# Imaging Microstructure on Optically Rough Surfaces Using Spatially Resolved Acoustic Spectroscopy
## 2 Materials and Methods
### SRAS Instrumentation for Optically Rough Surfaces  
SRAS uses two lasers for the non-contact generation and detection of acoustic waves; the basic optical diagram of an SRAS instrument is given in Figure 2a. Considering first the generation arm of the system, a pulsed near infrared laser (NIR) illuminates an amplitude grating of period \(M\lambda_{g}\) (1:1 mark space ratio). This is then re-imaged onto the sample surface with magnification of M, as determined by the ratio of the two lenses used, producing an image of the grating on the sample surface with a period \(\lambda_{g}\). Through thermo-elastic absorption of the pulsed laser energy, acoustic waves are generated in the specimen. A schematic of the image formed on the sample surface is shown in Figure 2b, where the distance between the fringes of light correspond to the wavelength of the generated SAW, \(\lambda_{g}\). Therefore, the SAW velocity for a given point can then be found by \(v_{SAW}=f\lambda_{g}\)  
Figure 1: (**a**) Diagrams illustrating how light reflects off a smooth surface where the _form_ is such that it appears locally flat to the detection (left), a _wavy_ surface (middle), and a _rough_ surface (right). (**b**) diagram showing the centred beam returned to the detector from the smooth surface reflection, and a photographs of a green laser reflected off the surface of an optically smooth surface (left). (**c**) shows the beam reflecting at a different angle from a wavy surface and photograph showing the light returned from a WAAM sample. (**d**) shows the speckles on the detector from the fine-scale rough surface, and the L-PBF sample shows the effect on the detection laser. (**e**) decomposition of surface profile (black) of an as-deposited L-PBF specimen into the three regimes of roughness: form (blue), waviness (green), and roughness (red). The inset figure shows a zoom of the roughness value across of length of 100 \(\upmu\)m—on the order of the diameter of the detection spot size of the rough surface SRAS instrument. The generation lasers used have pulse energies from 800 uJ-4 mJ, with repetition rates from 1 to 5 kHz. The detection beam is shown in green; it is important to note that the frequency, \(f\), is determined by the material under the generation patch, it is non-dispersive and so does not vary with propagation distance, and thus, the SAW velocity recovered is the same regardless of the detection beam being placed at location (i) (within the same grain as the generation) or (ii) (neighbouring dissimilar grain). This makes for a very robust measurement system where the signal amplitude, generation and detection efficiency, and acoustic aberrations do not affect the measurement. Importantly for rough surfaces, this allows the detection beam to be positioned very close (\(\sim\)1-3 wavelengths) to the edge of the generation patch, minimising the effects of attenuation. SRAS instruments make use of broadband Q-switched lasers for the generation of ultrasound, with pulse widths in the range of 1-10 ns. These short pulse widths allow access to acoustic waves of frequencies from the low MHz to the high hundreds of MHz, which allows flexibility in the bandwidth of the detector used. The principle of the SRAS technique is agnostic to the type of detector system used. By way of example, Figure 2c-f present SRAS velocity maps captured using a number of different detector systems. An optical image is also given--so that the surface condition of the samples can be seen--along with a photograph of the detector head. The KED (c) is used for prepared-mirror-like surfaces using a split photodiode for balanced detection and noise cancellation. [PERSON] et al. have previously introduced and demonstrated the quadrature demodulation technique for the measurement of acoustic waves [35], and systems using this approach are now available commercially (the example in Figure 2d uses the fibre-coupled Quartet manufactured by Sound and Bright).