## 3 Separate Analysis per Individual Components
### Identification of Optical Elements Contributing to Phase Shifting
#### 3.1.1 Refractive Index Test  
The experiment proposed above makes it possible to identify that there is a different phase contribution from each element, but it does not make it possible to determine the contribution of each of these or whether only one of them contributes. Therefore, an experiment (Figure 5) was performed by assembling a Mach-Zehnder interferometer outside the optical trap system to test each element separately on a macro scale (air, glass, distilled water, and oil), while they were excited with a second laser beam (different from the interferometer). The interferometer had a He-Ne laser source with a \(\lambda\) of 633 nm (\(\lambda_{Pr}\)) and a power of 12 mW. The beam was spatially expanded and filtered. In addition, it had two non-polarized 50:50 beam splitters. On the observation plane was a PIXELINK (Ottawa, ON, Canada) camera (model PL-B741F) with a CMOS sensor, 6.7 um pixel size (1.3 Mpc), and 1280 \(\times\) 1024 pixel resolution. The camera sensor was exposed without having a lens attached. The laser used to excite the elements of interest was a SPECTRA-PHYSICS (Milpitas, CA, USA) solid-state laser (model Excelsior-532-100) with a \(\lambda_{Ex}\) of 532 nm and a fixed power of 100 mW; the beam diameter that is obliquely incident (45\({}^{\circ}\)) on the sample was 0.7 mm. This angle of incidence was determined due to the setup geometry, which is not critical in the results. Although it would have been possible to excite on-axis with the excitation laser, in order to prevent the exposed beam from hitting the camera sensor and saturating or damaging it, it was necessary to illuminate obliquely, resulting in that angle. Figure 4: IR power required to cause a \(2\pi\) shift depending on trap position. To study glass, water, and oil, an optical container was fabricated consisting of a 1.1 mm thick glass slide with a central perforation of 10 mm in diameter. A coverslip was placed on each side of the slide; one was fixed with optical adhesive and the other was attached only through atomic interaction with each element in question. To characterize air, the container was completely removed. For the glass analysis, a regular slide was placed, without perforation. For distilled water, the container filled with this liquid was positioned in the area of interest, and the experiment was carried out in a similar fashion with the immersion oil. Figure 6 shows the changes in the refractive index of the four analyzed media after 20 s of excitation with the green laser. These results allow us to identify oil as the element that makes the greatest contribution to the additive phase to be removed from the measurements made with the optical trap and Mach-Zehnder interferometer system. In both air and glass, only problems of interferogram detuning are observed, without any contribution from the excitation of those elements. However, the change in the refractive index of distilled water and immersion oil is easily observed; specifically, taking the difference between the maximum and minimum values for each figure, Figure 6c (\(5.47\times 10^{-6}\)) and Figure 6d (\(4.47\times 10^{-5}\)), the change in oil is 8.17 times higher than that of water. The refractive index changes shown in Figure 6 were calculated from the phase recovered from the interferograms corresponding to each element by the following expression:  
\[n_{f}=n_{i}-\left(\frac{\phi}{2\pi}\frac{\lambda_{p_{f}}}{h}\right), \tag{5}\]  
where \(n_{f}\) is the medium refractive index when it responds to the excitation laser, \(n_{i}\) is the unexcited medium refractive index, and \(h\) is the sample thickness.