Applications of the Speckle Pattern Techniques to theVisualization of Modulation Transfer Functions andQuantitative Study of Vibrations of Mechanical Structures

J. Bulabois, M. E. Guillaume, and J. Ch. Vi6not

Some statistical properties of a speckle pattern can be characterized by its autocorrelation function andthe intensity distribution in its Fraunhofer diffraction pattern, which depends on the granularity of thediffused wave and the contour of the pupil that limits the diffusing surface. It is shown that this proper-ty can apply to the visualization of modulation transfer functions, namely, those of synthetic apertures.A method for measurement of tilt angle for diffusing elementary surfaces is also derived. The informa-tion that can be extracted from a time-average photographic record of the intensity distribution scatteredfrom a vibrating rough surface is discussed. It is shown that a complete mapping of the surface can becarried out by a suitable spatial filtering of the speckle pattern. As an example, in vibration mode anal-ysis areas of singularity are displayed on the filtered image of a plate.

I. IntroductionThe phase of the wave diffused by a rough surface

coherently illuminated is random. It results in theobservation of the well-known speckle phenomenon,since in turn the intensity distribution is directly re-lated to the random structure of the surface. Theproperties of the speckle pattern can be used to de-termine the displacements, deformations, or vibra-tion modes of the rough surface without any addi-tional reference beam. Many workers, namely,Goldfischer' and others,2 ' 3 have investigated thetheory of the speckle and its statistical properties.A great many applications are described in the lit-erature (e.g., Refs. 4 to 17).

The purpose of the present paper is twofold: (1)using the diffused waves allows the visualization ofthe modulus of the optical transfer function of vari-ous synthetic apertures; (2) choosing the contour ofthe illuminated region on the diffusing surface takenas the object leads to-in double exposure-interfer-ence phenomena, the average intensity of which isnearly constant across a large area. From the re-sults, we have derived a particular approach to thestudy of vibrations. The speckle pattern techniquesare appropriate for determining the vibration modesof any rough surface of a mechanical structure butnot the quantitative amplitudes. Determination of

The authors are with the Laboratoire de Physique Gn~rale etOptique, Facult6 des Sciences et des Techniques, F. 25030 Besan-con, France.IReceived 13 October 1972.

the latter is carried out by means of a suitable spa-tial filtering process applied to the speckle pattern.The technique gives the measure of rotation anglesof surface elements close to the nodal regions:

II. Visualization of Modulation Transfer Function ofSynthetic Apertures

Let there be a plane diffusing surface (D) consist-ing of randomly distributed high frequency scatterersof uniform average reflectivity (Fig. 1). For constantillumination, the phase distribution of the diffuserd(x,y) is affected by the pupil function p(x,y), sothat the complex amplitude distribution is describedby

f(x, y) = p(x, yd(x, y), (1)

where p(x,y) = 1 inside the contour and zero other-wise.

In any observation plane 0't1~ parallel with Oxy,the scattered amplitude distribution is proportionalto the Fourier transform F(,7) of f(x,y), whateverthe separation between that plane and the diffusesurface may be. The energy distribution E(,7) isthe square modulus of the amplitude

E(, r7) = F(Q, n)12 = I [f(x, y)]12* (2)

After the autocorrelation theorem, one has succes-sively

E = F-F-* = 1 (f) ir(f*) = (f ( f *) = $(f * f*) (3)

(as an index the asterisk denotes the conjugatequantity of f, and the subscript indicates that thecurrent variables are preceded by the minus sign inthe autocorrelation and convolution integrals, repre-sented by* and i, respectively).

1686 APPLIED OPTICS / Vol. 12, No. 7 / July 1973

(L:\Ilf R

Fig. 1. Schematic diagram for speckle pattern recording in aO'~n plane. The diffuser (D) of constant average reflectivity isdefined by the phase distribution d(x,y) and contour fction

P(XY).

