# Optimization of Optical Trapping and Laser Interferometry in Biological Cells
## 1 Introduction
The aim of this study is to clarify the necessity of the technology for conducting precise OT and LI in living cells by investigating the performance of the feedback-tracking technique and in-situ calibration in various conditions. In addition, we seek the means to further improve the methodology. First, we investigated the dependence of the position sensitivity of LI (hereafter referred to as LI sensitivity) on the refractive index of the media surrounding the probe particle. When aqueous glycerol solutions were used as a reference sample with a well-determined and homogeneous refractive index, measured LI sensitivities conformed to theoretical predictions for all measured probe particles. The LI sensitivity in living cells was precisely measured under the 3-D feedback tracking. Nevertheless, the distribution of the sensitivity in living cells was much greater than that in homogeneous reference samples (aqueous solution) and systematically deviated from theoretical predictions, especially when the refractive index of the probe particle is close to that of surrounding cytoplasm. We then conclude that the in-situ calibration of the LI sensitivity is a prerequisite for conducting LI precisely in living cells. It is to be noted that the stable tracking of a probe particle is required, not to mention the LI experiments in living cells, but also for the precise in-situ calibrations as mentioned above. Ensuring the feedback stability is as important as increasing the measurement sensitivity of LI. In the second part  
Figure 1: (**a**) Schematic description of the optical trap. A representative laser ray incident along \(z\) axis is traced and deflected at the particle surface as shown by the red arrow. The compensating force is then applied to the particle towards the focus of the laser (blue arrow), that is chosen as the origin of the Cartesian coordinate (\(x\), \(y\), \(z\)). (**b**) Schematic illustration of back-focal-plane laser interferometry (LI). Image of the interference pattern at the back focal plane (BFP) was projected on to the quadrant photodiode (QPD). The average position of the interference pattern shifts in proportion to the displacement \(x\) of the particle from the laser focus (black arrow). of this article, we seek the means to achieve the best performance of both these requirements at the same time. We investigated the LI sensitivity and the feedback stability as a function of probe offsets from the laser focus. When probe offsets (\(x,y\)) in directions perpendicular to the optical axis (\(z\)) are concerned, the most sensitive LI and the most stable feedback tracking are achieved when a probe particle is located on the optical axis (\(x=y=0\)). The feedback tracking in the \(z\) direction (along the optical axis) is the most stable at the focal plane (\(z=0\)) when the ordinary setup of the commercial microscope is used. However, the probe particle located at \(z=0\) does not show the best LI sensitivity. The sensitivity indicates a remarkable \(z\) offset dependence and the best height of the probe position deviates from \(z=0\) by the order of wavelength of visible light. We then show that the LI sensitivity and the feedback-tracking stability are optimized independently. The best \(z\) position for the feedback-tracking stability can be shifted to match to the best position for LI sensitivity by tuning the optical settings for the microscope imaging. As a conclusion for the second part of this article, we emphasize that the feedback tracking in the \(z\) direction, that requires more subtle and careful tuning of the system, is as important as \(x\) and \(y\) directions for conducting OT and LI in living cells.