Ultrasonic elastic wave motion is often used to measure or characterize material properties. Through the years, many optical techniques have been developed for applications requiring noncontacting ultrasonic measurement. Most of these methods have similar sensitivities and are based on time domain processing using interferometry. Wide bandwidth is typically employed to obtain real- time surface motion under transient conditions. However, some applications, such as structural analysis, are well served by measurements in the frequency domain that record the randomly or continuously excited vibrational resonant spectrum. A significant signal-to-noise ratio improvement is achieved by the reduced bandwidth of the measurement at the expense of measurement speed compared to the time domain methods. Complications often arise due to diffuse surfaces producing speckle that introduces an arbitrary phase component onto the optical wavefront to be recorded. Methods that correct for this effect are actively being investigated today

Deason, V. A.

Ricks, K. L.

Schley, R. S.

Telschow, K. L.

UNT Digital Library

Proceedings of the Eighth International Symposium on Nondestructive Characterization of Materials, Boulder, CO, June 15-20, 1997 r- PHOTOREFRACTIVE LASER ULTRASOUND SPECTROSCOPY FOR 7 MATERIALS CHARACTERIZATION . x- 3 V\ - I '  * r 7 ' - - L  j ,  6 K.L. Telschow, V.A. Deason, K.L. Ricks and R. S. Schley, L _ l , ~  is ,. - d L' * ' F$,$,gyj 2 3 T $ g  O Q $ U  lp. =T Idaho National Engineering and Environmental Laboratory Idaho Falls, ID 834 15-2209 Lockheed Martin Idaho Technologies Company INTRODUCTION Ultrasonic elastic wave motion is often used to measure or characterize material properties. Through the years, many optical techniques have been developed for applications requiring noncontacting ultrasonic measurement. Most of these methods have similar sensitivities and are based on time domain processing using interferometry'. Wide bandwidth is typically employed to obtain real-time surface motion under transient conditions. However, some applications, such as structural analysis, are well served by measurements in the frequency domain that record the randomly or continuously excited vibrational resonant spectrum. A significant signal-to-noise ratio improvement is achieved by the reduced bandwidth of the measurement at the expense of measurement speed compared to the time domain methods. Complications often arise due to diffuse surfaces producing speckle that introduces an arbitrary phase component onto the optical wavefront to be recorded. Methods that correct for this effect are actively being investigated today. Adaptive interferometry, which utilizes the photorefractive effect in optically nonlinear materials, offers a potentially powerful method to automatically correct for environmental and speckle  effect^."^ Photorefractivity employs optical excitation and transport of charge carriers to produce a hologram of the interference pattern developed inside the material. A spatially and temporally modulated charge carrier distribution results that is a direct measure of the phase information impressed onto the optical object beam by the vibrating surface. This hologram stores phase information from all the surface points on the vibrating specimen simultaneously. The hologram developed then can be detected through diffraction of a readout beam off this photoinduced volume grating. Several optical frequency domain measurement methods of vibration have been proposed using photorefractive two-wave and four-wave mixing in select  material^.^*^^^ These have provided a response that is a nonlinear function of the specimen vibration displacement amplitude. R Vibrating Surface Detection Laser d Lock-in Amplifier I I Excitation (0s) (0 = ms*r> Photodetector Figure 1. Photorefractive detection of resonant vibration, BS (beamsplitter), EOM (electro-optic modulator), (PRC) photorefractive crystal. Recently, a method was developed for vibration detection7” that employs the photorefractive effect in an optical lock-in synchronous detection manner.’ This method phase modulates the object and reference beams such that a moving photorefractive grating at a fixed beat frequency is established within the material regardless of the specimen vibration frequency. The intensity of a readout beam scattering off the photoinduced grating is a direct measure of the vibrational amplitude and phase. It can be used for spectral analysis with a response proportional to the Bessel function of order one, providing a linear output for small amplitudes. The method accommodates rough surfaces and exhibits a flat frequency response above the photorefractive cutoff frequency. A minimum detectable displacement of 2 x nm has been recorded; however, the limitation was from optical phase noise, not shot noise, suggesting that further improvement is possible. The corresponding demonstrated detectability was 4.5 x nm (W/Hz)”* , in terms of the light power received at the photodiode. In this paper, the ability of the optical lock-in process to provide absolute calibration of measured displacement