The energy is then the autocorrelation function ofthe amplitude distribution inside a particular regionof the object under test. In this respect the specklepattern can be considered as a consequence of thesuperposition of a great many fringe patterns run-ning in all directions, generated by individual scat-terers taken two by two. This energy is the sum oftwo terms

where E represents the varying component of E, thatis, the fluctuations of the illumination about the av-erage value E. The random distribution E(Q,77) maybe defined by its autocorrelation function

H =E*E=1E12 E*E5

Supposing a perfect diffuser, the cross-correlationterms involving the vibrations issued from the vari-ous scatterers vanish, and the autocorrelation func-tion of d(xy) tends to a Dirac function . It is easilyshown" that the autocorrelation product of the fluc-tuating term is proportional to the Fourier transformof the autocorrelation function of the pupil contour

E*E- = +T(p*p). (6)

Let us record a photograph of the speckle taken asa transparency and assume that the amplitudetransmittance is linear with respect to the energydistribution v

t(t , ,) = a + b[E(D,77)], (a, b = parameters). (7)

After Eq. (4) the amplitude distribution in the spec-trum is

T(w, v) = [t(Q, i)] = a'6(w, v) + b [E(t, I)],

and the intensity can be written as

I(w,v) = A6(w,v) + B [E(t, 1 )*(E(, )],

or, taking into account Eq. (6),I a: p*p,

tem of uniform transparency limited by the pupilp(x,y).

Conversely the previous conclusion suggests a sim-ple method to determine the MTF of a given pupil.The experience that we obtained from the theoreti-cal as well as experimental study of the MTF of vari-ous synthetic apertures carried out in our laboratory5

incited us to consider, as an example, a pupil in theshape of two bars perpendicular to each other. Thishas been referred to as the Mills' cross aperture incurrent literature. Indeed, this pupil has proved ofinterest in the determination of vibration ampli-tudes, as will be seen later on.

The experimental procedure consists of recordingthe speckle produced by a uniformly diffusing sur-face limited by the pupil under test, then observingthe spectrum of the transparent negative obtained.The first part of this experiment is schematicallyshown in Fig. 2(a). Note that in Fig. 2'(b) the pho-tograph taken in a plane (O'Sn) exhibits privilegeddirections in the speckle pattern due to those of thecross. Alternately this aspect stresses out the im-portance of the shape of the pupil on the statisticalfeatures of the speckle pattern.

Figure 3 shows a photograph of the intensity dis-tribution in the spectrum of the speckle, i.e., animage of the MTF For the sake of comparison thecomputed MTF has been reported on the same fig-ure.

Ill. Measurement-of Tilt AnglesOn a unique photographic plate let us record two

or more speckle' patterns corresponding to differentpositions of the diffusing surface. The situation is

DIFFUSINGSURFACE t

½~~~~~~~~~~~

MILLS CROSS APERTURE

SPECKLE(a} 1

(8)

(9)

(10)

apart from the central term A6(w,,v).This result is of great interest, since it shows that

the intensity in the spectrum of the photographicallyrecorded speckle describes the autocorrelation of thepupil contour function, which is in turn the opticaltransfer function of 'an aberration-free imaging sys-

(bI

Fig. 2. The photograph of the speckle pattern (b) is a magnifica-tion of the intensity distribution obtained in plane O'ti0 as thediffusing surface at rest is illuminated by a coherent beam and

the contour function p(x,y) is a Mills cross aperture.

July 1973 / Vol. 12, No. 7 / APPLIED OPTICS 1687

MILLS'CROSS

APERTURE

OBSERVED MTF

COMPUTED MTF

Fig. 3. Top left: pupil under test; top right: intensity in thespectral plane of the speckle pattern recorded from a diffusingsurface limited by that pupil; bottom: representation of the

computed MTF (one quadrant).

SEGMENTED

MILLS CROSS |

APERTURE

COM PU TED M T F

Fig. 4. As in Fig. 3 but the two bars of the cross have been seg-mented.

similar to that encountered in double- or multiple-exposure holographic interferometry. The result isthe superposition of identical speckles shifted inspace and chronologically delayed. This holds if thesurface displacements are small: such is the casewith vibration studies as tilt angles of elementarysurfaces stay generally small. Consequently thespeckle patterns are shifted by quantities propor-tional to the tilt angles, If the object does not sufferany distortion during the rotation, it has been

proved 8 that the recorded patterns behave as identi-cal pupils shifted one with respect to the others, pos-sibly overlapping each other. If m(Q,-) describes thedisplacement and t,7) the same quantity as before,[Eq. (7)], the transparency is

(11)

The intensity distribution is derived in the samemanner as in the previous section:

I'(W, v) = I(w, v)I TI[m(, n)]2. (12)

One finds again the term I(w,v), which representsthe intensity in the Fourier spectrum of the specklepattern and is modulated by a function that de-scribes an interference phenomenon.' 8 The periodi-city and profile of the fringes depend on the form ofthe function m(,7). One might point out that the'seconsiderations led to the introduction several yearsago7 of the fundamental concept of homologous raysin holographic interferometry.

