We present a new arrangement for contouring by electronic speckle pattern interferometry with four illumination beams, thereby making it unnecessary to move anything during the measurement

Diao, Hongyan

Peng, Xiang

Tiziani, Hans J.

Zou, Yunlu

Online Publikationen der Universität Stuttgart

Contouring by electronic speckle pattern 
interferometry with quadruple-beam illumination 
Y. Zou, H. Diao, X. Peng, and H. Tiziani 
Institute o f Applie d Optics , Universit y o f Stuttgart , 
Pfaffenwaldring 9 , 7000 Stuttgart 80, Germany. 
Received 16 October 1991. 
0003-6935/92/316599-04$05.00/0. 
© 1992 Optical Society of America. 
We present a  new arrangement for contouring by  electronic 
speckle pattern interferometry with four illumination beams, 
thereby making it  unnecessary to move anything during  the 
measurement. 
Key words: Contouring,  interferometry, speckle phenom-
ena, metrology 
Optical contouring techniques applie d o n a  rough surfac e 
by mean s o f electroni c speckl e patter n interferometr y 
(ESPI) hav e bee n develope d fo r three-dimensiona l shap e 
analysis an d topograph y measurement. 1-5 Correlatio n 
fringes ar e shown afte r th e subtractio n o r addition o f the 
video signals fro m tw o speckl e patterns. On e can obtai n 
the contou r dat a fro m th e correlatio n fringe s b y using a 
phase-shifting metho d an d algorithm. 6 Th e existing con-
touring methods by ESPI consis t of using two-wavelength 
illumination1 or altering the object illumination beam2,3 in 
a conventiona l ESP I syste m wit h a  smoot h interferenc e 
reference bea m an d alterin g th e object 4 o r shiftin g th e 
illumination beams5 in a dual-beam system. 
We presen t a n inexpensiv e ESP I arrangemen t wher e 
nothing i s move d t o obtai n contou r fringes . Onc e thi s 
system i s well adjusted , i t ca n be used simpl y and practi -
cally, e.g., in a black box with a complete program package 
for fringe analysis. Th e schematic of such an arrangement 
is shown in Fig . 1 . Th e collimated lase r beam i s split by 
the first  bea m splitte r BSi , then combine d agai n with th e 
second prism beam splitter BS2 with a small angle difference. 
Mirror M 5 play s th e rol e o f a  directio n compensato r fo r 
forming correct contour planes.5 Th e first speckle pattern 
is taken by the CC D camera when shutte r S 1 i s open an d 
shutter S 2 is closed an d the n subtracte d fro m th e secon d 
1 Novembe r 199 2 /  Vol . 31, No. 31 /  APPLIE D OPTICS 659 9 
speckle patter n whe n S 1 i s close d an d S 2 i s open . Th e 
resulting correlation fringes are displayed on a TV monitor, 
and the fringe video signals are taken and processed by the 
computer incorporating an image frame grabbe r board fo r 
fringe analysis when the phase-shifting method is used. 
The geometr y fo r formin g th e correlatio n fringe s i s 
similar t o tha t i n Ref . 7 . Th e intensit y differenc e a t 
viewpoint P (see Fig. 2) between these two speckle patterns 
is 
where I 1 an d I 2 ar e th e intensitie s o f tw o illuminatio n 
beams scattered from poin t M in the object for one speckle 
pattern, φ sl an d φ s2 ar e th e rando m phase s o f thes e tw o 
beams, Ψm and φm' ar e the phase differences between these 
two beams caused by the objec t shap e for th e two speckl e 
patterns, respectively , an d ΔΨ m =  Ψ m' -  Ψ m. I 1, I 2, φ sl, 
and φ s2 are assumed t o hav e undergone n o change in th e 
two speckl e patterns. 1 Th e si n ter m wit h th e rando m 
phases φsl and φs2 in Eq. (1) disappears after averaging and 
high-pass filtering  whil e th e signa l i s displaye d o n th e 
monitor. Henc e th e correlatio n fringe s depen d o n onl y 
the phas e ter m ΔΨ m. ΔΨ m ca n b e determine d fro m th e 
discussion below. 
In Fig. 2 K1 and K2 are the unit directio n vectors of the 
two illumination beams during the first  exposure , K1' an d 
K2' ar e thos e a t th e secon d exposure , Δ 0 i s th e angl e 
difference betwee n th e illuminatio n beam s fo r th e tw o 
speckle patterns, 9 is the illumination angle of both illumi-
nation beams if they are set at the same angle with respect 
to the view direction Z, rm i s the position vector from poin t 
P t o poin t M , β  i s th e angl e betwee n r m an d th e Z  axis . 
If we ignore the constant optical paths of the two illumina-
tion beams from the light source to viewpoint P, the phase 
advances of the two illumination beams scattered from M to 
P for the first speckle pattern are 
Fig. 2. Geometr y of the ESPI contouring. 
respectively, where λ is the wavelength of the illuminating 
light and rm is the scalar magnitude of rm. Therefor e 
Similarly, for the second speckle pattern we have 
Then 
where ΔK 1 =  K 1' -  K 1 an d ΔK 2 =  K 2' -  K 2. I t ca n be 
