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M ECHANIKA
TEORETYCZNA
I  S TOS OWANA

2,  26( 1988)

APPLICATION S  OF   TH E  D IF F EREN CE  H OLOG RAM  IN TERF EROM ETRY*

ZOLTAN   FUZESSY

FERENC  GYIMESI

JANOS  KORN IS

Institute  of  Physics,  T echnical University  Budapest

1. Introduction

The  aptitude  of  hologram  interferometry  for  measurement  of  quantities  being  of
industrial  importance  has  undoubtedly  been  proved.  H ologram  interferometry  can  be
used  to produce a  fringe  pattern which  represents  the field  of  surface  displacement  of  an
opaque object  in response t o  an arbitrary  type  of  loading.  It has  successfully  been  applied
for  investigating  phase  object  as  well  where  the  change  in  refractive  index  distribution
is  stored  by  an  interference  pattern.  Among  numerous  applications  of  holography  the
contouring  has  also  to  be  mentioned.

There  are  different  techniques  for  quantitative  evaluation  of  interferograms.  N ever-
theless, the main difficulty  in applying  hologram  interferometry  stems  from  the numerical
evaluation  of  interferograms.  F irst,  the  extraction  Of  th e  tremendous  data  set  from  the
requires a considerable  amount of time. Second, the lack  of the zero order fringe  (unmoved
points within  the illuminated  area)  can introduce  ambiguity  at  the interpretation of  inter-
ferograms  and  lead  to  decrease  of  accuracy.

Frequently,  there  is  n o  need  to  determine  the  total  three- dimensional  deformation
to  specify  the shape  of  an  object,  or  to  calculate  the temperature  and mass  distributions.
The  main  interest  can  only  lie  in  the differences  (e.g.  in  shapes)  of  two  objects.  One  of
them can be referred  to as th e master  one, the other as th e test object  at large scale produc-
tion  sampling.

The  comparison  can  be  done  by  the  difference  hologram  interferometry  [1].  As  its
inherent  property  a  new  object  being  compared  is  illuminated  holographically  by  recon-
structing  the real  images  of  the first  object.  The  idea  of  the holographic  illumination  was
proposed  by  D .  D enby  at  al.  [2],  its  potentiality  to  compare  two  objects  by  hologram
interferometrie techniques was  formulated  by  D . B. N eumann [3], I n the following  a  short
discussion  of its principles  will be given and selected  applications will be presented.

*  Praca wygłoszona  na XII  Sympozjum  Doś wiadczalnych  Badań  w  Mechanice  Ciała  Stałego,
Warszawa- Jadwisin,  1986



244  Z.  FU ZESSY  i  IN N I

2.  Basic  considerations

Let  us  survey  the  steps  of  making  difference  interferogram,  i.e.  pattern displaying  the
difference  in  characteristic  quantities.

I n  the first  step, the  conventional hologram  interferometry  is  used  to  record  an inter-
ference  pattern  which  contains  information  concerning  deformation,  shape,  or  refractive
index  changes  of  the master  object.  This interferogram  is considered  as a  way  of  recording
an d  storing  two  wavefronts  with  a  given phase  difference.

F o r  a while let  us thin k in terms  of  the conventional hologram  interferometry,  keeping
in  mind the task  of  comparision. Then, the second step would  be recording another double
exposure  interferogram  related  to  a  new  (test)  object.  Its  fringe  system  would  contain
information  about  deformation,  shape  or  refractive  index  change  of  the  test  object.  So,
the  test  interferogram  would  also  store  two  wavefronts  with  definite  phase difference.  •  •

D etermining  differences  between  the two  objects  both interferograms  are to  be  evalua-
ted,  because  numerical  results  are  comparable,  only.

If  the  difference  hologram  interferometry  is  applied,  there  is  no  need  for  separate
recording  an d  evaluation  of  the interferograms.  The test  object  is  illuminated  by  the  rea
images  of  th e master  objects.  As  it  was  stated  above  th e phases  of  the illuminating  wave-
fronts  were  determined  by  the  states  of  th e  master  object.  The  states  of  the  new  object,
due  to  the  applied  illumination,  modify  those  phases  and  their  subtraction/ addition  is
realized  by  recording a  new  interferogram.  Bearing  the subtraction of  the phases  in mind^
the  difference  in  the  states  of  the two  objects  is  recorded  by  the new  holographic  interfe-
rogram .  .  :  '  .<>• .;;'•.  ,.rr,;y!t- :?!  "My.- '^ '- vilii  HP,  vvi  li/ i'- j.': ;.:•

W i t h  c o m p u t e r  a i d e d  e va lu a t io n  t h e  differen ce  in t er fer en c e  p a t t e r n  p r o vid e s  a  very
q u ic k ,  e a sy  t o  h a n d le ,  o p t ic a l  m e a su r i n g  t o o l  fo r  t h e  c o m p a r i so n  of  t wo  o bjec t s  wit h
i n t e r fe r o m e t r i e  p r e c isio n .  U sin g  fa st  r e c o r d in g  m a t e r i a l, nthe  t e c h n iq u e  in t h is  r ea liza t io n
c a n  b e  u se d  as  a n  o n - line  m e a su r i n g  d evice.  •   x-   .r- ru'"'  .:: .;..• • - .• .<,•  • • '• ::.:.  '  V  • • • :;.;::;.< -̂ .v:.

T h e  q u a n t i t a t i ve  r e p r e se n t a t i o n  of  wh a t  h as. been  sa id  a b o ve  is a s  follows  [4].  F o r t h e
sa k e  o f  sim p lic it y  we  r e st r ic t 1  tóurselves  t o t h e p h a se  o bjec t  c o n sid er a t io n s. ; N a t u r a lly, t h e
a n a lysis  is  a lso  valid  fo r  o p a q u e  object  in vest igat io n s.  .•   •   ;  • •; ?• :.'  '  ••   • ::• .• :• .••

L e t  t h e  t e st  o b je c t i n '  its in it ial  st a t e  b e illu m in a t ed , by  t h e  first  r e a l  im a ge  o f t h e  m a st e r

o bjec t .  T h e  c o m p l e x  a m p l i t u d e  Ł/ x
 sof t h e  ligh t' a r r ivin g  a t t h e  p la t e  c an , be  exp ressed  a ś :: / ;

A,,  ,  - I- ./1 lirh  l< nt  •   Z$M$&MAl- >  •   ITri  o't,- '-   - \ - • ',:'•
where  U

o
  an d  0

Q
  are both functions  of the spatial  coordinates at the plate. The quantities

U
o
  an d  0

O
  con tain all  the  informations  related  to  the wavefield  which  is  determined by-

the  refractive  index  distributions  of  the master  and  as  well  as  test  objects  in the^r i

states,   • • • ;.-  • -, ,;•   ,/ '• '- '  '''• • ;• ;  ' ' o  ':"- \ y.:- '.• '''• - '•  • i ll  g

T h e  complex  amplitude  U
2
  arriving  at  the plate  during the second  expdsiirrejwtajctlire

test  object  is  subjected  tola  given  load,  e.g. Jieating,-   can"be  expressediast  aitts.mo'rehsJai

U
2
=U

0
fixp[- j($

0
+A&- A<t>')],

  l  l

• • wl&rS ^ ; i a fa d  0^ , are  as  before;  A&  iś the phase  differencecM §e*byth® !reiraictJv^  fhdex
change in th e m aster object  and A0'  is th at  of  the  test  object.



APPLICATIONS  OF  THE  DHJ 245

of  the  master  wavefronts  the  phase  differences  A0  and  A&'  should  be  taken  of  opposite
sign when both  of them  belong to  the  object  change  of trie same character,  e.g.  increasing
the  refractive  indices  in  transparent  object  case.

