w.— —-—Jw—.-—w -— AN AC Pi'iD'FOMULWPLEER FQR MEASUMNG THE ENTfiNSITY N THE FRESNEL {ENE} FRAISNHOFE’R ‘LEGWNS {I}? UGHT DIFFMC'S'ED BY ULTRASONKQ WAVES Thesis for 1419 flag?” of M. S. MECHifiAN STAW UNS‘v’E‘FiSfi'Y Arthur jarred Cranfiafi' i964 J'HESIS WWI 11111111111111?!“le WI 1 ('2‘ 3 129301704 0019 .— LIBRARY Michigan Scan University PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE 1/” Mafia“ ABSTRACT AN AC PHOTOMULTIPLIER FOR.MEASURING THE INTENSITY IN THE FRESNEL AND FRAUNHOFER REGIONS OF LIGHT DIFFRACTED BY ULTRASONIC WAVES by Arthur Jared Crandall An ac photomultiplier is described which is used to measure the time dependent light modulation caused by a continuous progressive ultrasonic wave of varying beam width. The width of the beam is varied to change the relative amount of amplitude modulation produced by the ultrasonic grating. The ac photomultiplier is also used to measure Fraunhofer diffraction patterns produced by a pulsed progressive ultrasonic wave in a glass block. The photomultiplier has good dc stability, good transient reSponse, 15 Mc frequency response and high sensitivity. AN AC PHOTOMULTIPLIER FOR.MEASURING THE INTENSITY IN THE FRESNEL AND FRAUNHOFER REGIONS OF LIGHT DIFFRACTED BY ULTRASONIC WAVES BY Arthur Jared Crandall A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Physics and Astronomy 196k ACKNOWLEDGEMENTS The author wishes to thank Dr. E. A. Hiedemann for his guidance without which this work could not have been attempted. Dr. B. D. Cook gave valuable suggestions for the construction of the ac photomultiplier. Dr. W. G. Mayer and Mr. W. R. Klein have given freely of their time for helpful discussions. A. J. C. ii I. II. III. IV. VI. TABLE OF CONTENTS Introduction . . . . . . . . . . . Theory . . . . . . . . . . . . . . Measurements in the Fresnel Field Pulse Measurements . . . . . . . . Resume . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . iii Page 17 23 25 10. LIST OF FIGURES Coordinate System - Diffraction Theory . . . Coordinate System - Interference Patterns . Photomultiplier Circuit . . . . . . . . . . Visibility Measurement Circuit . . . . . . . Optical Arrangements 0 o o 0'. o o o o c o o Visibility Patterns for a Sound Intensity v:3.15 Visibility Patterns for a Sound Intensity Vsn/Z Visibility Patterns at the Sound Beam . . . Circuit for Pulse Optical Measurements . . . . . Zero and First Orders for p polarization lightinEDFIGIaSSo00000000oooo Oscilloscope Traces from Pulse Optical MeasurementSoooooo000000.00 iv Page 10 10 11 1h 16 20 21 22 I. INTRODUCTION 1 Lucas and Biquard and Debye and Searsz observed in 1932 that light transmitted through ultrasonic waves in a transparent medium produces interference phenomena very similar to those produced by 3 an optical grating. Hiedemann and his co-workers have shown that the "grating" produced by ultrasonic waves can be directly observed. Bachem used a stroboscope to study the ”grating" produced by pro- 5 gressive ultrasonic waves. Debye, Sack and Coulon and Bar demon- strated that the "image" of the grating is produced by the interference 7 between the diffraction orders. Hiedemann and Schreuer pointed out that "images of gratings" can always be observed in the Fresnel zone of the grating. Using optical gratings, they demonstrated that the aspect of the interference patterns depends on the plane in which the patterns are observed and that true grating images can only be observed in discrete planes as predicted by Rayleigh8. The inter- ference or visibility pattern produced by stationary ultrasonic 9 waves was extensively studied by Nomoto , who measured the light intensity distribution in the Fresnel zone. Pisharotylo, Nath11 and recently Cook12 developed theories to describe the Fresnel in- terference of a sinusoidal phase grating, an arbitrary periodic phase grating and an arbitrary periodic grating, respectively. They used the method of superposition of waves which avoids the use of the complicated Fresnel-Kirchhoff integral. For many years quantitative measurements of the Fresnel inter- ference of light produced by ultrasonic waves were limited to the case of stationary waves. Colbert and Zankel13 were the first to make such measurements in the case of progressive ultrasonic wave by using an ac photomultiplier. Later Aronl,+ used an ultrasonic stroboscope and a dc photomultiplier. Aron's results agree very well with those obtained by Colbert and Zankel. The ac photomultiplier described here was developed not only for the purpose of verifying the results of Colbert