Optical tweezers technique and its applications. Controlled mechanical motions of microparticles in optical tweezers. Observation of a single-beam gradient force optical trap for dielectric particles. These studies will be of great help to understand the particle-laser trap interaction in various situations and promote exciting possibilities for exploring novel ways to control the mechanical dynamics of microscale particles.Īshkin A, Dziedzic JM, Bjorkholm JE, Chu S. Even in a simple pair of optical tweezers, the dielectric micro-sphere exhibits abundant phases of mechanical motions including acceleration, deceleration, and turning. The particle trajectory over time can demonstrate whether the particle can be successfully trapped into the optical tweezers center and reveal the subtle details of this trapping process. With the influence of viscosity force and torque taken into account, we numerically solve and analyze the dynamic process of a dielectric micro-sphere in optical tweezers on the basis of Newton mechanical equations under various conditions of initial positions and velocity vectors of the particle. In this paper, we utilize the ray optics method to calculate the optical force and optical torque of a micro-sphere in optical tweezers. In order to advance the flourishing applications for those achievements, it is necessary to make clear the three-dimensional dynamic process of micro-particles stepping into an optical field. We can now really clearly see the hotspots and how they have occurred at the four ‘corners’ of the sphere.Known as laser trapping, optical tweezers, with nanometer accuracy and pico-newton precision, plays a pivotal role in single bio-molecule measurements and controllable motions of micro-machines. Although the whole picture is quite a distorted version of the surface of the sphere, the density of the points has been conserved by the projection as we proved above. We could choose to unwrap around a different point – if there was a particular feature that we wanted to get an undistorted look at then we could unwrap around that instead. In our case the sphere has been unwrapped from the side farthest away from us, onto a plane that is in contact with the close side. Points that are near the plane suffer less distortion and points that are near the hole get very stretched. Think about placing a ball on a plane, making a hole in top and then flattening the sphere down onto the plane by pulling open the hole. What are we looking at here? First and foremost we can see the whole surface (well, except the point \((0,0,1)\)). Let’s see what it looks like (back in Cartesian coordinates now): import matplotlib.pyplot as plt import numpy as np data = np. Now we can be confident that the projection is not going to mess with the way we view the distribution of points on the surface. Instead it is conformal (conserves angles), which the Lambert projection is not. Which is an area element in the planar coordinates! Great! As a quick point of comparison, the stereographic projection (which is another very common projection) does not have this property. I looped the above code over a number of values for theta between \(0\) and \(\frac\right)d\Theta \\ We could try doing some sort of coordinate transformation to rotate the sphere: theta = np. In figure 4 we can see there is something going on in the four corners but it’s not really clear what. In addition, we really only have a good view of the front of the sphere whereas on the edges its hard to see what’s going on as it’s very compressed. What if there were more points on the back than the front? We wouldn’t know. When we do this we lose all information about whether the points are on the front or the back of the sphere. Earlier we took the most naïve way of taking the 3D data and making it 2D, we unpacked the \(z\) coordinate into an empty variable _ x, y, _ = data. Now that we have a nice way of dealing with large data sets we can tackle the bigger problem. Figure 5: 2,000,000 points in 20 bins Figure 6: 2,000,000 points in 2,000 bins Making use of the z coordinate
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |