Optical Detection of the Elastic and Anelastic Properties of Heterogeneous Materials

Abstract

The propagation of elastic waves through a material is used to interrogate media in a variety of research and industrial applications. In the time domain the elastic moduli can be estimated from the propagation speeds of primary waves (also called compressional waves, or P-waves), secondary waves (shear, or S-waves), and surface waves. For an isotropic medium, two elastic constants and the density uniquely define elastic wave propagation. Furthermore, heterogeneity in the material results in scattering, and internal friction causes attenuation of the elastic waves. Such heterogeneities range from fractures in composites and rocks, to vessels and fats in tissue. Traditionally, elastic waves are generated and detected using mechanically coupled piezoelectric transducers (PZTs). PZTs are relatively inexpensive with a high dynamic range. At the same time, PZTs have a relatively large footprint, are difficult to couple to the sample consistently and automatically, and are prone to mechanical ringing. These concerns can be overcome with all-optical, non-contacting systems. This thesis reports on optical alternatives to PZTs. The theory and hardware for novel contacting and non-contacting optical devices to determine the elastic properties of many materials are presented. Further, we apply our techniques to areas of interest to New Zealand primary industries, estimating the elastic properties of apples and timber used for construction. Laser Doppler Vibrometers (LDVs) are heterodyne interferometers which detect surface particle velocity via the Doppler shift of an incident laser beam. We present a home built, robust and relatively inexpensive detector, which consists of a heterodyne interferometer and phase locked loop frequency demodulator, as an open-source alternative. We illustrate the broadband capabilities with the detection of ultrasonic waves in a mudstone sample, and low-frequency (100Hz) vibrations of a piston. These results are compared to a Polytec OFV-505 sensor head coupled with the VD-09, 50 mm/s/V velocity decoder, and a correlation of 0.97 was found between the two devices. The home built detector was found to have a higher noise floor at elastic wave frequencies greater than 1.5 MHz, which is the highest rated frequency of the VD-09, 50 mm/s/V velocity decoder. We also adapt the LDV to be capable of detecting the sum of the surface particle motion at two locations in a single channel. The Green’s function, or impulse response, can be estimated from the autocorrelation of this signal; the result containing some predicted artefacts. Typically the cross-correlation of independent, equipartioned wavefields is used to estimate the elastic Green’s function, commonly termed seismic interferometry. The underlying theory and hardware required to estimate the Green’s function from the auto-correlation of the sum of two wavefields is presented and compared to traditional seismic interferometry. This technique is used to estimate the elastic Green’s function between two locations on an aluminium block with surface scatterers. The Green’s function estimate is dominated by artefacts near t = 0, however we find that these can largely be ignored as the spacing between the receivers is much larger than the Rayleigh wavelength. This method could be an effective, low cost and non-contacting technique for structural monitoring, particularly where ambient noise has established equipartitioned wavefields in the structure. Additionally, we use short duration pulses of light to excite broadband waves in an apple, via the photoacoustic effect, for the first time, and detect these waves using an LDV. The firmness of an apple is a commonly used indicator of quality and maturity during sorting and cold storage. Because the resonant modes of an apple are dependant on the elastic properties, vibration tests are favoured over other – often destructive – tests. Laser-generated and laser-detected elastic waves are used to infer the elastic moduli and attenuation of elastic waves in an apple. Furthermore, we repeat our measurements periodically for 15 days to monitor changes in the apple at room conditions. Although the elastic and anelastic properties all decay with age, we find that attenuation of the Rayleigh wave decreased by 75%, which is greater than both the Firmness Index (30%) and Elastic modulus (19%). Next, we excite elastic waves in samples of New Zealand Radiata pine. Wood is an orthotropic material which shows a dramatic difference in elastic moduli relative to grain growth and ring layers. Monitoring the elastic properties of wood has been conducted using contacting transducers, and grain orientation has been determined using light. We use short duration laser pulses to excite elastic waves in the wood samples and detect these waves using an LDV. The elastic moduli perpendicular to the grain growth are determined using the wavespeeds of P- and Rayleigh waves. We find that on average high grade SG12 wood has an elastic modulus perpendicular to the grain 2.7 times greater than lower grade SG6 wood. Furthermore, we translate the samples to observe lateral variations in the wood structure, such as knots. Many materials, such as sedimentary rocks, exhibit a large frequency and strain amplitude dependence of their elastic moduli. To determine the elastic properties at low frequencies we develop a high sensitivity strain meter using a distributed feedback fibre laser. All-fibre lasers offer several advantages over resistive strain meters; they are robust, immune to electrical noise, can be multiplexed and are highly sensitive. The frequency of the light emitted by the fibre laser is down-shifted using a heterodyne interferometer. A low-pass filter and power meter demodulate the interferometer signal to produce a voltage dependent on the strain. We present some preliminary results by attaching our optical strain sensor to a Tuff sample from White Island. Strain is measured at amplitudes on the order of 0.1 µε, which is similar to seismic events, and a change in resonance is observed with increased water saturation.