and Zankel, and Aron, but also for the study of light diffraction by progressive ultrasonic waves in transParent solids. In solids most measurements of light diffraction by ultra- sonic waves were made using standing waves because of the difficulty in obtaining progressive waves in a solid. Two notable exceptions 15 are the measurements by Protzman and by Mayer and Hiedemann1 carried out in Plexiglas. A progressive wave was obtained by using a long sample of Plexiglas which has very high acoustic attenuation. In the case of an ultrasonic pulse, when the length of the pulse is small in comparison with the length of the medium, the pulse acts as a progressive wave except near reflecting surfaces. Thus light diffraction by progressive ultrasonic waves in solids can be studied by examining the instantaneous diffraction pattern produced when the sound pulse crosses the light beam. An ac photomultiplier is placed on the particular Fraunhofer diffraction order to be 'measured and its output displayed on an oscilloscope. Sound inten- sity measurements may thus be made at any point in a transparent solid except near a reflecting boundary. The purpose of this investigation is to determine the usefulness of ac photomultiplier techniques for some experimental problems. Two examples are described: Measurement of the light intensity in the Fresnel zone of an ultrasonic "grating". (Part III) Measurements of the Fraunhofer diffraction patterns produced by a pulsed ultrasonic wave in a glass block. (Part IV) II. THEORY A.sound beam consists of periodic condensations and rarefac- tions of the medium which in turn produce a periodic variation in the refractive index. If a light beam is passed through this "sound grating" in general both phase and amplitude modulation of the light beam occur. If the resulting Fraunhofer diffraction spectrum is observed, the light is found to travel in directions described by sin 6n = :35 II where n is an integer and A and X* the wavelengths of the light and ultrasound, respectively. This is the usual grating equation where the grating spacing is replaced by the ultrasonic wavelength. The central problem in light diffraction theory is to deter- ‘mine the amplitudes of the light in the various orders. In the case of Fresnel interference, one is then concerned with the way in which the light traveling in these different directions interferes to pro- duce the Fresnel pattern. Cbnsider the interaction of a monochromatic plane light wave and a sinusoidal, progressive, plane sound wave (Fig. 1). Let the light travel in the z direction and the sound in the x direction. Hllllll itllllll" “ Coordinate system 4. Z Diffraction Theory b, * * Let k and w and k and a be the wave numbers and the circular frequencies of the light and ultrasound, respectively. The index of refraction of the medium can be expressed as 'X' * u(x,t) = no + usin(k x - an t) where no is the index of refraction of the undisturbed medium and p is the maximum variation of u(x,t). The time dependence of this wave will be neglected because the sound beam appears stationary with respect to the time for light to travel the distance L through the sound beam. Then the wave equation can be written in the form 2 var - (mo/eff; - o (1) Since‘W is independent of y, 3-21 3312. u: + zuou sin(k*x- ”*t) 3—21 3x2 + )zz - ficz 31:2 I O (2) where the term in p2 is neglected because of the smallness of u(v010-5po). The light amplitude‘W(x,z,t) can be expanded in a fourier series in x and t. ikpoz in(k*x - “ix-t) Vl(x, z,t) = e1“ tchn(z)e e (3) By substituting eq. (3) into eq. (2), comparing coefficients , * * of eln(k x- eo’t) and neglecting second order terms in smallness one obtains the difference differential equation: ckp 2 .41 L _ -_n__<1

. SYNC FROM PICKUP COIL WIDEBAND AMPLIFIERS K 1 MULTIPLIER J PHOTO- ,.._.§ 300 A FICA». VISIBILITY MEASUREMENT CIRCUIT 10 .25. Pzw2u024¢m< Ado-hao 0.9.... ”Om—Dom ll 12 A standard Optical arrangement shown in Fig. 5 was used. An Osram.HBO 100 W/Z high pressure percury arc (dc) and a GE H 100 Ah mercury are (ac) were used as light sources S. The Osram HBO 100 W/Z lamp has a very high pressure, concentrated are which tends to be unstable in most of the lamps tried. The are rotates around the electrodes changing the amount of light passing through the source slit S The GE H 100 Ah lamp has a moderately low pressure discharge cohtained in a large envelope. This dis- charge is very steady and is found to have less random fluctuation in intensity than the Osram lamp. A green filter