MILLS CROSS APERTURE

D

0 NI N2

0o

Jo&,O NJ

z ~~~~~~~~~~~~~~~~~~1 IU

CIRCULAR APERTURE

D

1-,,

0 N1 N2

DENSITOMETER TRACES

a0

0 N1

( U

Fig. 5. Fourier spectra obtained in the diffraction plane of a lensfrom the superposition of speckle patterns corresponding to twosuccessive positions of the diffusing surface rotated by a. If A iswavelength, f is focal length, s is fringe spacing, R is separationbetween the diffusing surface and the plane where the speckle isrecorded (cf. Fig. 1), 0 is incidence angle of the illuminated beamon that surface, a = Af/sR(1 + cosO), as the recording direction isalso 0 or about. The interference fringes are observable inside anarea directly related to the MTF range. The microdensitometersections along axes passing through the center of the fringe pat-terns () and aside (2) show that the number of visible fringesis larger for a Mills' cross aperture than for a circular pupil, al-

though the maximum frequency N2 is the same in both cases.

1688 APPLIED OPTICS / Vol. 12, No. 7 / July 1973

t, W, 771 = 0�1 77 ) OMQn).

LINE

I-a} D J(1+ai E1I

VIBRATING PLATE

(a)

LOCATION PROBABILITY

IN THE SPECKLEWbI

Fig. 6. Example of a vibration mode of a metallic plate. a is

the tilt angle of diffusing elements such as N situated in theneighborhood of the nodal line (a); the curve (b) represents the

position function of these diffusing elements as they oscillate (aswell as that of the corresponding regions of the speckle).

For double exposure, the same speckle occupiestwo positions, which can be identified by two 8 func-tions:

MQt, 77) 7 - VI) + Q-4 2,- -2). (13)

The intensity distribution I(w,v), corresponding tothe modulus of the optical transfer function of thepupil p(x,y) is then spatially modulated by a sinus-oidal function.

Suppose now that we want to measure the tiltangle of a moving surface very accurately from oneexposure to the next. It is necessary that the pre-vailing term in Eq. (12) be the second one, that is tosay, the fringe pattern be as little disturbed as possi-ble by the MTF I(w,v) of the pupil contour. There-fore the best aperture is that whose autocorrelationfunction presents a uniform level across an extendedfield, in other words, whose three-dimensional repre-sentation shows a wide plateau (compare, for in-stance, Fig. 3). This is obviously not the case with acircular aperture. Figure 5 illustrates our state-ment. For comparable sections chosen perpendicu-lar to the main directions of the fringes, the numberof those and the regularity of their profiles are higherin the case of a Mills cross aperture than with a cir-cular aperture (in both situations the maximumfrequencies N2 are the same).

A. Case of Sinusoidal VibrationThe function of position m(,i) can be calculated

for a diffusing pupil oscillating sinusoidally (Fig. 6).For half a period, it is assumed that a given portionof the surface is rotated by a tilt angle a about anaxis situated in the plane of the plate. Since the ve-locity of the displacement varies, m(Q,7) is related tothe sweeping duration corresponding to any angularsection Acxi (such as 2;in o Aai a; practically nwas chosen equal to 200). Therefore a description ofm is given by weighting each section represented bya 6 function: Fig. 6(b) then appears as the probabil-ity of presence of a given point Q of the surface asposition (QO), for instance. It comes to say that theweighting parameters indicate how long the speckle

pattern occupies a given average location. The pro-file of the fringes resulting from the movement m isassessed by Fourier transformation (see, for instance,Ref. 9).

The theoretical and experimental curves are drawnin Fig. 7: the optical densities are reported vs thedistance from the center of the pattern. As an illus-tration of this, the maximum tilt angle is 1.5 X 10-4

rad in the vicinity of a nodal line of a metallic plate(300 mm X 200 mm X 2 mm) vibrating at the fre-quency 430 Hz (the diffusing region is a Mills cross,the bars of which are 20 mm long). The resolvingpower of the conventional emulsion (PAN F 50 ASA)and camera aperture limits the range of measure-ment from 10-2 rad to 10-7 rad.