At  the  reconstruction  of the  holograms  the  irradiance  of  the  object  will  be proportio-
nal to:

/ =  \U1 +  U2\
2=*2U0[l+cos(A<P'-A&)).

The number of fringes in the difference interference pattern is determined by the stim of
A0' and (-A&).

3. Realization of the difference hologram interferometry

The analysis discussed above has been carried out in terms of separate uses of the
master object wavefronts for illumination, and can be realized by dual reference beam
method which permits dynamic control of the reconstructed real images of the master
object and adds flexibility to the adjustment of the holographic illumination.

The master wavefronts can be recorded on a single plate with single reference beam,
too [5]. The pecularities of the experimental set up are as follows:

Two-reference beam method: the two master holograms are recorded by two reference
beams. The simplified experimental set up without beam expanding elements is shown in
Fig. 1. The laser light coming from the right hand upper corner is devided into two beams.

Fig. 1. Experimental arrangement: two-reference beam
method

The beam passing through the first beamsplitter is the master object beam. The reflected
light after consecutive splitting produces reference beam Rt for recording the difference
pattern during the second step on the plate Ht; reference beams Rml and Rm2 for recording
the master holograms on the plate Hm and the adjusting beam AW. Symbols Om and Ot
denote master and test objects, respectively- Mirrors Mr reverse the reference beams Rml
and Rm2 for the illumination of the test object.

The two states of the master object are recorded on the same plate (i?m) by the two
reference Rml and Rmz coming from different directions. For fine alignment of the mirrors
Mr, reversing the reference beams, an additional spherical wavefront AW is recorded by
both reference beams. Reconstructing it by both conjugate reference beams simultaneously,
its fringe free image indicates the correct alignment of the reversing mirrors.



246 Z .  FUZESSY  I  INNI

Single  reference  beam  method  1.  (without  beam  splitting  the  object  beams).  The cor-
responding arrangement is the simpliest one because one reference beam is used, only,
as in conventional double exposure holography. When the master hologram is illuminated
by the reversed reference beam, both master object wavefronts are reconstructed and
used in both illuminations. A double exposure interferogram is made for test object.
When the test interferogram is reconstructed interference of four wavefronts can be obser-
ved. They are the difference interference pattern, and disturbing interference fringe systems:
sum of the displacements and twice the actual displacement of the test object.

If the displacement of the master and test objects is to large that their frings systems
are unresolvable, the difference interference pattern will be the only visible fringe system.
The disturbing interference patterns result in a decrease in the visibility of the difference
interference pattern.

The schematic drawing of the corresponding experimental arrangement is shown in
Fig. 2 with main notations as in Fig. 1.

Single reference beam method 2 (with beamsplitting of object beams). An intermediate
arrangement between the two reference beam technique and a single reference beam method
1 is shown in Fig. 3. A single reference beam is used for recording master wavefronts on
a single plate. The significant element of the experimental set up in Fig. 3 is the beamsplitter
BS separating the master object wavefronts on their way toward the hologram plate  Hm.
As a result of the beamsplitting they arrive on the hologram plate from different directions.
During the wavefront reversal the appropriate path is open only while the alternate one
is blocked.

Fig. 2. Experimental arrangement: single reference Fig. 3. Experimental arrangement: single reference
beam method; no beamsplitting the object beam beam method; beam splitting the object beam

All the other steps in producing difference interference pattern are the same as those
discussed above. It is worth mentioning that there are another ways to split the object
beams, e.g. using a michelson interferometr type beamsplitting.

4. Applications

4.1. Displacement difference measurement. In the case of displacement measurement the
master object surface under study was the bottom of a pressure chamber. Between the



APPLICATIONS  OF  THE  DHJ  247

two  exposures the pressure  was  increased  in  it  causing  a  bulging  of  the  bottom  and  pro-
ducing concentric fringe system.