found from Fig. 2 that |ΔKX | = |ΔK 21 = Δθ |K1 | = Δθ|K 2| = 
Δθ, wher e |K 1| =  |K 2|= 1  and fro m Fig . 3  tha t |ΔK 1 -
ΔK21 = 2 sin θ |ΔK1 | = 2 sin θΔθ.  Finall y we have 
where h is the depth of the object along the view direction Z 
when th e angl e change s o f K 1 an d K 2 ar e antisymmetri c 
(see Fig. 2). Therefor e the contour interval is as follows: 
Fig. 1. Schemati c of the ESPI arrangement with quadruple-beam 
illumination. L , collimator lens. Fig. 3. Vecto r geometry. 
6600 APPLIE D OPTICS /  Vol . 31, No. 31 /  1  November 199 2 
Fig. 4. Result s obtained when the illumination angle 9 is 30° and the angle difference Δ9 is 0.77 mrad: 
(c) three-dimensional plot, (d) contour map. 
(a) contour fringes, (b) phase map, 
The sensitivity can be controlled by altering the size of Δ0 in 
our arrangemen t a s we did in Fig . 1  by tilting mirror M 1 o r 
mirror M 2. 
A 10-m W He-Ne lase r wa s use d a s a  coheren t illumina -
tion source . Th e tes t objec t wa s a  pyrami d wit h a n ape x 
angle of 120°. Th e CCD camera was a Sony XC-77CE wit h 
a resolutio n o f 1 1 μm . Th e illuminatio n angl e θ  was 30° , 
and th e angl e difference Δθ  wa s 0.7 7 mrad . Not e tha t w e 
used a cube (prism) beam splitter BS2 in the arrangement t o 
simplify th e adjustmen t o f the four beams . Th e piezoelec-
tric-transducer-(PZT)-driven mirro r M 5 introduce d phas e 
shifting durin g th e secon d exposur e fo r phas e evaluation . 
The image s wer e processe d b y a n Epso n hos t compute r 
with a  FG-100-A T fram e grabbe r board . Thre e interfero -
grams with a  shifted phas e of ττ/2 with respect t o one othe r 
were used fo r evaluatin g the phases.4 A  30 ×  2 9 samplin g 
array wit h a  gra y leve l o f 1 0 wa s employe d t o digitiz e th e 
interferograms; 3  ×  3  and 5  ×  5  convolutio n filterin g wa s 
used sequentiall y t o smoot h th e speckle s i n th e interfero -
grams. Figur e 4(a) shows the contour fringes o f the objec t 
surface. Figure s 4(b) , 4(c), and 4(d ) sho w th e phas e map , 
the three-dimensional plot , and the contou r ma p evaluate d 
from th e three phase-shifted intensit y data , respectively . 
A naturall y supplementa l resul t i s show n b y a  simila r 
arrangement wit h thre e illuminatio n beams . On e bea m 
plays only the role of a reference wav e to form th e interfer -
ence speckl e patterns . Th e othe r tw o beam s wit h smal l 
angle differences , whic h ar e the illuminatio n wave s for th e 
first an d secon d exposures , respectively , shoul d b e a t 
incident angle s o f ~90 ° t o th e vie w direction 7 s o tha t 
contour fringe s ca n be obtained . 
The new ESPI arrangemen t presente d above has obviou s 
advantages. Th e setu p i s relativel y stabl e durin g th e 
process because ther e i s no furthe r mechanica l movemen t 
after adjustment ; thu s fas t automati c processin g results . 
The sensitivit y ca n b e selecte d durin g th e adjustmen t an d 
corrected for further measurements . 
The author s than k G . Padrin i fo r helpfu l discussions . 
The financia l suppor t fro m th e Alexande r vo n Humbold t 
Foundation to X. Peng is gratefully acknowledged . 
References 
1. R . Jones and C. Wykes, Holographic and Speckle Interferometry 
(Cambridge U. Press, Cambridge, 1989), Chap. 5, p. 204. 
2. B . D. Bergquist and P. Montgomery, "Contouring by electronic 
1 Novembe r 199 2 /  Vol . 31, No. 31 /  APPLIE D OPTICS 660 1 
speckle patter n interferometry, " i n Optics  in  Engineering 
Measurement, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. 
Eng. 599, 189-195 (1985). 
3. S . Winther and G. Slettemoen, "An ESPI contouring technique 
in strain analysis," in Symposium Optika  '84,  G. Lupkovics and 
A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 473, 
44-47 (1984). 
4. C . Joenathan , B . Pfister , an d H . Tiziani , "Contourin g b y 
electronic speckle pattern interferometry employin g dual beam 
illumination," Appl. Opt. 29, 1905-1911 (1990). 
5. X . Peng, H. Y. Diao, Y. L. Zou, and H. Tiziani, "Contouring by 
modified dual-beam ESPI based on tilting illumination beams," 
Optik (Stuttgart) 90, 61-64 (1992). 
6. K . Creath, "Phase-shifting speckl e interferometry," Appl . Opt. 
24, 3053-3058 (1985). 
7. Y . Zou , H . Diao , X . Peng , an d H . Tiziani , "Geometr y fo r 
contouring by electronic speckle pattern interferometr y base d 
on shifting illuminatio n beams, " Appl. Opt. 31, 6616-6621 (1 
1992). 
6602 APPLIE D OPTICS /  Vol . 31, No. 31 /  1  November 199 2 


Contouring by electronic speckle pattern interferometry with quadruple-beam illumination

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Contouring by electronic speckle pattern interferometry with quadruple-beam illumination

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