IV. Determination of Vibration Modes of a DiffusingMechanical Structure

A. Recording and Useful Properties of Time-Average Speckle Pattern

Whereas the time-average holographic techniquesallow the determination of the configuration of thevibration modes as well as their amplitudes at anypoint of the surface under test, the speckle patterntechniques usually appear as qualitative in the sensethat they only provide an approach to the parame-ters that define the vibration modes.

In this section we intend to describe a method ofrecording and processing time-average speckle pat-terns consistent with the fundamentals developed sofar and capable of providing quantitative informa-tion on the configuration and amplitudes of the -vi-bration modes in various regions of the object (pres-ently a 300 mm X 200 mm X 2 mm metallic plateexcited through acoustic coupling: a loudspeaker isused, vibrating at a tunable frequency of a few hun-

D i

.... COMPUTED CURVE

DENSITOMETER TRACE

Fig. 7. Photograph of the interference phenomenon obtained by

Fourier transform from a sinusoidal vibration of a rough plate

(time-averaged speckle pattern). The microdensitometer trace

(solid line) shows the variations of the optical density along the X

axis, the dashed line is the corresponding computed curve (Fouri-er transform of the curve represented in Fig. 6b).

July 1973 / Vol. 12, No. 7 / APPLIED OPTICS 1689

LASER

VIBRATINGPLATE

OBJECT

SPECKLE PLANE

Fig. 8. Principle of recording of themethod).

speckle pattern (Massey's

pupil ci limiting the angular size of the entrancebeam-the diffusing element of size (DD is responsiblefor the energy at P' on the film. The 4

ID contribu-tion to the speckle at P, therefore to the intensity atP', depends on the nature of the movement of theelement D. In other words, the time-average grainstructure is a function of the position of (DD on theplate. Any rotation of 4 D produces a lateral shift ofthe speckle around P, thus of P' on the film. Thisresults in a blurring effect, the importance of whichis related to the tilt angle of the element cID. Forinstance, if the whole plate oscillates sinusoidallyabout an axis in its own plane without any deforma-tion [Fig. 10(a)], all the elements ciD rotate by thesame angle and all points such as P' are stretched bythe same quantity. In the spectral domain the in-tensity distribution of the recorded speckle is similarto that drawn in Fig. 7. On the other hand, if anydeformation occurs, the various elements rotate bydifferent angles varying from zero in the antinodalregions to a maximum in the nodal regions [Fig.10(b)]. As before, one ought to consider all the in-

Fig. 9. Geometry of the recording system. D is an element of thediffusing surface corresponding to the point P' image of point Psituated in the aerial speckle object plane, as the aperture size of

the imaging system is (.

dred hertz). The method consists in a mapping ofthe vibration on the surface, the essential data beingextracted from a photographic recording of the spec-kle pattern in a suitable spatial filtering operation.Then one measures the tilt angles of the diffusingelements situated in the close vicinity of the nodallines. An assessment of the maximum amplitudes isderived from the measurement.

Several authors4 ,6 ,10 -17 ,19 have exploited the spec-kle properties in vibration analysis. Basically threeways can be used in the recording of the pattern:(1) following Massey,6 one takes a picture of thenear-field speckle pattern due to the rough surfacecoherently illuminated; (2) Mottier4 puts a diffuserbetween the source and the object, and the picture isnow that of the speckle pattern due to the initial dif-fuser disturbed by the vibrating elements of theobject; (3) one may record the interferogram ob-served by superposition of the speckle pattern upona coherent background.' 0 In our experiments wehave employed Massey's technique as schematicallyrepresented in Fig. 8. The laser light scattered bythe vibrating plate in the direction of the cameraproduces a speckle pattern. The film is conjugate ofa plane O',q parallel with xOy and sufficiently closeto it as to keep the information about the shape ofthe object. The major role of the geometry of thesetting is shown in Fig. 9: since the two points Pand P' are conjugated by the imaging system-the

(a)

(0

A

I 2

Wb

Fig. 10. Influence of the deformation on the variation of the tiltangle: (a) oscillating plate, all the elements of the plate D rotateby the same angle ao; (b) vibrating plate, the angular displace-ment of the elements of the plate vary continuously from aMax in

the nodal regions N to 0 in the antinodal region A.

q INPUT PLANE

LI FOURIERIs PLANE

L2 OUTPUTV- _ TIlI PLANE

ANALYSIS OF TIME-AVERAGED PHOTOGRAPHS

BY OPTICAL FILTERING

Fig. 11. Schematic arrangement for analysis of time-averagedphotographs by spatial filtering (double-diffraction device). Thenarrow slit is placed in the Fourier plane of the first lens; thelocus of the elementary diffusing surfaces whose rotation axes areparallel with the direction of the slit w is displayed in the output

plane.