For the sake of simplicity the same chamber was used for the test object as well, but
in the latter case the bottom was repainted and the chamber position changed a little to
simulate the different microstructure.

The first step is the recording a double exposure interferogram, corresponding to the
two states of the bottom before and after the load. The developed plate  Hm (Fig. 1) is
placed back (with interferometrie precision), the master object  Om taken away and the
test object  Ot placed as shown in the figure. A new holographic plate  Ht is placed in the
direction where the master object had been illuminated from.

The reference beams  Rml and  Rm2 were plane waves, their reversal is simply realized
by the mirrors  Mr. The test object  Ot is illuminated by reconstructed real images of the
master chamber in turn, corresponding to the sequence at the recording of the master
holograms. If the pressure change between the two exposures in the master and test cham-
bers is different, the bulging of the bottom will be different. This difference can be recorded
in the form of interference pattern by the plate  Ht.

Fig. 4. Deformation measurement with two-reference beam method: composite interferogram (I)

The working of DHI can be demonstrated quantitatively on a composite interferogram.
in Fig. 4. The lower left quarter shows a quarter of the fringe system of the master object
the upper half shows the half of the fringe system of the test object and the lower right
quarter shows the essence: a quarter of the fringe system displaying the difference between
the master and test object bulging. The bulging of the master object results in 15 (light)
fringes, that of the test object only 3 fringes and their difference is really 12 fringes.

The composite interferogram of Fig. 4 is not composed by phototechnics but the holo-
graphic recording of the test object"itself is composite: it was made in three steps and with
different coverings of the test object. The coverings marked with lines and the illuminations
belonging to them are explained in Fig. 5. First the lower half of the test object is illumi-
nated with the image of the master object in its undeformed state (/ml). In the second



248 Z .  FOZESSY  I  INNI

step the test  object,  in its undeformed  state yet, is illuminated with  the image of the master
object  in  its  deformed  state  (7m2)  and  the  lower  right  quarter  is  covered.  After  that  the
deformation  of  the  test  object  follows.  Then  the  last  step  is the  illumination  of  the  test
object  with  the  image  of the  master  object  in its deformed  state  (7,,,2) while the lower  left
quarter  of  the  test  object  is  covered.

I m 1 , l r t i 2

Fig.  5.  Deformation  measurement  with two-reference beam method: steps of making the composite
interferogram

Summarizing the three steps, the following has happened on the different parts of the
test object (Fig. 5, lower part). The lower left quarter of the test object was illuminated
only in the undeformed state of the test object by  Iml and  Tm2, thus the interferometrie
fringe system of the master object arose. The upper half of the test object was illuminated
before and after its deformation with the same wavefront, with the image of the master
object in its deformed state (7m2), thus the interferometrie fringe system of the deformation
of the master object arose. Finally, the lower right quarter of the test object was illuminated
before and after its deformation with different images of the master object and in the right
order (7m2 after 7ml), thus the required difference arose.

Fig. 6, Deformation measurement with two-reference beam method: composite interferogram (ID



APPLICATIONS  OF  THE  DHJ  249

The  advantage  of  all  of  this  is  that  the  fringe  system  of  the  deformation  of  the  test
object  and  the  difference  fringe  system  could  be  recorded  from  nearly  the  same  viewing
directions  at  the  same  deformation,  happening  once,  of  the  test  object.  Thus  the  source
of error that  the repeated  deformation  of the  test object  may  be a  bit different  is  omitted.
(Of  course,  the  recording  of  the  two  fringe  systems  at  the  same  deformation,  happening
once, of  the test  object  could be done  without  covering  as well. One should  put  a beams-
plitter in the path of the test object wavefront and use two hologram plates. However,
this would have increased the already very dangerous light poverty of the set up.)

Fig. 6 is very similar to Fig. 4, only the fringe systems to be subtracted are too dense
to be observed by the naked eye. Nevertheless their small difference can be seen in unchan-
ged quality. Thus DHI works in the case of invisible dense fringes as well.