amplitude is described and application of the method to full-field imaging of vibrating square plates is presented. Typically, the nonphotorefractive interferometric methods do not allow imaging of more than one surface point at a time. However, since the photorefractive process records a volume hologram of all vibrating surface points simultaneously, imaging can be achieved. Both four-wave and two-wave mixing configurations have been employed for reading out the vibration-induced phase grating image. Results are presented for vibration modes of a free square stainless steel plate with diffusely reflecting surfaces that is driven piezoelectrically at one corner. PHOTOREFRACTIVE OPTICAL LOCK-IN METHOD Figure 1 shows the experimental setup for optical detection of a specimen undergoing continuous vibration. A diode-pumped Nd:YAG laser source (532 nm, 200 mW) is split into object and reference beams. The excited vibrational modes of the specimen determine the frequency-dependent displacement amplitude of the surface, which 2 , DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employm, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or use- fulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any spe- cific commercial product, process, or senice by trade name, trademark, manufac- turer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. Frequency (kHz) Figure 2. Photodetector DC and AC voltages from the vibration spectrum of two modes of a square stainless steel plate. is transferred into phase modulation of the object beam. The reference beam is frequency modulated by an electro-optic modulator at a fixed modulation depth. The modulated beams are then combined and interfered inside a Bismuth Silicon Oxide (BSO) photorefractive crystal. A four-wave mixing configuration is used for readout of the photorefractive index grating for the single-point measurements. The reference beam is reflected back into the crystal along a counter-propagating path that matches the Bragg angle of the photorefractive grating in the medium. The resulting scattered wave is then sampled at the plate beamsplitter and deflected toward the photodetector. Subsequently, the photodetector signal is processed with conventional electrical lock-in methods to provide a measurement bandwidth of 1 Hz. A recorded spectrum showing three spearate modes of a 1.5 inch square, 0.015 inch thick, stainless steel 304 plate is shown in figure 2; the plate is driven piezoelectrically at one corner. A model of the lock-in process has been developed using one-dimensional plane wave coupled mode analysis. Both optical beams reaching the photorefractive crystal experience phase modulation due to the path lengths. In addition, the signal beam is modulated by the 4x6 vibrating surface according to Q, = Q, sin(w t + p >, Q, = 2. The reference beam is s so s s  so iz phase modulated by the EOM according to <p = or0 sin(w t + q . The interference distribution and subsequent charge migration within the crystal generates a corresponding space charge electric field distribution, E controlled by the charge carrier mobility and trapping that produces, in the diffusive operation regime, a single relaxation time response given by r r r . The dynamic behavior of this field is sc 3 1 1 1 I I 50 1 00 150 200 250 300 -0.2 0 Displacement (nm) at 2.4 kHz Figure 3. Measured DC and AC photodetector voltages for a square plate resonance as a function vibration amplitude. of the where z is the material response time, is the interference fringe contrast, and E is 4 the maximum achievable space-charge field, controlled by the concentration of available charge trapping sites and the fringe spacing. In the above configuration, the photorefractive crystal acts as a mixing and low-pass filtering element, providing the benefits of lock-in detection. Therefore, the space charge field responds to slowly varying phase modulations occurring within the material response time, allowing only the terms around the difference frequency R = w - w s r  refractive index through the linear electro-optic effect. This effect creates a diffraction grating within the crystal that contains the low frequency phase information desired. Several methods can be used to read out the space charge field and diffraction grating, including four-wave mixing, two-wave mixing with polarization selection, and electrical measurement through conduction of photoexcited carriers. In the four-wave mixing arrangement, the reference beam that passes through the crystal is reflected back and diffracts into the signal beam direction, see figure 1. The magnitude of the index of refraction grating produced is proportional to the space charge field and the orientation-dependent electro-optic coefficient in BSO. The diffracted beam intensity is a direct measure of the grating established and produces DC and AC output photodetector voltages given by N('y ') IO to be important. The space-charge field modulates the local 'DC (@ SO 1 'DCO - 'DC (@ SO =0) = C J i F r o )  'DCO 4 . . -, W0 (0) A so I /  -- (a) I-. .. , Figure 4. Vibrational mode images of a free square plate at (a) 1.5 kHz, (b) 2.4 kHz where tan( tp) = Q z  . Since the reference modulation and the photorefractive time constant are known, measurement of the DC and AC voltage magnitudes provides a direct calibration of the vibration amplitude in terms of the known optical wavelength through (4) where B ( Q , ~ ~ , Q z )  is the controllable parameter given by the bracketed term in eq. 3. 