1690 APPLIED OPTICS / Vol. 12, No. 7 / July 1973

a.

b.

DIRECTIONSOF THE SLIT X \

Fig. 12. Results obtained by filtering process. The directions ofthe orientable slit are represented below each column. In (a)width of the slit is 1 mm, then 0.1 mm in (b); the pictures in (c)are obtained by replacing the slit by a rectangular aperture ofsmall size, oriented perpendicular to the studied direction atsome distance from the center of the diffraction pattern (see Fig.

13).

terference patterns due to the various elements Drotating by angles a varying continuously. Theperiodicity of the fringes also varies continuously andtheir visibility rapidly vanishes as soon as one de-parts from the center of the diffraction spectrum:merely the central fringes remain observable. Thesituation is then summarized as follows. In the dif-fraction spectrum each direction of an elementaryset of fringes is associated with one direction of thepossible rotation axes. Conversely the selection of aparticular direction in the diffraction plane permitsreaching a given set of diffusing elements 'FD, whichhave rotation axes parallel one with the other.Practically this also suggests the use of a spatial fil-ter in vibration mode analysis dealing with specklepattern, as will be seen in the next section.

B. Extraction of Information by Means of SpatialFiltering

The technique of isolating a given direction in theFourier spectrum of any complex amplitude distri-bution is well known among those working in optics.Since Abbe, it has been widely used, namely, associ-

ated with Schlieren methods, for example, in the vi-sualization of the tracks of ionizing particles in bub-ble chambers or in the determination of the main di-rections of stratifications in geophysics (rapid inves-tigations are often made by rotation of a so-calledbutterfly mask of small angles). The principle is re-called in Fig. 11. An orientable slit S is set in theFourier plane of the first lens L, of a double-diffrac-tion setting; the mask M located at the center of thespectrum is intended to remove the low frequencyterms, i.e., the background. A transparency of thespeckle taken as the plate was vibrating is placed inthe input plane of the system. The spatial filter(S,M) only transmits the information related to thediffusing elements that have been affected by a rota-tion about axes parallel with the direction w. Thesecond lens L2 performs a second Fourier transform,resulting in a filtered image of the transparency inthe output plane '-q'. Actually this image repre-sents the vibrating plate on which one observes,bright areas corresponding to elements (DD whoserotation axes are parallel with w. Such reconstruct-ed images as reported in Fig. 12 for three directionsof the slit concern the modes of the previous plate vi-brating at a frequency of 430 Hz. As expected, threedifferent configurations are observed. The three pic-tures at the top (a) have been obtained with a 1-mm-wide slit while we obtained those in the center(b) with a slit ten times thinner. Note that thebright areas are better defined. However, the spreadfunction of the slit is no longer negligible: it comesas spots elongated along a direction orthogonal tothat of the filtering slit. This situation is not favor-able and we thought it better to observe streaks par-allel with the rotation axes of the diffusing elements[Fig. 12(c)]. This is performed by replacing the ini-tial filtering slit by a small rectangular aperturewhose longer dimension is perpendicular to w (Fig.13). Finally, assuming that an annular aperture isequivalent to an infinite number of small rectangularapertures set perpendicular to the radii, a pupil inthe form of a ring used as a filter enables the visual-ization of every direction of rotation axis correspond-ing to any diffusing element simultaneously. This isalso related to what was said in the last part of Sec.IV.A. Figure 14 illustrates the use of a ring filter.It shows an antinodal region in the center with foursaddle points around. This is a pictorial descriptionof the vibration evincing remarkable points. Thedetermination of the tilt angles as explained in Sec.III completes the quantitative aspect of the method.

