Contour holography can be a powerful tool for contactless measurements. Its application in real time is even more useful for the engineer. The BSO crystal was found to be appropriate for real-time contour holography using two wavelengths

Küchel, Michael

Tiziani, Hans J.

Online Publikationen der Universität Stuttgart

Volume 38, number 1 OPTICS COMMUNICATIONS 1 July 1981 
REAL-TIME CONTOUR HOLOGRAPHY USING BSO CRYSTALS 
F.M. KOCHEL and H.J. TIZIANI 
Institut ffir Technische Optik der Universitfit Stuttgart, 
7000 Stuttgart 80, Fed. Rep. Germany 
Received 17 March 1981 
Contour holography can be a powerful tool for eontaetless measurements. Its application in real time is even more useful 
for the engineer. The BSO crystal was found to be appropriate for real-time contour holography using two wavelengths. 
1. Introduction 
Contour-line holography as described by Hildebrand, 
Varner and others [1-4]  is a useful tool for contactless 
measurements of  contours of  objects with optically 
rough surfaces. Applying the technique in real time is 
even more attractive and leads to an easier adjustment 
of the object as by recording on photographic emul- 
sions. Electro-optical crystals uch as Bil2SiO20 (BSO) 
are appropriate for real time recording. They were al- 
ready used for real-time holography [5-8]  and speckle 
applications [9]. For the application to be described, 
the BSO crystal was biased with a transverse electric 
field E 0 in the 110 crystallographic direction. Illumi- 
nating the crystal with structured information in the 
T10 direction as indicated in fig. 1, a space-charge field 
is built-up, leading to a refractive index variation in 
the crystal via linear electro-optic effect. A phase vol- 
\ 
T 
/! 
3 X' 
I. 2 
Fig. 1. Arrangement for real-time contouring. LI, L2, L3 lenses. Q, R illumination- and reference point sources. A polarization 
sheet. 0q, O r offset angles of illumination and reference plane waves. 
0 030-4018/81/0000-0000/$ 2.50 © North-Holland Publishing Company 17 
Volume 38, number 1
ume hologram is created. Floading with uniform illu- 
mination leads to the erasure of the stored information 
by space-charge r laxation. Consequently, reading out 
with a recording wavelength is destructive. 
For an optimised iffraction efficiency a BSO crys- 
tal of thickness 2.3 mm was chosen. For contour holo- 
graphy in real :ime a krypton laser was used lasing in 
neighbour wavelengths pairs appropriate for the exper- 
iments to be described. 
OPTICS COMMUNICATIONS 
I~(x', X2) = C 2 {Ih'r(X')I IZ'(x')l 
i2 Lll X [exp( i2~'L~+exp( -~-  2 x 2  ,/ ]J 
+ IA'r(x')l 2 + IA'(x')12}, 
where 
2. Principle of  the contour  l ine holography 
A brief analysis of the method adopted will be given. 
The experimental arrangement is shown schematically 
in fig. 1. A telecentric configuration is chosen to form 
the image of the object illuminated with a plane wave 
at an incident angle of 0q. The image of the object is 
superimposed bythe reference plane wave incident at 
an angle O r in the image plane where the electro-optical 
crystal stores the information. 
The complex amplitude immediately in front of a 
reference plane of the object can be written, using one 
dimensional notation only, as 
A(x)=Ao(x)exp(-1-~--x'27r sin0q) 
Xexp l i -~( l+cos0q)Az  1. 
Ao(x ) descries the object as well as the optically rough 
surface. Furthermore, a perfect optical system is con- 
sidered, hence A(x)~ A'(x'). The interference of the 
complex amplitude of the image A '(x') of the object 
and the reference plane waveA~(x') incident at an an- 
gle Or, as shown in fig. 1, leads to an interference pat- 
tern in the crystal. The intensity of the fringe pattern 
in the crystal is proportional to I~ (x', X 1) for the wave- 
length X 1 andI~(x', X2) for X 2 
I~(x', Xl)= C 1 { [A'r(X')[ Ia'(x')l 
• 2rr .2~r 10xp(, L) ox,( 
+ Ih'r(x')l 2 + IA'(x')I 2} 
\ 
and 
1 July 1981 
L = -(f~/f~) x' sin Oq + x' sin O r - (1 + cos 0q) Az, 
C 1 and C 2 are constants. 
The holograms for X 1 and k 2 are recorded simulta- 
neously by using a laser mitting the two wavelengths. 
The field distribution leads to a photoinduced 
change of the refractive index in the BSO crystal pro- 
portional to I'(x', X1, X2) ~ I~ (x', X 1 ) + I~(x', ~k2). 
The complex transmission 
