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Computation of the differential signals Á x and Á y given the signals from the quadrant detector. The differential signal Á x represents a particle’s motion along the flow channel ( x -direction). The differential signal Á y represents a particle’s motion transverse to the flow channel ( y -direction). 

Computation of the differential signals Á x and Á y given the signals from the quadrant detector. The differential signal Á x represents a particle’s motion along the flow channel ( x -direction). The differential signal Á y represents a particle’s motion transverse to the flow channel ( y -direction). 

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Article
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We present a detection scheme for nanoscale particles based on the gradient force and torque near a tightly focused laser beam. The focus affects the path of nanoparticles passing by and a quadrant detector records the particle trajectory. A feedback system continuously adjusts the laser power and thereby prevents the particles from being trapped....

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... object in a microscope can be monitored by measuring the intensity shifts in the back focal plane of the lens that collimates the outgoing laser field. The detected intensity shift originates from interference between the original laser field and the scattered field from the particle. The signal depends on the relative position of the particle with respect to the focus. Defining the signal from each quadrant by A , B , C and D ( figure 2), motion in the x -direction will induce a change in the signal ð A þ C Þ À ð B þ D Þ . On the other hand, motion in the y -direction can be detected by monitoring the signal ð A þ B Þ À ð C þ D Þ . The two signals can be made independent of the laser intensity by normalization with signal A B C D . In order to understand the process of position tracking, let us calculate the scattered field at the position of the detector. Assume that the focus is located at the origin and the particle is located at the point r 0 1⁄4 f x 0 ; y 0 ; z 0 g . The particle radius is R and the field incident on the particle is E ð r 0 Þ . The incident beam is a paraxial Gaussian TEM 00 mode polarized in the x -direction ( E 1⁄4 E n x ) and propagating along the z -direction. The centre of the detector is located at the point ð 0 ; 0 ; z Þ (c.f. figure 3). Since we consider particles much smaller than the laser wavelength we treat the particles in the dipole (Rayleigh) limit. The polarizability of a particle ...

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