F selects the mercury 5h60 A line. The source slit and the collimating lens Lc control the angular spread in the light beam. With a short focal length lens and wide slit the angular Spread will be large. This spread must be a small fraction of a sound wavelength at the photomultiplier location or the visibility pattern will be smeared out. This effect becomes more pronounced as the photomultiplier is moved away from the sound beam. The source slit should be narrowed and a collimating lens of sufficient focal length selected consistent with adequate illumina- tion. The tank contains water and has a castor oil termination to insure progressive waves. The sound beam intensity may not be uniform in Space. In order to obtain visibility patterns of constant “v" a schlieren system was used to observe the homogeneity of the sound beam. Then an aperture A about 2 cm in height selected the most homogeneous part of the sound beam. Two air backed quartz transducers were used. The quartz plates were 5.08 cm in diameter with electrodes made of silver print. Variation of the width of the electrode allowed the width of the sound beam to be changed. The transducer used for the visibility patterns was driven on its fundamental frequency, 1.7h-Mc. In order to increase the parameter q a second transducer was used. It had a nominal fundamental frequency of 1 Mc and was used on its third harmonic at 3.05'Mc. 13 A Variac was used to vary the rf voltage applied to the trans- ducer. The Variac allowed voltage changes in small but discreet steps only. The accuracy in setting the voltage to a predetermined value was thus limited to at most‘: 1.5% of the maximum possible value. Values of v were obtained either from diffraction measurements or from comparison of the observed visibility patterns with theoreti- cal predictions. A comparison showed the results of the two methods to be equivalent within experimental error. Typical visibility patterns are shown on the following pages. One can see the increase in complexity of the patterns as v is in- creased from n/Z to I. These values were used for comparison with the results of Colbert and Zanke113. The theoretical calculation for v=3.15 is shown for comparison. The curves agree remarkably well. Some asymmetries were observed. In these cases it was often traced to the tendency for the electronic circuits to ring. UIN UIN f’ a,” _ UIN UIN I I I UIN UOIH m Fig. 6a Visibility Patterns for a sound intensity V= 3315. Experimental oscilloscope traces and theoretical curves. AAA); UIN ’ UIN UIN UIN UIN UIN UIN UIN MN wlw ' m 15 Fig. 6b Visibility Patterns for a sound intensity V=3I/20 Fig. 7 Visibility patterns at the sound beam. a) b) d) d) a) Pattern a repetition distance D from the exit plane for V = 204 and Q = 0045. Same conditions as in (a) but with the photomultiplier'moved -slightly to observe minimum amplitude modulation. Theoretical pattern at exit plane for v = 3 and Q = 0.57. Theoretical pattern for minimum amplitude modulation at z :'§.L. . The amplitude is three times its“ normalized value to show detail. Patterns for Q 2 0.15 at a distance D/2 trom.the center of the transducer (v: 10), and minimum.amplitude positions for v : 10,8,6,4,and 2 in that order. IV. PULSE MEASUREMENTS A. Optical Arrangement The Optical system is the same as that used in the visibility measurements (Fig. 3) with the addition of lens Lf and a polarizer located just in front of the photomultiplier slit. Sound waves produce birefringence in the case of an isotrOpic transparent solid. (However, the Raman-Nath theory can still be applied if one uses plane polarized light whose direction of polarization is either parallel to or normal to the direction of sound propagation. The ac light source was used because of its superior stability. The source slit is adjusted so that the width of its image at the photomultiplier slit is approximately 1/3 the Spacing between ad- jacent diffraction orders. The photomultiplier slit is adjusted to be the same width as the source slit image. This arrangement allows maximum light transmission with a minimum of stray light. B. The Ultrasonic Beam For a continuous wave the homogeneity of the sound beam may be readily examined with a schlieren technique. Since the pulse duty cycle in this experiment is approximately 10-3, one cannot observe a schlieren picture. One could try to use a time-exposure photograph but this would give an average of all the transits of the sound pulse before decaying. By reducing the dimensions of the aperture and using