Ultrasonic vibration modal analysis of ICF targets using a photorefractive optical lock-in

Abstract

A photorefractive optical lock-in is discussed in relation to ultrasonic vibration modal analysis of inertial confinement fusion (ICF) targets. In this preliminary report, the method is used to analyze specimens with similar response characteristics to ICF targets with emphasis on both the displacement and frequency resolution of the technique. The experimental method, based on photorefractive frequency domain processing, utilizes a synchronous detection approach to measure phase variations in light scattered from optically rough, continuously vibrating surfaces with very high, linear sensitivity. In this photorefractive four-wave mixing technique, a small, point image of the object surface is made to interfere with a uniform, frequency modulated reference beam inside a Bismith Silicon Oxide crystal. Optical interference and the photorefractive effect of electronic charge redistribution leads to the formation of a refractive index grating in the medium that responds to the modulated beams at a frequency equal to the difference between the signal and reference frequencies. By retro-reflecting the reference beam back into the crystal, a diffracted beam, counter-propagating with respect to the original transmitted beam, is generated. Using a beamsplitter, the counter-propagating beam can be picked-off and deflected toward a photodetector. The intensity of this diffracted beam is shown to be a function of the first-order ordinary Bissel function, and therefore linearly dependent on the vibration displacement induced phase modulation depth (delta) , for small (delta) ((delta) < 4 (pi) (xi) /(lambda) < < 1) where (xi) is the vibration displacement and (lambda) is the source wavelength; analytical description and experimental verification of this linear response are given. The technique is applied to determine the modal characteristics of a rigidly clamped disc from 10 kHz to 100 kHz, a frequency range similar to that used to characterize ICF targets. The results demonstrate the unique capabilities of the photorefractive optical lock-in to detect and to measure vibration signals with very narrow bandwidth and high displacement sensitivity. This level of displacement sensitivity is particularly important in detecting changes in vibrational mode shapes and frequencies that might be associated with asymmetries in ICF targets.