'The measured vibration amplitude dependence support this result as shown in figure 3, which shows results from a single mode with Q = 1.1 and Qz = 1. In this figure, the vibration amplitude was determined by the best fit of the data to eq. 3 at small drive amplitudes. The overall consistency of the results supports the model and the calibration procedure. rO VIBRATION IMAGING A two-wave approach, based on polarization rotation through anisotropic self- diffraction,"'*" was used for imaging as it offers improved light throughput from diffusely reflecting surfaces compared to the four-wave method. Figure 4 shows images of two modes of a free square stainless steel plate excited by a contact piezoelectric transducer at one corner. The nodal lines are clearly defined, and the relative phases of the vibration displacements are indicated by the light and dark areas. The entire modal pattern can be made to switch from light to dark by varying the offset frequency,apn (in this case, equal to 2 Hz) between the object and reference excitations. This provides a powerful tool for visual mode searching and suggests processing methods that can be employed to enhance the detectability of specific modes. The minimum detectable displacement in the imaging mode (-1 nm) is much larger than for the point detection method as no post electronic lock- in processing was performed for the data of figure 4. 5 CONCLUSIONS A photorefractive optical lock-in vibration spectral measurement method has been described that provides a simple method for quantitative determination of the vibration amplitude. The method uses optical synchronous or lock-in detection which can also include conventional electrical lock-in detection for narrow bandwidth high sensitivity measurements. A minimum detectable displacement of 2 x using the single-point vibration detection method with a I Hz bandwidth. Readout methods employing four-wave or two-wave mixing produce an output intensity directly proportional to the amplitude of the vibration being measured, for amplitudes small compared with the optical wavelength, and provide the capability for mechanical phase measurement if synchronous excitation is used. Vibration imaging was shown from a diffusely scattering surface showing detectable displacements in the 1-45 nanometer range. The method is capable of flat frequency response over a wide range above the cutoff of the photorefractive effect and is applicable to rough surfaces. nm has been demonstrated ACKNOWLEDGMENTS This work was supported through the INEEL Laboratory Directed Research & Development program under DOE Idaho Operations Office Contract DE-AC07- 94lD 13223. REFERENCES I J. W. Wagner, "Optical Detection of Ultrasound," Physical Acoustics, Vol.XIX, Eds. Thurston, R.N., and Pierce, A.D., (Academic Press, New York, 1990) Chp. 5. P. Yeh, Introduction to Photorefractive Nonlinear Optics, (John Wiley, New York, 1993). S. I. Stepanov, International Trends inOptics, (Academic Press, New York, 1991) Chp. 9 J. P. Huignard and A. Marrakchi, "Two-wave mixing and energy transfer in Bi12SiOzo crystals: application to image amplification and vibration analysis," Opt. Lett., 6, (12), 622 (1981). H. R. Hofmeister and A. Yariv, "Vibration detection using dynamic photorefractive gratings in KTN/KLTN crystals," Appl. Phys. Lett., 61 (20), 2395 (1992). H. Rohleder, P. M. Petersen and A. Marrakchi, "Quantitative measurement of the vibrational amplitude and phase in photorefractive time-average interferometry: A comparison with electronic speckle pattern interferometry," J. Appl. Phys., 76 ( l ) ,  81 (1994). T.C. Hale and K. Telschow, "Optical lock-in vibration detection using photorefractive frequency domain processing," Appl. Phys. Lett. 69,2632 (1996). T.C. Hale and K.L. Telschow, "Vibration modal analysis using all-optical photorefractive processing," Proc. SPIE Vol. 2849 , Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications 11, Francis T. Yu; Shizhuo Yin; Eds., p. 300 (1996). J. Khoury, V. Ryan, C. Woods and M. Cronin-Golomb, "Photorefractive optical lock-in detector," Opt. Lett., 16, 1442 (1991). R.C. Troth and J.C. Dainty, "Holographic interferometry using anisotropic self-diffraction in Bi12Si020r" Opt. Lett., 16 ( l ) ,  53 (1991). T.C. Hale, K.L. Telschow and V.A. Deason, "Photorefractive optical lock-in vibration spectral measurement," submitted for publication to Applied Optics. 6 ’ubl. Date (11) m 9 7  /o Sponsor Code (18) 00 E J C Category (1 9) t DOE 

Photorefractive Laser Ultrasound Spectroscopy for Materials Characterization

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Photorefractive Laser Ultrasound Spectroscopy for Materials Characterization

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