differ- ent portions of the sound beam to produce a diffraction pattern one can obtain a good estimate of the homogeniety of the sound field. If the diffraction pattern remains constant in the region investigated for a fixed transducer voltage, this region is probably homogeneous. After finding the most homogeneous part of the sound beam near the transducer the dimensions of the aperture were increased in order to allow adequate light to pass and still select a reason- ably homogeneous portion of the sound field. The resultant aper- ture dimensions were about 2mm x hmm. In this experiment the medium was a l"xl"x8" glass Block of type EDF-l. The transducer was mounted so that the light traveled ’parallel to its l".dimension. 17 18 C. The Photomultiplier Circuits For pulse-optical measurements, that is measurements of the light diffraction pattern of a pulsed ultrasonic wave, the photo- multiplier requirements of sensitivity and frequency response still hold. Dc stability was an additional requirement. When pulse optical measurements are made in solids, the sound pulse must be Short compared to the pulse travel time in the solid. For a 3cm cube of glass the transit time iS 6 usec. So that the sound pulse should be on the order of 1 “sec long, a photo- multiplier risetime of 0.3 psec is necessary. The pulsed oscilla- tor used here had a risetime of 0.5 fisec. Therefore a much longer sample had to be used. This also allowed longer pulses of 3 -10 usec which was much longer than any photomultiplier risetime. The basic photomultiplier circuit is shown in Fig. 3. In making measurements of zero order light intensity all of the light is in the central order except for that brief portion of the time, when the sound pulse crosses the light beam. Conversely in measurements of the higher diffraction orders the photomultiplier receives light only when the sound pulse crosses the light beam. The differences in the average current in the photomultiplier circuit associated with these different average light intensities produce unequal sensitivities of the system unless the dc voltage between the last dynode and the anode is well regulated. In addition the 0.05 uf capacitors C stabilize the voltages on the dynodes where the dynode current becomes appreciable. The 931 photomultiplier tube was used in Spite of its re- duced sensitivity since its maximum anode current may be greater than the maximum anode current for the 1P21. This allowed a smaller value of the shunt resistor RL for the same voltage to the oscilloscope. The value of RL is practically dictated by the gain of the oscilloscope. The rise time and sensitivity of the photomultiplier circuit decrease with decreasing values of the load resistance. In order to obtain as fast a rise time as possible at a given sensitivity the gain of the oscilloscope was set at the maximum and the value of the load resistance was 19 set to give full scale deflection of the oscilloscope for full light intensity. The phase shifter (R.L.C. circuit) shown in Fig. 8 is used to trigger the General Radio lZl-A unit pulser at the moment when the source light intensity is maximum. The unit pulser triggers the Tektronix 515A oscilloscope and the Arenberg PG 650 pulsed oscillator every 1/60 sec. This pulse repetition rate allows ample time for the sound pulse to decay. The unit pulser also produces a variable length 1-50 psec square negative pulse which modulates the pulsed oscillator. An impedance matching circuit connects the output of the pulsed oscillator to the l"xl/2" barium titanate 5 Mo transducer which is attached to the end of the glass block. Lens Lf focuses the various diffraction orders on the plane of the photomultiplier Slit. The light pulses are detected by the photomultiplier and displayed on the oscilloscope. Inserting a small capacitor across the output terminals of the photomultiplier reduced the high frequency fluctuations caused by the source (Fig. lOabc). The capacitor and load resistor RL were of such a size that the rise time in- crease was only slightly perceptible in the oscilloscope trace. The rf pulse to the transducer is displayed through the second input. D. Results Typical measurements of the zeroth and first diffraction orders appear on the following page (Fig. 9). Higher orders were also measured but are not included. All of the measurements indicate that the Raman-Nath theory is applicable under the ex- perimental conditions used. No significant asymmetries were observed in the diffraction Spectrum. . moaho> m2... 0». mpzm2mmam