# Heterodyne Angle Deviation Interferometry in Vibration and Bubble Measurements
## 3 Experimental Results
### Bubble Measurements  
Another angular sensor is an SPR sensor. The phase shift between the s- and p-polarizations in a SPR sensor [10] (self-made)--which is a right-angle prism (made of BK7) coated with a thin gold film with a thickness of 66 nm--is shown in Figure 6. The phase sensitivity is about 100 (degree/degree) and the resonant angle is at 43.7\({}^{\circ}\) for the wavelength of 632.8 nm. It is also shown as element number 8 in Figure 7, which shows the structure of the bubble measurement system.  
Figure 4: **(a)** Sketch of the speaker’s vibration; the speaker’s vibration responses at (**b**) 100 Hz and (**c**) 250 Hz driving frequencies.  
Figure 5: The amplitude response of speaker vibration versus input drive frequency.  
From Figure 7, the heterodyne light source is combined with a laser (1), two polarization beam-splitters (PBS) (2 and 4), two mirrors (10 and 12), and two acousto-optic modulators (AOM) (3, 11). The structure and the beat frequency are the same as in Figure 3. The iris (5) shelters the zero-order and the other-order diffraction lights to prevent their going through the optical system.  
From Figure 7, the main structure of the CPHI is similar to Figure 3 and combines with a heterodyne light source, a beam splitter (6), two analyzers (13 and 14), two photodetectors (15 and 16), and a lock-in amplifier (17). The photodetectors (15) and (16) receive the reference signal \(l_{r}\) and the test signal \(l_{t}\), respectively. The modulation signals and beat frequency are the same as before. The incident  
Figure 6: The measurement and simulation results of a surface plasmon resonance (SPR) sensor with 66 nm thickness of gold.  
Figure 7: The bubble measurement system. 1: He-Ne laser; 2 and 4: Polarization beam splitters; 3 and 11: AOMs; 5: Iris; 6: Beam splitter; 7 and 21: Water pipes; 8: SPR sensor; 9: Rotation stage; 10 and 12: Mirrors; 13 and 14: Analyzers; 15 and 16: Photodetectors; 17: Lock-in amplifier; 18: Counter; 19: Water pump; 20: Water tank.  
angle of the angular sensor is adjusted at the resonant angle (43.7\({}^{\circ}\)) by using the rotation stage (9). The lock-in amplifier (17) reads and transfers the phase difference between the reference signal \(I_{r}\) and the test signal \(I_{t}\) into a DC voltage when the phase difference is kept a constant. Thus, when the bubble passes through the cross-section of the test beam in the water pipe (7), the phase changes abruptly and the output signal is a pulse. From Figure 8a, a bubble is passing through the cross-section of the test beam, and the beam is deflected beginning at \(t_{1}\) and goes straight at \(t_{3}\). The phase signal from the output of the lock-in amplifier (17) generates a pulse signal due to the bubble transmitting (see Figure 8b). The pulse triggers a counter (18) to count the number of phase changes. Thus, the number of bubbles can be counted. The speed and size of bubbles are dependent on the driving voltage of the water pump (19). Along the water tank (20) and water pipe (21), the bubbles are in the loop moving in cycles.  
The measurement system sketch is shown in Figure 7 and the actual experimental setup is shown in Figure 9. The measurement results, including the velocity of water flow, relative percentage error between the counter and a digital camera, and the number of bubbles per minute are shown in Table 1. If the bubble sizes vary in the test tube with the velocity of water flow from 9 to 20.5 cm/s, the maximum relative error percentage is about 0.2  
To estimate the available minimum sizes of bubbles in different water flow velocities, we use transparent plastic particles instead of bubbles to measure and count.  
The estimated minimum measurable bubble's sizes of 0.2 and 0.6 mm water flow velocities of 2 and 60 (cm/s) are shown in Table 2. The maximum counter frequency is 1000 Hz for the beat frequency of 10 kHz.