4.2. Shape difference measurement. As the second example of application a two-refractive
index contouring will be presented [5]. As for the first step in DHI contouring, the quality
of difference holograms and their reproducibility were the main aspects at the choise
of the proper DHI method. They had been found quite problematic at the authors previous
deformation measurements as well. The lower quality may be connected with the diffuse
holographic illumination itself although simple interferograms of good quality could be
produced by using the same holographic illumination in both steps. The reproducibility,
however, must depend upon the disturbing effects of the surroundings only.

The two-refractive-index contouring has got the special requirement that at least the
observation of the object has to be perpendicular to the window of the container [6].
At DHI contouring, where the observation and illumination change their role at producing
the difference, this means that in any case both have to be perpendicular to the window
of the container. A beamsplitter can ensure this but with significant loss of light power
only. Therefore, a compromise was chosen and the beamsplitter was replaced by a pair
of mirrors cemented on the faces of a prism close to each other. Through this pair of mir-
rors, the observation of the master object (and the illumination of the test object) was
perfectly perpendicular and the illumination of the master object (and the observation
of test object) was only nearly perpendicular.

J /

Fig. 7. Experimental arrangement for contouring Mr

The sketch of the experimental setup is shown in Fig. 7, and the pair of mirrors is denoted
by  MM. The lens  Lt focuses the beam of the collimator  C, onto the right mirror of the
pair of mirrors  MM and the lens  L ensures the parallel object illumination. The obser-

3 Mech. Teoret. i Stos. 2/87



250 Z .  FOZESSY  I  INNI

vation from  parallel directions  is achieved  through the lens L  again and after  the  reflection
on  the  left  mirror  of MM  through  the aperture  Ao  and  the  lens  Lo.  The pair  of  mirrors
MM  is placed  at  the foci  of the lenses Li, L  and Lo  that the illumination  and  observation
directions  could  get  quite  close  to  each  other  Rmi  and  RmZ  are  the  two  plane  reference
waves  and  A W is the  additional  spherical  wave for  the  master  hologram  Hm.  (The beam
expanding  elements  are  not  shown.)

The  changes  required  to  the  production  of  the  difference  interferogram  of  the  test
object  are shown  by dotted  lines in the figure. The mirrors Mr  reverse the reference  beams
Rml  and  RmZ  and  the  mirrors  M,  reflect  the  reference  beam  Rt  and  the  test  object.beam
onto  the  hologram  plate  Ht.  The  lens  Lt  makes  a  very  reduced  image  of  the  test  object
on the hologram  plate to increase the intensity of the weak object  beam.

The  object  is  an  aluminium  membrane  of  60 mm  diameter,  the  middle  of  which  can
be  loaded  with  a  micrometer  screw  to  change  its  shape  in  a  controlled  way.  Its  surface
was  machined  by  surface  grinder  and  was corroded  by  NaOH  to  get a  plane  and  diffuse
surface  which  could  be  contoured  with  10 y.m sensitivity.  It  is placed  in  a  container  with
an  optically  flat  planparallel  window.

To  get  10 (Am sensitivity,  alcohol and  water  are used in the  container  in  the  two steps
of  contouring  at  the  argon  laser  line  X -  488 nm.  First  the  contour  image of  the master

Fig.  8. Master-, test and difference contour fringes



APPLICATION S  or  TH E DHJ  251

object  is  produced.  The  two  exposures  of  the  master  hologram  H
m
  are  taken  with  the

reference  beams  R
ml

  and  R
m2

  separately  while  the  additional  wave  AW   remains  always
present.  At  the reconstruction of  the master  hologram  H

m
,  the reference  beams  R

ml
  and

R
m2

  are reversed  to produce real  images.  Their coincidence is  achieved  by  observing  and
eliminating  the  interference  fringes  of  the two  real  images  of  the  additional  wave  AW .
Then  the  contour fringes  of  the  master  object  appear.  These  images  are  used  separately
for  the illumination of  the test  object  in the second step  at  the recording  of  the test holo-
gram  H

t
.  The  liquids  and  reference  beams  R

ml
  and  R

m2
  are  used  in  the  same  order  as

before.  Thus the difference  contour image  of  the  two  objects  is  produced by  the test holo-
gram  Hf