t'(x', Xl, X2) = exp[i (3I'(x', Xl, )'2)] 
can be written as 
t'(x', Xl, X2) = 1 + i (3I'(x', kl, X2) , 
because 
~I'(x', Xl, X2) ,~ lr/2. 
The reconstructing wave can be either the conjugate 
reference wavefront of X 1 or X 2. The constructed im- 
age-wavefronts travel backwards through the telescope 
and are coupled out with a beamsplitter as shown in 
fig. 1. The reconstruction with the conjugate reference 
wave with wavelength X 2 leads to an intensity pattern 
proportional to 
I = I 0 + T cos (27r/Xres) L. 
Constructive interference is obtained for 
(27r/kres) L = 2~rm, m = 0, -+ 1, +2... 
where Xre s = X 1X2/(~ 1 - ~2) can be considered as an 
equivalent wavelength. 
For m = 1 
)kre s=-- (f~/f~) X' Sin 0q + X' sin O r - (1 + cos 0q) Az. 
For (fl/f2) sin 0q = sin Or, the separation of the con- 
tour lines is 
Az = X1X2/(1 + cos 0q) (~k 1 --X2). 
With the configuration chosen, the following practical 
advantages are achieved: 
- the use of a grating for compensating the angles 
18 
Volume 38, number 1 OPTICS COMMUNICATIONS 1 July 1981 
Fig. 2. (a) Image of part of  a coin. (b) Real t ime contour lines of  (a). ~,1 = 520.83 nm, ~2 = 530.87 rim, contour line spacing is 
13.88 ~m. 
Fig. 3. (a) Contour lines on a metallic surface; contour line spacing = 13.88 #m. Co) Two sets of  superimposed contour lines. Spac- 
ings are 18.45 ~m and 2.67 ~m with two pairs of  laser lines (7~1 = 476.24 nm, 7, 2 = 482.52 nm and 7~2 = 482.52 nm, ~3 = 530.87 nm). 
19 
Volume 38, number 1 OPTICS COMMUNICATIONS 1 July 1981 
of the reference wave for the two wavelengths i
avoided; 
- the angles 0q and 0 r can be small, for the tele- 
scope lenses to be used as collimators. 
3. Experimental results 
The experimental rrangement is shown in fig. 1. 
As light source a krypton-ion laser was used. Pairs out 
of five laser lines were chosen. For a good diffraction 
efficiency of the BSO crystal a grating constant of 5 
p_m was envisaged, leading to 0q of 10 degrees,f~/)'~ 
= 0.56... Furthermore, 6000 Volts were applied to 
the BSO crystal. 
For a spacing of the contour lines of 13.88 pzn, the 
two laser lines X1 = 520.83 nm, ?~2 = 530.87 nm were 
selected. Fig. 2a shows an image of a coin, fig. 2b the 
real-time contour lines. Fig. 3a shows another metallic 
object contoured with the same pair of  wavelengths as 
in fig. 2b. For fig. 3b three laser lines were used to- 
gether, leading to two superimposed sets of contour 
lines. The wavelengths X1 = 476.24 nm and ~2 = 
482.52 nm form contour lines with 18.45/am spacing, 
the wavelengths ?~2 = 482.52 nm and ~'3 = 530.87 nm 
the finer lines with a spacing of 2.67 tan. The writing 
power density on the crystal was roughly 200/aW 
cm -2,  the time constant for writing the hologram 
about 0.2 s. Furthermore it should be mentioned, that 
for good image and fringe quality the appropriate 
orientation of a polarizer was found to be important. 
4. Conclusion 
Real time contouring with BSO crystals is found to 
be a very powerful tool for different applications for dif- 
fusing or transparent objects. The separation of the 
contour lines can be selected by choosing the appro- 
priate wavelength pair with a properly chosen colour 
or interference filter. The adjustement of the object is 
carried out in real time. 
We would like to thank the DFG for the financial 
support and B. Burger for carrying out some of the ex- 
perimental work. 
References 
[1] K.A. Haines and B.P. Hildebrand, J. Opt. Soc. Amer. 57 
(1967) 155. 
[2] S. Zelenka nd J.R. Varner, Appl. Optics 7 (1968) 2107. 
[3] J.R. Yarner, Appl. Optics 10 (1971) 212. 
[4] W. Schmidt, A. Vogel and D. Preussler, Appl. Physics 1 
(1973) 103. 
[5] J.P. Herriau, J.P. Huignard an P. Aubourg, Appl. Optics 
17 (1978) 1851. 
[6] J.P. Huignard, J.P. Herriau, P. Aubourg and E. Spitz, 
Optics Lett. 4 (1979) 21. 
[7] J.P. Huignard, J.P. Herrian, G. Rivet and P. Gtlnter, 
Optics Lett. 5 (1980) 102. 
[8] A. Marrakchi, J.P. Huignard an J.P. Herriau, Optics 
Comm. 34 (1980) 15. 
[9] HJ. Tiziani, K. Leonhardt and J. Klenk, Optics Comm. 
34 (1980) 327. 
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Real-time contour holography using BSO crystals

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Real-time contour holography using BSO crystals

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