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Figure 7. a) Schematic of an line excitation in x-direction, which excites phonons in water and hydrogel, which after some time will reach the probe beam. When the water phonons transmit through the interface, they will propagate through the probe beam. b) Schematic of the volumetric effect, where due to the angle u the probe beam is reflected both in water and hydrogel, even though the center of the probe beam is in hydrogel.
Figure
8. Individually normalized spectra at different x positions when scanning a line excitation over a hydrogel-water interface, starting in hydrogel, showing the slope of the frequency change.
frequency is detected. This indicates a strong attenuation of the acoustic waves or a weak coupling between the two materials. The two different materials can be clearly distinguished after 180 lm, corresponding to the effective spatial resolution along the x-axis.
6 Discussion
The noise suppression capability of the exponential window comes at the cost of a reduced spectral resolution of the system. The reduction in spectral resolution depends on the decay coefficient of the exponential and can be tuned, resulting in a spectral resolution which is up to 3 times larger compared to the analysis without a window. By tuning the decay coefficient you trade off a higher spectral resolution against the noise suppression capability and spectral leakage. Small decay coefficients offer a higher spectral resolution, but increased spectral leakage, while using larger decay coefficients improves noise suppression but at a lower spectral resolution. Thus, according to the SNR of the signal the decay coefficient should be picked. For low SNR signals a high decay coefficientisbeneficial due to the noise suppression, but for higher SNR signals a lower decay coefficient can be viable.
Crucial parameters for measurements are the maximum allowable light dose and the sensitivity of the detection. These parameters limit the usable peak and average powers of the pump laser and thus the SNR and the achievable measurement rates. It is generally desirable to approach the imposed limits of the sample in order to obtain the best possible SNR. For long-time observations, the pulse energy should be reduced because at a repetition rate of 50 kHz and a pulse energy of 20 lJ the induced heating changes the speed of sound inside the sample.
For a fixed spectral resolution the speed of sound resolution could be further improved by decreasing the interference fringe distance d. This changes the expected frequency f e following the equation for excitation f e = v u / d, with v u being the ultrasonic velocity. This is a linear equation which grows steeper with decreasing interference fringe spacing, see Figure 9. Following the equation of the fringe spacing d = k pump /( 2sinh), with h being half the intersection angle of the pump beams, d is at its smallest value when the angle between the pump beams is increased to 180 °, leading to counter propagating pump beams. When two materials exhibit similar v u’ s, it is easier to distinguish both materials with small fringe distances because a small change in v u leads to a larger difference in frequency compared to bigger fringe distances, which in theory is easier to detect.
The advantages of the steeper slope are two-fold regarding the spatial and speed of sound resolution respectively. Under the assumption that the phonon attenuation is approximately constant for the frequency range used, the signal duration for a given spatial resolution is constant. This means that the spectral resolution is also constant, resulting in a higher speed of sound resolution. There exists a relationship of the phonon frequency to the attenuation of phonons in solids [ 43 ], but it has to be investigated on how it affects the signal duration in liquid or biological samples.