A laser beam with a beam width larger than the width of the bubble is trained on the bubble. In the classical or ray optics limit, the light scattered within a given angle is proportional to the square of the radius of the bubble (q a R2(t)). The dimensionless constant that governs scattering into an angle is given by;
As R varies the exact formulae for scattering into a fixed angle goes roughly as the square but shows variations due to the fringes moving through an angle. The signal from the PMT is proportional to the intensity of the scattered light, so the square root of the signal is proportional to R. This scattered light is also proportional to the difference in the dielectric constant at the gas/fluid interface presented by the surface of the bubble. Application of the exact Mie scattering formulae indicates that the classical ray optics limit is only approached very slowly as the size of the bubble increases. The light scattered within a specific angle displays many diffraction peaks which are seen straddling the classical limit. The signal is very sensitive to angular alignment. Convergence to the classical limit is attained by using a lens with a short focal length and collecting the scattered light from several different angles, 25o-60o (46-90°, in 1992 paper resulting in R2 to within 10% for R>2mm or 20% for R>1mm), from the forward direction which averages out the fringes. The angles are chosen to say away from directly forward because the averaging is least effective and regions of backscatter where the intensity is orders of magnitude smaller.
The laser used is either a Helium-Neon laser (10mW) or a Helium-Cadmium laser. A filter which blocks the wavelength of the laser light is placed between the bubble and the PMT, which is therefore only sensitive to the flash of the SL. This serves as the trigger for the zero of time and enables the average of about 500 runs to be taken.
The scattered light is collected by a lens and an aperture is placed at the image to reduce the light detected from scattering from impurities it then passes through a line pass filter, which blocks the broadband sonoluminescence flash, onto a photodetector. The signal from the detector must have the background noise taken away. The noise level is measured by shining the laser light through the flask in the absence of a bubble, the noise is assumed to be stray light and scattering from impurities.
The constant of proportionality is found by making an absolute calibration of at least one point. This is achieved by matching a numerical calculation of the hydrodynamic theory of the bubble motion to that portion of the cycle where the hydrodynamics must be valid i.e. where the bubble wall velocity is less than mach 1. The ambient radius and the amplitude of the acoustic drive pressure determine the solution of the hydrodynamic theory.
This is the Rayleigh Plesset equation modified to include acoustic radiation damping and the Van der Waals hardcore, a (for air R0/a » 8.5) and the surface tension has been neglected. Where u is the kinematic velocity; r and c are the fluid density and sound velocity; P0 and Pg are the ambient and gas pressures; the acoustic field is given by a sinusoidally varying pressure variation.
where g is the ratio f specific heats and we see that Pg = P0 when Rg = R0 . The bubbles have a characteristic ratio of the maximum radius to the ambient radius the ratio can be varied by changing the Acoustic pressure. The ambient size is found from the rate of expansion of the corrected signal on the PMT. There is a best solution of the hydrodynamic theory with a specific acoustic pressure and ambient radius that will match the data. The fits are very good. Once there is a match the equation becomes;
where Tm is the value of T at Rm and T is the square root of the corrected signal;
The acousto-optic modulator can be used to expand an area of the cycle that is of specific interest e.g. the minimum. The high gain PMT (e.g. Hamamatsu R2027) used must have a nanosecond response time however they are not fast enough to avoid convolving light scattered from different times during the rapid final collapse.
R and dR/dT can also be found by fitting the data to structure in Mie scattering (Lentz et al, 1995), or by interfering scattered and unscattered light (Delgadino and Bonnetto, 1996) and by backlighting the bubble and videotaping the motion, this could also be used to monitor the deformations in the bubble shape (Tian et al, 1996).
To resolve the time of the collapse the continuous wave laser is replaced by a short flash titanium sapphire laser (Barber et al 1997). The laser has 200fs wide pulses at a rate of 76MHZ (13ns) between pulses. Therefore e the response of the PMT can be directly attributed to the laser flash and so to a very precise window of time. This results in a peaked graph. The width of each peak is attributed to the finite response time of the PMT. However this is shorter than the time between consecutive pulses so there is no spill over of the response from one pulse t another. The height of the peaks is proportional to the square of the instantaneous radius of the bubble. The flash serves again as a temporal reference point in the alignment of many traces.
The traces are acquired on a digital oscilloscope with a bin separation of 0.5ns. The integrated area of each peak is ascribed to the bin corresponding to the time difference between the maximum of the peak and the sonoluminescence flash. As data is acquired at different phases relative to the SL flash (as the repetition rate of the laser is not commensurate with the frequency of the sound field). The traces are calibrated using the same method as in the CW scattering. The complete sound cycle is matched to the theoretical equation, and the blowups are calibrated by using the value of the radius at a point on the large picture.
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