<title>Vibration modal analysis using all-optical photorefractive processing</title>

Abstract

A new experimental method for vibration modal analysis based on all-optical photorefractive processing is presented. The method utilizes an optical lock-in approach to measure phase variations in light scattered from optically rough, continuously vibrating surfaces. In this four-wave mixing technique, alloptical processing refers to mixing the object beam containing the frequency modulation due to vibration with a single frequency modulated pump beam in the photorefractive medium that processes the modulated signals. This allows for simple detection of the conjugate wavefront image at a CCD. The conjugate intensity is shown to be a function of the first-order ordinary BesseI function and linearly dependent on the vibration displacement induced phase 6, for 6 = 4n@. cc 1 where 5 is the vibration displacement and h is the source wavelength. Furthermore, the results demonstrate the unique capabilities of the optical lock-in vibration detection technique to measure vibration signals with very narrow bandwidth (< 1 Hz) and high displacement sensitivity (sub-Angstrom). This narrow bandwidth detection can be achieved over a wide frequency range from the photorefractive response limit to the reciprocal of the photoinduced carrier recombination time. The technique is applied to determine the modal characteristics of a rigidly clamped circular disc from 10 kHz to 100 W z . INTRODUCTIONMany optical techniques for vibration detection used in applications such as laser ultrasonics are based on time domain processing using homodyne or heterodyne interferometry. 1 Vibration displacement amplitudes are recorded through interference at the photodetector and subsequent signal processing. * Wide bandwidth is typically employed to obtain real-time surface motion under transient conditions.Some applications, such as structural analysis, are better served by measurements in the frequency domain that record the randomly or continuously excited vibrational spectrum. A significant signal to noise ratio improvement is gained by the reduced bandwidth of the measurement compared to the time domain methods, but at the expense of additional processing and complexity. A shortcoming of optical approaches has been the sensitivity to speckle reflections from the specimen surface. This can be corrected by limiting detection to a single speckle or by use of self-beating interferometers, such as the Fabry-Perot. A potentially more powerful method is to utilize the photorefractive effect in optically nonlinear materials. This method provides an active mechanism for compensation using the spatial and temporal characteristics of photorefractivity.Several all-optical photorefractive processing measurement methods of vibration in the frequency domain have been proposed using photorefractive two and four wave mixing in select material~.3-~ Most provide a response that is a nonlinear function of the specimen vibration displacement amplitude and do not provide a measure of the vibration phase. We present an extension of those earlier methods that u...