## 2 Materials and Methods  
To enable in situ pad surface monitoring, the proposed method adopted a common-path optical interferometer configuration [14], as shown in Figure 1. Unlike the dual-arm interferometer, the common-path interferometer has a single arm, which is shared by the reference beam and the sample beam. In our set-up, the scheme is achieved by simply placing a light-transparent flat glass over the sample; interference can be generated by a recombination of lights retro-reflected from the glass and the subsequent sample. Importantly, this co-channeling can effectively prevent the interference from fluctuating due to external noise. This is because the lights travelling along the single arm are equally experienced with the perturbation-induced displacement in the optical path length (OPL). Subsequently, due to co-channeling, interference signals are inert to any ambient noise. As shown in Figure 1, a 700 mW, 637 nm light-emitting diode (LED) (M625L4, Thorlabs Inc. NJ, USA) with a spectral band of 17 nm at full width at half maximum (FWHM; graph  
Figure 1: A schematic of the implemented system for CMP pad surface measurement. PZT, piezo electric actuator. \(l_{c}\), coherence length. Insets (left top and right) are a spectrum of the light source and a picture of the common-path of the system, respectively. inset in Figure 1) was used as a partially coherent light source to generate the interference within a limited coherence gate (or a coherence length). The output beam from the LED was passed through a laser line filter (FL632.8-1, Thorlabs Inc., Newton, NJ, USA) to increase its coherence length. Given that the coherence length \(l_{c}\) is defined as \(\left(2\ln 2/\pi\right)\cdot\left(\lambda_{0}^{2}/\Delta\lambda\right)\), where \(\lambda_{0}\) and \(\Delta\lambda\) are a central wavelength and a spectral bandwidth of light, respectively, \(l_{c}\) can be increased by reducing its spectral bandwidth. After passing through the filter, the final bandwidth of the beam was reduced to 1.3 nm, theoretically extending \(l_{c}\) to approximately 136 \(\upmu\)m. The filtered beam was redirected by a beam splitter and then illuminated onto the sample through a 10\(\times\) water-immersion objective lens (UMPLFLN 10 XW, 0.3 N.A., Olympus) and a 1 mm thick microscope slide (a reference glass). The use of a liquid-immersion lens allows the beam to easily penetrate the watery sample in slight contact with the slide, while minimizing strong specular reflections at the glass interfaces and fulfilling the numerical aperture (N.A.). Interference occurs due to the recombination of reflected light waves coming from the bottom of glass and the sample surface, respectively, between which the gap (see Figure 1) filled with a water mixture should be less than the \(l_{c}\) overlaid on a confocal gate (a focal plane). Thus, an interference pattern across the illuminated area of sample is projected onto a 2-D pixel array of a CMOS camera (VC-2 MC, 2048 \(\times\) 1088 pixels, Camera Link, Viewworks). Once the interference pattern was generated, phase-shifting interferometry (PSI)--a well evaluated technique [15]--was applied to the system to obtain the surface structure of the sample. The reference glass--of which one side is firmly attached to a metallic piezoelectric actuator (PZT) with a neodymium magnet--travels axially (up to 150 nm) by sinusoidal oscillation of the PZT at 5 Hz. This results in temporal variation in the magnitudes of the interference signals at each pixel, representing spatial modulation in the interference pattern. Four interference images--resulting from the interference patterns obtained during each quarter of the PZT oscillation period--were captured by the camera at 20 Hz, which had been synchronized with the PZT motion.