  each facet i s  interferometr ical ly  recorded under computer control. 
The computer t r ans l a t e s  the film behind a mask so t h a t  individual face ts  can be 
sequent ia l ly  exposed, and def lec ts  the  recording beam t o  produce the r equ i s i t e  spa- 
t i a l  frequencies. 
3 This image production method produces r e su l t s  similar t o  those from kinoforms 
i n  t h a t  a l l  of the incident l i g h t  is  transformed in to  an  i m a g e .  The present produc- 
t i o n  technique has the advantage, however, t h a t  one only needs t o  control  a t r a n s -  
verse s p a t i a l  frequency instead of a longitudinal phase sh i f t .  
A resu l tan t  image from t h i s  type of hologram i s  shown i n  Fig. 8. Here a 181 
face t  hologram is used t o  form a simple image. 
CONCLUSION 
We have demonstrated three types of multi-facet holographic op t i ca l  elements 
which combine opt ica l  f l e x i b i l i t y ,  high eff ic iency,  and large space-bandwidth pro- 
ducts. These elements should prove useful for  a la rge  number of custom op t i ca l  
appl icat ions.  
REFERENCES 
1. S. K. Case, P. R. Haugen, and 0. J. Lokberg, "Multifacet Holographic Optical 
E lemen t s  for  Wavefront Transformation," Appl. Opt. 2p, 2670 (1981 ). 
2. S. K. Case and P. R. Haugen, "Parti t ioned Holographic Optical Elements," Opt. 
Engin., March 1982, 
3. B. Lesem, P. M. Hirsh, and J. A. Jordan, Jr., "The Kinoform: A New Wavefront 
Reconstruction Device," IBM J. Res. Develop. - 13,  150 (1969). 
3 2 1  
OUTPUT 
BEAM 
H O L ~ M  I 
-8PATIAL 
REDI1TRII)UTION 
HOLOGRAMt 2 
-PHASE CORRECTION 
' /  
Figure 1.- Wavefront t ransformation v i a  t w o  holograms. 
HOLOG RA P HlC 
P L A T E  
A P E R T U R E  
VARIABLE ANGLE 
REFERENCE 
BE AM 
Figure 2.- Multi-facet hologram recording method. 
322 
MOLOGRAY 
. I  
Figure 3 . -  Light red is t r ibu t ion .  
323 
c 
_ - - - _  . . 
\ 
\ 
\ 
\ 
\ 
REFERENCE \ 
I 
I 
I 
I 
WAVE 0 BJ ECT 
I 
/ 
/ 
I 
0 
0 
4 .
- - _ _ - e  
’. t 
HOLOGRAM 
Figure 4.- Side view of multi-facet hologram producing 
segmented focus on object surface. 
Figure 5.- Line focus formed by con- Figure 6.- Line focus formed by multi- 
ventional cylindrical lens. facet holographic cylindrical lens. 
324 
Figure 7.- Image formation. 
PARTITIONED 
HOLOGRAM 
Figure 8. - Output image. 
325 


Multifacet holographic optical elements

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