# Heterodyne Angle Deviation Interferometry in Vibration and Bubble Measurements
## 3 Experimental Results
### Vibration Measurement  
In order to obtain better sensitivity and larger phase variation, we design a face-to-face parallel metallic plane mirror pair as an angular sensor [9] and let the test light pass through it with twelve reflections for the purpose of magnifying the phase shift. The test light from a heterodyne light source has a beat frequency of 10 kHz (\(f=10\) kHz). The test light is reflected from a mirror which is stuck on a speaker, and then is incident into the angular sensor. The speaker is modulated by a sine wave generator with a specific frequency. The test signal is obtained by using an analyzer with a transmission axis of 45\({}^{\circ}\) to extract the partial components of the s- and p-polarizations on the axis and to obtain the  
Figure 1: The base configuration of Heterodyne Angle Deviation Interferometry (HADI). \(AN_{\mathrm{r}}\): reference signal from analyzer; \(AN_{\mathrm{t}}\): test signal from analyzer; \(BS\): beam splitter; \(D_{\mathrm{r}}\): detector. interference signal detected by a photodetector (New Focus, Model 2051, Santa Clara, CA, USA). The signal is compared with the reference signal of the same frequency by a lock-in amplifier to achieve the phase difference between them. The change of deviation angle of the test beam (the change of incident angle of the mirror pair) is proportional to the phase shift of the test signal. These measurement results are shown in Figure 2, where the symbol \"\({}^{\ast}\)\" represents the measurement result and the sold line represents the fitting result. The function of the fitting line is given as \(\phi=-276.48\phi+12386\) (degree). The linear slope is about \(-276.48\) (degree/degree) for twelve times of reflection. From this curve, we could calculate the angle deviation of the light by using the phase curve. The experimental setup of the speaker's vibration measurement is shown in Figure 3. A heterodyne light source is combined with a laser (1), two polarized beam-splitters (2 and 3), two mirrors (4 and 5), and two acousto-optic modulators (AOM) (6, 7). The modulated frequencies of the AOMs (6) and (7) are 80.00 MHz and 80.01 MHz, respectively. Thus, the beat frequency is 10 kHz. Figure 3: Experimental setup of speaker’s vibration measurement. 1: Laser; 2 and 3: Polarization beam splitters (PBS); 4, 5 and 11: Mirrors; 6 and 7: acousto-optic modulators (AOMs); 8 and 12: Irises; 9: Beam splitter (BS); 10: Speaker; 13 and 14: Mirrors; 15: Rotation stage; 16 and 17: Analyzers; 18 and 19: Photodetectors; 20: Controller; 21: Function generator; 22: Lock-in amplifier. Figure 2: The phase shift characteristics curve of a parallel metallic plane mirror pair versus the incident angle in twelve reflections. From Figure 3, a He-Ne Laser (1) with a wavelength of 632.8 nm is split into two beams by a polarization beam splitter (PBS) (2). Thus, the polarizations of the two beams are orthogonal to each others and the beams then passes through two AOMs (6 and 7), respectively. The selected outgoing lights are both diffraction lights of the first order. Adjusting mirrors (4 and 5) is used to make them coincide and another PBS (3) is used to exactly combine two orthogonal polarized lights on the same path. The iris (8) shelters the zero order and the other order of lights to prevent them from going through the optical system. The CPHI is combined with a heterodyne light source, a beam splitter (9), two analyzers (16 and 17), two photodetectors (18 and 19), and a lock-in amplifier (22). The heterodyne light passing through the iris (8) and the beam splitter (9) is divided into the reflected light and the transmitted light. The reflected light will pass through the analyzer plate (16) with the transmission axis of 45\({}^{\circ}\) and be detected by the photodetector (18) to produce the interference signal with a beat frequency of 10 kHz, and then the electrical signal is connected to a lock-in amplifier (22) (Stanford Research Systems, model: SR830, phase resolution: 0.01\({}^{\circ}\)) as the reference signal \(I_{r}\).