In  Fig.  8 the evidence of  difference  making is illustrated numerically. The arrangement
used was  the predecessor  of  the arrangement outlined above.  The illumination and  obser-
vation directions subtended wider  angle and the lens L  was  put quite  obliquely  in the light
path to avoid the disturbing  reflections.  The concentric fringe  system  of the  approx. 65  \ x,m.
bulging  at  the centre is  shown  in  F ig.  8 in the case  of  th e master  object.  The test  object
was  simulated  by  changing  the shape  of  the same  object  to approx.  100 fjim  bulging.  Its
fringe  system  is  shown  in  F ig.  8.  The  fringe  system  of  the  difference  bulging  (approx.
35 [j,m) of the centre is  displayed  in F ig. 8 within  half  a fringe  accuracy.

References

1.  Z .  FU ZESSY,  F .  G YIM ESI, Industrial  Applications of  laser  T echnology,  W.  F . F agan , ed., P roc.  SP I E  398,
240  (1983)

2.  D .  D EN BY,  G . E.  QU IN TAN ILLA,  J. B.  BU TTERS,  P roc.  Strathclyde  conf.  1975,  Cambridge  U niversity
Press,  p.  323/ 1976.

3.  D . B.  N EU MAN N ,  T ec.  Digest,  T opical  Meeting  on  Hologram  Interferometry  and  Speckle  Metrology
Opt.  Soc.  Am.,  MB  2 - 1  (1980)

4.  Z .  FU ZESSY,  F .  G YIM ESI,  Opt.  C om m un .  57,  1,  31  (1986)
5.  F .  G YIMESI,  Z .  F U ZESSY,  Opt.  C om m un .  53,  1,  17  (1985)
6.  R . K .  E R F .  (ed.),  Holographic  nondestructive  testing, Academic  P ress,  N ew  York,  1974,  p .  139.

P  e  3  jo  M e

PA3H OCTH Ofł   rO J I O rP At H ^ E C K O fł   HHTEP<t>EPOMETPHH

B  pa6oTe  npeflcraBJieH o  MeTOflw  pa3iiocTH oft  rojiorpadpiwecKOH   H H TepdiepoMeTpH .
COCTOHTCH  B Bo3Mo»CHocrK  cpaBH em m  MOKfly flByM H  o6ibei<TaMH  u  n pitrofleH   Korfla  H er  H eoBxo-

BBrqHCJieHHH  sc e x  KOMnoHeHT nepeMemeH H H   H JI H   dpopiMti  o 6t eK T a,  a  Mbi  3aH H TepecoBaH Bi  o n e -
H JI H   H3MeHeHHH  (Jropiwti  o6i.eKTa.

S t r e s z c z e n i e

ZASTOSOWAN IE  R ÓŻ N I C OWEJ I N T E R F E R O M E T R I I  H O LO G R AF I C Z N E J

Praca  przedstawia  krótki  opis  zasad  róż nicowej  interferencji  holograficznej.  Jej  istotn a  zaleta  polega
na  moż liwoś ci  porównywania  (znajdowania  róż nic)  pomię dzy  dwoma  obiektami.  M etoda jest  przydatn a
gdy  nie  ma  koniecznoś ci  wyznaczania  wszystkich  skł adowych  przemieszczenia,  lub  wyznaczania  kształ tu
obiektu  a wówczas  gdy  interesuje  nas  róż nica  kształ tu lub  zmiana  kształ tu  obiektu.

Praca  wpł ynę ł a do  Redakcji  dnia  1  czerwca 1987  roku.

3*