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Fiber optics speckle interferometer for diffusivity measurements
D. Paoletti, G. Schirripa Spagnolo
To cite this version:
D. Paoletti, G. Schirripa Spagnolo. Fiber optics speckle interferometer for diffusivity measurements.
Journal de Physique III, EDP Sciences, 1993, 3 (4), pp.911-914. �10.1051/jp3:1993171�. �jpa-00248967�
Classification Physics Abstracts
42.40F 66.10C
Fiber optics speckle interferometer for diffusivity
measurements
D. Paoletti and G. Schirripa Spagnolo
Dipartimento di Energetica Universith di L'Aquila, Localith Monteluco di Roio, 67040 Roio
Poggio, L'Aquila, Italy
(Received 9 September 1992, revised 31 December 1992, accepted 20 January 1992)
Abstract. A digital speckle pattem interferometer with optical fibers is proposed for the real
time measurement of the diffusion coefficient of liquid binary mixtures. Some examples of
application of the technique are reported.
Introduction.
Interferometric and holographic techniques have been applied successfully to measure the
diffusivity of liquid transparent mixtures [1-3]. For two liquids mutually diffusing, the concentration gradient and tl~erefore tl~e refractive index, linearly related, changes during tl~e diffusion process ; tl~is introduces a phase difference between the waveflonts reconstructed from the general element of the mixture at two different times, so that the concentration
changes are visualized as interference fringes. The diffusion coefficient D can be found with the equation [4, 5]
w2 tl' t( '
~
8 In (t~/tj)
where w is the distance between tl~e extremes of tl~e reflactive index variation curve along the diffusion cell and tj, t~ two different instants of the diffusion process. The combination of a system of carrier vertical fringes [6, 7] with the horizontal fringes, due to the diffusion process, has simplified the procedure allowing optical differentiation of the interferogram, with a direct
visualization of tl~e concentration variation curve along tl~e cell. In spite of obvious advantages
over otl~er physical or chemical methods, the practical applications of holographic techniques
encounter some difficulties : among these, the stability requirements of holography and the notable time delay due to recording and reconstruction process. In this note we propose to utilize for diffusivity measurements an out-of-plane sensitive interferometer with a smooth
reference beam. This arrangement, combining the properties of digital speckle pattem
interferometry with the flexibility of optical fiber illumination, allows to operate under difficult
912 JOURNAL DE PHYSIQUE III N° 4
condifiions and in out laboratory environments, with a minimum of adjustments and the same
sensitivity as holographic techniques. The ease of use and the cheapness of the system may eventually lead to a much greater acceptance of optical techniques as an altemative to other
methods in diffusion coefficient measurements.
Experimental procedure.
The schematic diagram of the fiber optic DSPI is given in figure I. A graded-index lens (Gin)
is used to couple the laser light into a single-mode fiber ; this beam is later split into a reference
wrn and an object illuminating wrn by a bidirectional coupler. The transparent diffusion cell
Object beam
Diffusion cell
Grin
Ground glass
S>ngle mode fiber
tf~
Diffused I>ght
~'
Mon>nor ~°°~ f
V,deo Reference beam ~~~~' ~P~"~~
90/10 Coupler CCD
~icrocomputer
Fig. I. Schematic diagram of the fiber optic DSPI arrangement.
Fig. 2. Fringe pattem relative to an isothermal diffusion (18.5°) of an aqueous solution of Nacl (I M).
Fig. 3. -Fringe pattem of figure 2 modified by adding vertical fringes (tj = 3 300 s, t~ =
3 600 s, W
= 0.59 ± 0.01, D
= 1.26 ± 0.06 x 10~cm~/s).
