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3.3 Experimental Measurement and Comparison  103
                                              90
                                              80
                                                          Sphere
                                            Incident angle (deg)  60  3  4  5
                                              70
                                                   2
                                                          Radius
                                                           (mm)
                                              50
                                              40
                                              30
                                                                        9  10
                                                                     8
                                              20                   7
                                                                6
                                              10
                                                0              5               10
                                                        Off-axial distance (mm)
                            Fig. 3.24. Relationship between optimum fiber incident angle and radius of mi-
                            crosphere for F sz = F gz at maximum F g on off-axial position

                                              90
                                              80
                                            Incident angle (deg)   70

                                              60
                                              50
                                              40
                                              30
                                              20
                                                0     2     4     6      8     10
                                                         Sphere radius (mm)

                            Fig. 3.25. Variation in fiber incident angle as function of off-axial distance at F s =
                            F g, with microsphere radius as a parameter


                            3.3 Experimental Measurement and Comparison
                            of Experimental and Theoretical Predictions

                            The use of optical tweezers is seen as a method of manipulating[3.16],
                            aligning[3.17], fabricatingand rotating[3.8] microobjects mainly in aqueous
                            solutions. The optical trappingcharacteristics of spherical particles for these
                            types of application were analyzed theoretically in Sec. 3.2 and are analyzed
                            experimentally in this section. We not only describe the results of the exper-
                            iments required to determine the characteristics of the optical trap but also
                            compare the results with that of theoretical ones.

                            3.3.1 Experimental Setup

                            An experimental setup for trappingand manipulatingparticles usingupward-
                            directed and downward-directed YAG laser beams at a wavelength of 1.06 µm
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