__WE

NARROW

SLIT

V(l)

RECTANGULAR

APERTURE

Fig. 13. Explanation in caption to Fig. 12.

July 1973 / Vol. 12, No. 7 / APPLIED OPTICS 1691

Fig. 14. Image obtained as the filtering aperture is a ring placedin the Fourier plane of the correlator: the directions of the rota-

tion axes of all elements (D are simultaneously observable.

V. Conclusion

Some prevailing points can be stressed: (1) thestatistical properties of the speckle pattern yield tothe direct visualization of the optical transfer func-tion of any given pupil: the intensity distribution inthe diffraction pattern of the speckle is proportionalto the autocorrelation function of the pupil contourlimiting the diffusing surface. Actual examples havebeen presented. (2) A further application was givenin the study of the rotation of diffusing pupils, thetilt angles being determined from double-exposurephotographic recording. Hence in the case of vibrat-ing mechanical structures the amplitude of the dis-placement is assessed by means of time-average re-cording. (3) Quantitative description of the vibra-tion modes can be achieved by spatial filters match-ing the deformation of the granular structures duringthe displacement of the diffusing elements. The ex-perimental conditions are not so severe as those de-manded in holography, the only requirement beingsome reliable filtering process.

The authors wish to thank F. M. Mottier for theencouragement and facilities provided to one of them(M.E.G.) throughout a one-month stay at his labo-ratory in the summer of 1971.

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tional Symposium on the Applications of Holography, Besan-gon 1970 (viii), J. Ch. Vienot et al., Eds.

3. S. Lowenthal, H. Arsenault; and D. Joyeux, in Proceedings ofthe International Symposium on the Applications of Hologra-phy, Besanson 1970 (2.2), J. Ch. Vienot et al., Eds.

4. B. Eliasson and F. M. Mottier, J. Opt. Soc. Am. 61, 559(1971).

5. A. Caron, "Pupilles synthbtiques en lumiere spatialement in-cohrente, correction des images au moyen de fonctions parti-culieres," These de 36me cycle, Besanqon (1971).

6. G. A. Massey, (Nat. Technical Information Service, Spring-field, Va. 22151 1968), Study of Vibration Measurement byLaser Methods, NASA Rept. 68-14070.

7. J. Ch. Vibnot, C. Froehly, J. Monneret, and J. Pasteur, in Pro-ceedings of the Symposium on the Engineering Uses of Holog-raphy, Glasgow 1968, E. R. Robertson et al., Eds. (CambridgeUniversity Press, 1970).

8. C. Froehly, J. Monneret, J. Pasteur, and J. Ch. Vienot, pre-sented at Symposium on Applications of Coherent Light,Florence, Sept. 1968, Optica Acta 16 (3), 343 (1969).

9. J. Monneret, These de Doctorat d'Etat (1973).10. E. Archbold, J. M. Burch, A. E. Ennos, and P. A. Taylor,

Nature 222, 263 (1969).11. J. N. Butters and J. A. Leendertz, Optics Laser Technol. 3,

26, (Feb. 1971).12. L. Ek and N. E. Molin, Opt. Commun. 2, 9 (1971).13. N. Fernelius and C. Tome, J. Appl. Phys. 2, 2252 (1970).14. J. A. Leendertz, J. Sci. Instrum. 3, 214 (1970) and in Proceed-

ings of the Conference ICO on Optical Instruments and Tech-niques, Reading 1969, J. M. Dickson, Ed. (Oriel Press, 1970),p. 256.

15. S. Debrus, M. Francon, and M. May, in Proceedings of theConference ICO on Optical Instruments and Techniques,Reading 1969. J. M. Dickson, Ed. (Oriel Press, 1970), p. 318.

16. E. Archbold and A. E. Ennos, Optica Acta 19, (4), 253 (1972).17. H. J. Tiziani, Optica Acta 18, 891 (1971).18. This phenomenon is observable if the scattered waves come

from the same rough surface and the autocorrelation degree isdifferent from zero. The visible fringes appear if the homolo-gous grains of each wave are partially superposed.

19. M. E. Guillaume, "Contribution a l'6tude d'une onde coh6-rente diffusee et a la determination optique des modes de vi-bration de yotbmo§ mocanique§," ThW d 36me cycl 1 Be-sanson 1972.

1692 APPLIED OPTICS / Vol. 12, No. 7 / July 1973