(1 x I x 5 cm), filled with a mixture of Nacl I M is located behind a ground glass diffuser, and the laser beam is passed through this cell and the ground glass, as shown in figure I. The
phase of the beam is distorted by the refractive index variation of the mixture, generating a speckle pattem at the ground glass which is similarly distorted [8]. The speckle pattem is
coupled to the reference beam through a beam splitter cube, placed between the photosensor
and the imaging lens of the charge-coupled device (CCD) camera. The speckle pattems are digitized and processed in a host computer and displayed on a monitor. A complete account of the technique is provided by the reference [9- II]. The basic equipment is contained in a closed
portable box, from which a fiber cable will provide the illuminating object beam. The cell is located on a rotating platform. The experimental procedure is the following : an image is stored
electronically at time ti then, during the diffusion process, the live video signal is subtracted from the stored wavefront. Correlations fringes, similar to conventional holographic fringes,
are obtained (Fig. 2). A slight tilt of the cell allows to introduce in this correlogram some carrier fringes of variable density. Electronically the vertical fringes are summarized to the
horizontal fringes in order to give the characteristic fringe pattem of figure 3, from that it is
possible to measure the distance w between the extremes of the curve. The fringes appear very noisy; for this reason, they are electronically treated for noise removal and contrast
enhancement with some conventional procedures [12]. For a correct quantitative evaluation of diffusion coefficient the same procedure of fringes treatment utilized for a holographic pattem [13] can be adopted.
Conclusion.
Many of the difficulties encountered with holographic techniques can be eliminated by using a
DSPI system. Problems of fringe localization are not present the stability requirements are not so strict. The major feature of this technique is the ability to present correlation real time
fringes displayed directly upon a TV monitor, without recourse to any form of photographic processing, plate relocation, and its tolerance toward cell instability, due to high sampling rate
and short exposures made possible by the sensitivity of the CCD camera (1/100s).
Additionally the system is easy to adjust, cheap, and can operate in day-light also in industrial environments.
914 JOURNAL DE PHYSIQUE III N° 4
References
[1] SzYDLOWSKA J. and JANOSKA B., Holographic measurement of diffusion coefficients, J. Phys. 15 (1982) 1385-1393.
[2] GABELMANN-GRAY L. and FENICHEL H., Holographic interferometric study of liquid diffusion, Appl. Opt. 18 (1979) 343-345.
[3] Ruiz-BEVIA F., CELDRAN-MALLOL A., SANTOS-GARCIA C. and FERNANDEz SEMPERE J., Liquid diffusion measurement by holographic interferometry, Can. J. Chem. Eng. 63 (1985) 765-771.
[4] CRANK J., The mathematics of diffusion (Oxford University Press, 1975).
[5] BOCHNER N. and PIPMAN J., A simple method of determining diffusion constants by holographic interferometry, J. Phys. D : Appl. Phys. 9 (1976) 1825-1830.
[6] PAOLETTI D., SCHIRRIPA SPAGNOLO G, and D'ALTORIO A., Liquid diffusion study by holographic
sandwich method, Can. J. Chem. Eng. 65 (1987) 508-511.
[7] PAOLETTI D., SCHIRRIPA SPAGNOLO G. and D'ALTORIO A., Sandwich Hologram for Displacement Derivative, Opt. Commun. 56 (1986) 325-329.
[8] VERHOEVEN D. D. and FARRELL P. V., Speckle interferometry in transparent media, Appl. Opt. 25 (1986) 903-906.
[9] LOKBERG O. J. and KRAKHELLE, Electronic speckle pattem interferometry using optical fibers, Opt.
Commun. 38 (1987) 153-158.
[10] JONES R., WYKES C., Electronic speckle pattem interferometry irt holographic and speckle interferometry (Cambddge University Press, 1983).
ii JONES R., The design and application of a speckle pattem interferometry for total plane strain field measurement, Opt. Laser Technol. 8 (1976) 1835-1842.
l12] YATAGAI T., NAKADATE S., IDESAWA M. and SAITO H., Automatic fringe analysis using digital image processing techniques, Opt. Eng. 21 (1982) 432-435.
Ii 3] PAOLETTI D. and SCHIRRIPA SPAGNOLO G., Automated fringe analysis in diffusivity measurements
by sandwich holography, J. Phys. III France 2 (1992) 13-19.
